A dynamic graphic explanation generation method based on geometric relationship topology evolution

Abstract

The application discloses a dynamic figure explanation generation method based on geometric relation topology evolution and relates to the technical field of figure analysis. Each candidate proof path Pat is converted into a standard node sequence Nod, whether the relationship basis before a candidate branch point Brk of different candidate proof paths Pat is consistent is determined according to a preceding relation closure Pre, and the reasoning result difference after the candidate branch point Brk is verified according to a subsequent relation closure Pos and a missing condition set Mis, so that a proof branch point Bpt is determined. A common preceding explanation section Com is generated based on the common standard nodes before the proof branch point Bpt, a branch deduction explanation section Bra is generated based on the non-common standard nodes after the proof branch point Bpt, and branched dynamic figure explanation content Dyn is output. The application reduces the repeated generation of the common preceding reasoning content, and makes the dynamic figure explanation content branch from the position causing the subsequent reasoning difference.

Description

Technical Field

[0001] This invention relates to the field of graphics analysis technology, specifically to a dynamic graphics explanation and generation method based on geometric relationship topological evolution. Background Technology

[0002] With the development of educational informatization and intelligent teaching content generation technology, the explanation of geometry problems is gradually evolving from static graphic display to dynamic graphic demonstration, process-oriented reasoning explanation, and interactive learning support. In the scenarios of junior high school geometry, plane geometry proof and auxiliary line construction explanation, it is usually necessary to analyze the text of the problem, the problem figure and the conclusion to be proved to obtain geometric objects and geometric relationships such as points, line segments, angles, triangles, equality relationships, parallel relationships, perpendicular relationships and subordinate relationships, and generate corresponding dynamic graphic explanation processes based on known conditions, auxiliary construction and geometric reasoning rules.

[0003] In specific geometric proof explanations, the same problem can often generate multiple candidate proof paths. For example, the proof can be advanced by connecting auxiliary lines, constructing perpendicular lines, extending line segments, constructing parallel lines, or calling different geometric theorems. Existing dynamic graphic explanation generation methods usually select one proof path to display based on the score of candidate auxiliary constructions, preset explanation templates, rule matching results, or the final proof reachability. When multiple proof paths need to be displayed, the complete explanation process is usually generated according to the construction actions, condition introductions, rule calls, and conclusion outputs in each proof path.

[0004] However, different candidate proof paths often overlap in known relations, prior reasoning relations, and some intermediate conditions. If a complete explanation process is generated for each candidate proof path, common prior conditions, common graphical foundations, and common intermediate reasoning will be generated repeatedly, affecting the generation efficiency of dynamic graphical explanation content. If branch switching is only based on the differences in construction actions, node order, or condition presentation order that first appear in the proof path, the difference in display that does not lead to changes in subsequent reasoning results may be misjudged as proof forks. The existing method lacks a fork point confirmation mechanism based on whether the prior geometric relations are equivalent and whether the subsequent geometric relations and missing conditions have changed, making it difficult for the branched dynamic graphical explanation content to unfold from the position that truly causes the difference in subsequent proofs. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention provides a dynamic graphical explanation generation method based on geometric relationship topological evolution, which solves the problems mentioned in the background technology.

[0006] This invention is achieved through the following technical solution: a dynamic graphical explanation generation method based on geometric relationship topological evolution, comprising the following steps:

[0007] S1. Obtain geometry problem data Inp, and construct a geometric relationship topology graph Top based on the geometry problem data Inp;

[0008] S2. Generate a candidate proof path set Pts based on the geometric relationship topology graph Top, and convert each candidate proof path Pat in the candidate proof path set Pts into a standard node sequence Nod, wherein the standard node sequence Nod includes multiple standard nodes arranged in the order of proof execution.

[0009] S3. Calculate the preceding relation closure Pre before the current standard node of the standard node sequence Nod for different candidate proof paths Pat. When the relation type and relation object in the preceding relation closure Pre corresponding to different candidate proof paths Pat are consistent, compare the node type, operation object and output relation between the current standard nodes, and determine the current standard node that first produces a difference as the candidate fork point Brk.

[0010] S4. Taking the candidate bifurcation point Brk as the starting point for further deduction, the subsequent relation closure Pos and the missing condition set Mis corresponding to different candidate proof paths Pat are obtained respectively. When there is a difference between at least one of the subsequent relation closure Pos and the missing condition set Mis, the candidate bifurcation point Brk is determined as the proof bifurcation point Bpt.

[0011] S5. Generate a common pre-explanation segment Com based on the standard nodes in the standard node sequence Nod that have the same node type, the same operation object, and the same output relationship before the proof bifurcation point Bpt. Generate a branch deduction explanation segment Bra based on the non-common standard nodes in the standard node sequence Nod after the proof bifurcation point Bpt. Output branched dynamic graphical explanation content Dyn based on the common pre-explanation segment Com and the branch deduction explanation segment Bra.

[0012] Preferably, S1 includes:

[0013] S11, the geometry problem data Inp includes text data Txt, graphic data Fig, and the relation to be proved Gol;

[0014] The text data Txt is at least one of the following: the text input of the question and the text content obtained after recognizing the text region in the question image;

[0015] The graphic data Fig can be at least one of the following: the graphic input of the question and the graphic content obtained by segmenting the graphic region in the question image;

[0016] The relation to be proved, Gol, is at least one of the following: a conclusion item in the question bank, or a conclusion content extracted from the text data Txt containing a statement with the meaning of the proof.

[0017] S12. Extract the geometry name and conditional statement from the text data Txt, generate a text object item Tob based on the geometry name, and generate a text relation item Trl based on the conditional statement. Each text object item Tob includes an object name and an object type, and each text relation item Trl includes a relation type and a relation object.

[0018] Extract graphic annotations, primitive endpoints, and primitive connection results from the graphic data Fig. Generate graphic object items Fob based on the graphic annotations and primitive endpoints. Generate graphic relationship items Frl based on the primitive connection results. Each graphic object item Fob includes an object name and an object type. Each graphic relationship item Frl includes a relationship type and a relationship object. Merge text object items Tob with the same object name and object type with graphic object items Fob into a geometric object.

[0019] Merge the text relation item Trl, which has the same relation type and relation object, with the graph relation item Frl into a geometric relation;

[0020] The geometric objects form a geometric object set Obj, the geometric relations form a geometric relation set Rel, and a geometric relation topology graph Top is generated based on the geometric object set Obj, the geometric relation set Rel, and the relation to be proved Gol.

[0021] Preferably, S2 includes:

[0022] S21. Read the geometric relationship set Rel and the relationship to be proved Gol in the geometric relationship topology graph Top, and call the preset reasoning rule library Rul. The reasoning rule library Rul includes multiple rule items composed of rule antecedent Ant, rule consequent Cns and construction action Cat.

[0023] S22. Search the rule item in the inference rule base Rul where the rule consequent Cns is consistent with the relation to be proved Gol, and read the rule antecedent Ant and the construction action Cat corresponding to the rule item;

[0024] S23. Compare the rule antecedent Ant with the geometric relation set Rel. The rule antecedent Ant that already exists in the geometric relation set Rel is formed into a satisfied condition set Sat. The rule antecedent Ant that does not exist in the geometric relation set Rel but is generated through the construction action Cat and the rule items in the reasoning rule base Rul is formed into a supplementary condition set Lac. At least two candidate proof paths Pat are generated according to the combination of the satisfied condition set Sat, the supplementary condition set Lac and the construction action Cat. The candidate proof path set Pts is formed by the at least two candidate proof paths Pat.

[0025] Preferably, S2 further includes:

[0026] S24. Convert the construction action Cat in the candidate proof path Pat into a standard proof node Stn of the construction class. The standard proof node Stn is a standard node in the standard node sequence Nod. Convert the relationship in the satisfied condition set Sat and the condition set to be supplemented Lac into the standard proof node Stn of the relationship class.

[0027] The action of triggering the rule consequent Cns after the rule antecedent Ant is satisfied is converted into the standard proof node Stn of the rule class;

[0028] The action of obtaining the relationship to be proved, Gol, is converted into the standard proof node Stn of the conclusion class;

[0029] The standard proof nodes Stn are arranged in the order of proof execution to form the standard node sequence Nod; wherein each standard proof node Stn includes a node type Nty, an input relation set Inr, an operation object set Opo, an output relation set Our, a target relation Tar, and a node number Ord.

[0030] Preferably, S3 includes:

[0031] S31. Select the current standard node Cur in the standard node sequence Nod according to the node number Ord, and form the preceding standard proof node Stn into a set of predecessor nodes Bef.

[0032] S32. Read the geometric relationship set Rel in the geometric relationship topology graph Top as the basic relationship;

[0033] Add the output relation set Our of each standard proof node Stn in the preceding node set Bef to the basic relation;

[0034] S33. When the basic relation after being added satisfies the rule predecessor Ant in the inference rule base Rul, the corresponding rule successor Cns is added to the basic relation. The addition process is repeated until there is no new rule successor Cns that satisfies the addition condition. The basic relation after the addition process is completed is determined as the predecessor relation closure Pre before the current standard node Cur.

[0035] Preferably, S3 further includes:

[0036] S34. Align the standard node sequences Nod corresponding to at least two candidate proof paths Pat according to the node sequence number Ord, and calculate the preceding relation closure Pre for the current standard node Cur under the same node sequence number Ord.

[0037] S35. When the relation items in the preceding relation closure Pre corresponding to different candidate proof paths Pat correspond one-to-one, and the relation type and relation object of each corresponding relation item are consistent, and the target relation Tar in the current standard node Cur corresponding to different candidate proof paths Pat are consistent, the preceding relation closure Pre before the current standard node Cur is determined to be equivalent.

[0038] S36. Under the condition that the preceding relation closures Pre corresponding to different candidate proof paths Pat are equivalent, compare the node type Nty, the operation object set Opo, and the output relation set Our corresponding to the current standard node Cur of different candidate proof paths Pat, and determine the current standard node Cur that first appears to have at least one of the following inconsistencies: node type Nty inconsistency, operation object set Opo inconsistency, and output relation set Our inconsistency as the candidate fork point Brk.

[0039] Preferably, S4 includes:

[0040] S41. Read the node number Ord corresponding to the candidate fork point Brk as the starting number, and form the current standard node Cur corresponding to the starting number and the standard proof node Stn located after the starting number into a subsequent node set Aft.

[0041] S42. Take the preceding relation closure Pre before the candidate bifurcation point Brk as the deductive relation set Der, and read the standard proof node Stn in the subsequent node set Aft in sequence according to the node number Ord.

[0042] S43. When the input relation set Inr of the standard proof node Stn is included in the deduction relation set Der, the output relation set Our of the standard proof node Stn is added to the deduction relation set Der. When the deduction relation set Der after being added satisfies the rule antecedent Ant in the reasoning rule base Rul, the corresponding rule consequent Cns is added to the deduction relation set Der.

[0043] Repeat the addition process until no new rule consequent Cns that meets the addition conditions is found, and determine the inference relation set Der after the inference is completed as the subsequent relation closure Pos.

[0044] Preferably, S4 further includes:

[0045] S44. During the subsequent deduction process according to S42 and S43, each time a standard proof node Stn in the subsequent node set Aft is read, the input relation set Inr of the read standard proof node Stn is compared with the currently formed deduction relation set Der, and the relations in the input relation set Inr that are not included in the deduction relation set Der are added to the missing condition set Mis.

[0046] S45. After reading the subsequent node set Aft, compare the relationship to be proved Gol with the subsequent relationship closure Pos, and if the relationship to be proved Gol is not in the subsequent relationship closure Pos, add the relationship to be proved Gol to the missing condition set Mis.

[0047] Preferably, S4 further includes:

[0048] S46. Compare the subsequent relation closure Pos and the missing condition set Mis corresponding to different candidate proof paths Pat:

[0049] When there is a relation in the subsequent relation closure Pos corresponding to any candidate proof path Pat, and there is no relation with the same relation type and relation object in the subsequent relation closure Pos corresponding to at least one other candidate proof path Pat, it is determined that different candidate proof paths Pat form different proof results after the candidate bifurcation point Brk;

[0050] When there is a missing relation in the missing condition set Mis corresponding to any candidate proof path Pat, and there is no missing relation in the missing condition set Mis corresponding to at least one other candidate proof path Pat that has the same relation type and relation object, it is determined that different candidate proof paths Pat form different proof gaps after the candidate bifurcation point Brk;

[0051] When at least one of the following conditions is met—that different proof results or different proof gaps—the candidate bifurcation point Brk is determined as the proof bifurcation point Bpt.

[0052] Preferably, S5 includes:

[0053] S51. Take the standard proof node Stn located before the proof bifurcation point Bpt, and having the same node number Ord, the same node type Nty, the same set of operation objects Opo, and the same set of output relations Our in different candidate proof paths Pat as common standard nodes, and form a common node set Cnd from the common standard nodes. Generate a common pre-explanation segment Com based on the common node set Cnd.

[0054] S52. Read the node number Ord corresponding to the proof fork point Bpt, and form a branch node set Bnd from the standard proof nodes Stn in different candidate proof paths Pat starting from the node number Ord corresponding to the proof fork point Bpt. Generate a branch deduction solution segment Bra based on the branch node set Bnd.

[0055] S53. Generate branched dynamic graphic explanation content Dyn in the order of outputting the common pre-explanation segment Com first and the branched derivation explanation segment Bra last.

[0056] This invention provides a dynamic graphical explanation generation method based on geometric relationship topological evolution, which has the following beneficial effects:

[0057] (1) This invention converts each candidate proof path Pat into a unified standard node sequence Nod, and combines the preceding relation closure Pre, the subsequent relation closure Pos and the missing condition set Mis to determine the proof fork point Bpt, avoiding the direct selection of any path among multiple proof ideas for explanation, so that the branched dynamic graphical explanation content Dyn unfolds the branch explanation from the position where the reasoning difference actually occurs.

[0058] (2) This invention calculates and compares the preceding relational closures Pre corresponding to different candidate proof paths Pat before determining the candidate bifurcation point Brk, distinguishing between differences in proof structure and differences in presentation order. For example, it avoids mistaking differences in order such as "emphasizing the equality of edges first" and "emphasizing the equality of angles first" as bifurcation of proof ideas, thereby improving the accuracy of determining the candidate bifurcation point Brk.

[0059] (3) This invention continues to deduce from the candidate bifurcation point Brk to form the subsequent relation closure Pos and missing condition set Mis corresponding to different candidate proof paths Pat, and confirms the proof bifurcation point Bpt accordingly, explaining the differences in relation results and condition gaps generated by different auxiliary constructions in subsequent reasoning, making the basis for the generation of the common pre-explanation segment Com and the branch deduction explanation segment Bra clearer. Attached Figure Description

[0060] Figure 1 A schematic diagram illustrating the process of a dynamic graphical explanation and generation method based on geometric relationship topological evolution.

[0061] Figure 2 A schematic diagram illustrating the process of constructing a geometric relationship topology graph and generating candidate proof paths;

[0062] Figure 3 To demonstrate the process of determining the bifurcation point and branching, a schematic diagram of the generation process is provided. Detailed Implementation

[0063] The technical solutions of the present invention will now be clearly and completely described with reference to the accompanying drawings in the embodiments of the present invention.

[0064] Example 1

[0065] In this embodiment, the application scenario is set as a dynamic graphic explanation generation scenario in a junior high school geometry online class. Teachers upload or input geometry proof problems through the teaching platform. Without changing the teacher's terminal, student's terminal, and classroom display device, the teaching platform processes the problem text, problem graphics, and the conclusion to be proved, and generates branched dynamic graphic explanation content Dyn.

[0066] Furthermore, subsequent embodiments will be illustrated using the problem "In △ABC, AB=AC, D is a point on BC, ∠BAD=∠CAD, prove BD=CD" as an example, where the problem text is formed as text data Txt, the problem figure is formed as graphic data Fig, and "prove BD=CD" is formed as the relation to be proved Gol;

[0067] This invention provides a method for generating dynamic graphical explanations based on the topological evolution of geometric relationships. Please refer to [link / reference]. Figure 1 This includes the following steps:

[0068] S1. Obtain geometry problem data Inp, and construct a geometric relationship topology graph Top based on the geometry problem data Inp;

[0069] S2. Generate a candidate proof path set Pts based on the geometric relationship topology graph Top, and convert each candidate proof path Pat in the candidate proof path set Pts into a standard node sequence Nod, wherein the standard node sequence Nod includes multiple standard nodes arranged in the order of proof execution.

[0070] S3. Calculate the preceding relation closure Pre before the current standard node of the standard node sequence Nod for different candidate proof paths Pat. When the relation type and relation object in the preceding relation closure Pre corresponding to different candidate proof paths Pat are consistent, compare the node type, operation object and output relation between the current standard nodes, and determine the current standard node that first produces a difference as the candidate fork point Brk.

[0071] S4. Taking the candidate bifurcation point Brk as the starting point for further deduction, the subsequent relation closure Pos and the missing condition set Mis corresponding to different candidate proof paths Pat are obtained respectively. When there is a difference between at least one of the subsequent relation closure Pos and the missing condition set Mis, the candidate bifurcation point Brk is determined as the proof bifurcation point Bpt.

[0072] S5. Generate a common pre-explanation segment Com based on the standard nodes in the standard node sequence Nod that have the same node type, the same operation object, and the same output relationship before the proof bifurcation point Bpt. Generate a branch deduction explanation segment Bra based on the non-common standard nodes in the standard node sequence Nod after the proof bifurcation point Bpt. Output branched dynamic graphical explanation content Dyn based on the common pre-explanation segment Com and the branch deduction explanation segment Bra.

[0073] This embodiment does not directly select any candidate proof path Pat from multiple proof approaches for dynamic graphical explanation through the above steps. Instead, it first converts each candidate proof path Pat into the standard node sequence Nod, then uses the preceding relation closure Pre to confirm whether different proof approaches are based on the same proof foundation before the fork, and verifies whether the candidate fork point Brk does indeed lead to different subsequent reasoning results through the subsequent relation closure Pos and the missing condition set Mis. This determines the proof fork point Bpt. Therefore, in real-world middle school geometry explanations, for example, the same When a problem presents two proof approaches simultaneously—"connecting the vertex to the base point" and "constructing a perpendicular auxiliary line"—this embodiment can first organize the common known conditions and derivations used by both approaches into a common pre-explanation segment Com. Then, starting from the proof bifurcation point Bpt where the differences truly arise, the branch derivation segment Bra is generated. This allows students to see at which step different auxiliary constructions lead to different subsequent geometric relationships and missing conditions, reducing the repetition of the same pre-existing content and making the output branched dynamic graphic explanation content Dyn more closely resemble the actual branching structure in the geometric proof process.

[0074] Example 2

[0075] Specifically: S1 includes:

[0076] S11, the geometry problem data Inp includes text data Txt, graphic data Fig, and the relation to be proved Gol;

[0077] The text data Txt is at least one of the following: the text input of the question and the text content obtained after recognizing the text region in the question image;

[0078] The graphic data Fig can be at least one of the following: the graphic input of the question and the graphic content obtained by segmenting the graphic region in the question image;

[0079] The relation to be proved, Gol, is at least one of the following: a conclusion item in the question bank, or a conclusion content extracted from the text data Txt containing a statement with the meaning of the proof.

[0080] In the application scenario set in Example 1, when the teacher directly enters the question text, the complete text entered by the teacher is saved as text data Txt. When the teacher uploads a question image, the question image is first divided into a text area and a graphic area. The text content in the text area is saved as text data Txt, and the geometric figure in the graphic area is saved as graphic data Fig. When the text data Txt contains "Prove BD=CD", "BD=CD" is saved as the relation to be proved Gol. The relation type in the relation to be proved Gol is equality, and the relation objects are line segment BD and line segment CD.

[0081] S12. Extract the geometry name and conditional statement from the text data Txt, generate a text object item Tob based on the geometry name, and generate a text relation item Trl based on the conditional statement. Each text object item Tob includes an object name and an object type, and each text relation item Trl includes a relation type and a relation object.

[0082] Specifically: In the process of processing text data Txt, the text data Txt is first segmented according to commas, periods, semicolons and mathematical symbols to obtain five text fragments: "In △ABC", "AB=AC", "D is a point on BC", "∠BAD=∠CAD", and "Prove BD=CD". When processing "In △ABC", text object items Tob with object names A, B and C and object type of point are generated for A, B and C respectively, and text object item Tob with object name ABC and object type of triangle is generated for △ABC.

[0083] Specifically: When processing "AB=AC", text object items Tob with object names AB and AC and object type line segment are generated for AB and AC respectively, and text relation items Trl with relation type equality and relation objects line segment AB and line segment AC are generated.

[0084] Specifically: When processing "D is a point on BC", a text object item Tob with object name D and object type point is generated for D, a text object item Tob with object name BC and object type line segment is generated for BC, and a text relation item Trl with relation type subordinate and relation objects point D and line segment BC is generated.

[0085] Specifically: When processing “∠BAD=∠CAD”, generate text object items Tob with object names ∠BAD and ∠CAD respectively and object type ∠CAD, and generate text relation items Trl with relation type equal and relation objects ∠BAD and ∠CAD.

[0086] Extract graphic annotations, primitive endpoints, and primitive connection results from the graphic data Fig. Generate graphic object items Fob based on the graphic annotations and primitive endpoints. Generate graphic relationship items Frl based on the primitive connection results. Each graphic object item Fob includes an object name and an object type. Each graphic relationship item Frl includes a relationship type and a relationship object. Merge text object items Tob with the same object name and object type with graphic object items Fob into a geometric object.

[0087] Specifically: In the processing of graphic data Fig, the text labels in the graphic are read first to obtain point labels A, B, C and D. Then, the endpoint positions and connection results of the graphic lines are read. If there is a continuous line segment between point label A and point label B, a graphic object item Fob with the object name AB and the object type of line segment is generated. If there is a continuous line segment between point label A and point label C, a graphic object item Fob with the object name AC and the object type of line segment is generated.

[0088] Specifically: If there is a continuous line segment between point label B and point label C, and point label D is located on the line segment path between point label B and point label C, then generate a graphic object item Fob with object name BC and object type line segment, a graphic object item Fob with object name BD and object type line segment, and a graphic object item Fob with object name CD and object type line segment, and generate a graphic relation item Frl with relation type subordinate and relation objects point D and line segment BC.

[0089] Specifically: When merging objects, if the object name in the text object item Tob is AB and the object type is line segment, and the object name in the graphic object item Fob is also AB and the object type is also line segment, then the two are merged into a geometric object representing line segment AB in the geometric object set. Point A, point B, point C, point D, line segment AC, line segment BC, line segment BD, and line segment CD are merged in the same way.

[0090] Merge the text relation item Trl, which has the same relation type and relation object, with the graph relation item Frl into a geometric relation;

[0091] Specifically: During the relation merging process, first organize each text relation item Trl into the format of "relation type + relation object", and then organize each graphic relation item Frl into the format of "relation type + relation object". If the text relation item Trl records the relation type as subordinate and the relation objects as point D and line segment BC, and the graphic relation item Frl also records the relation type as subordinate and the relation objects as point D and line segment BC, then the two are merged into a geometric relation set representing "point D on line segment BC" as a geometric relation.

[0092] Specifically: If the text relation item Trl records a relation type of equality and the relation objects are line segments AB and AC, but the graphic relation item Frl does not have a corresponding equality marker, then the text relation item Trl will still be retained as a geometric relation in the geometric relation set Rel. If the graphic relation item Frl records a relation type of connection and the relation objects are points A and B, but the text relation item Trl does not have a corresponding connection statement, then the graphic relation item Frl will still be retained as a geometric relation in the geometric relation set Rel.

[0093] The geometric objects form a geometric object set Obj, the geometric relations form a geometric relation set Rel, and a geometric relation topology graph Top is generated based on the geometric object set Obj, the geometric relation set Rel, and the relation to be proved Gol.

[0094] Specifically: When generating the geometric relation topology graph Top, points A, B, C, D, line segments AB, AC, BC, BD, CD, angles ∠BAD and ∠CAD in the geometric object set Obj are respectively established as object nodes. The relationships between the object nodes are established as follows: "Line segment AB is equal to line segment AC", "Point D belongs to line segment BC", "Angle ∠BAD is equal to angle ∠CAD", "Point A connects to point B", "Point A connects to point C", "Point B connects to point C", "Point B connects to point D", and "Point D connects to point C". The relation to be proved Gol is written into the target field of the geometric relation topology graph Top.

[0095] Specifically: During storage, each object node stores the object name and object type, and each relation edge stores the relation type and relation object. This allows subsequent steps to directly read the known objects, known relations, and relations to be proved in the geometric relation topology graph Top when generating the candidate proof path set Pts. For example, after a subsequent step reads that line segment AB is equal to line segment AC, angle ∠BAD is equal to angle ∠CAD, and point D belongs to line segment BC, it can continue to determine whether it is necessary to add line segment AD as an auxiliary construction object.

[0096] This embodiment first organizes the content of questions from different sources into text data Txt, graphic data Fig, and the relationship to be proved Gol in the geometry question data Inp. Then, it forms text object items Tob and text relationship items Trl from the text data Txt, and graphic object items Fob and graphic relationship items Frl from the graphic data Fig. The text-side information and graphic-side information are merged by ensuring consistency in object name, object type, relationship type, and relationship object. This generates a geometric object set Obj, a geometric relationship set Rel, and a geometric relationship topology graph Top. Therefore, in real-world geometry question input scenarios, such as when the question stem states "AB=AC" and the graph simultaneously labels points A, B, and C, and line segments AB and AC, this embodiment can match the line segment names in the question stem with the line segment endpoints in the graph, and uniformly write the question stem relationship and the graphic connection relationship into the geometric relationship topology graph Top. This avoids the situation where the text conditions and graphic objects are disconnected when generating the subsequent proof path, ensuring that the generation of the subsequent candidate proof path set Pts is based on the same set of object and relationship data.

[0097] Example 3

[0098] Please see Figure 2Specifically: S2 includes:

[0099] S21. Read the geometric relationship set Rel and the relationship to be proved Gol in the geometric relationship topology graph Top, and call the preset reasoning rule library Rul. The reasoning rule library Rul includes multiple rule items composed of rule antecedent Ant, rule consequent Cns and construction action Cat.

[0100] Specifically: In the application scenario set in Example 1, the geometric relationship topology graph Top has already recorded that line segment AB is equal to line segment AC, angle ∠BAD is equal to angle ∠CAD, point D belongs to line segment BC, and the relationship to be proved Gol is that line segment BD is equal to line segment CD. The reasoning rule base Rul pre-stores the reasoning rule items commonly used in junior high school geometric proofs.

[0101] For example, the consequent Cns of the first type of rule item is that line segment BD is equal to line segment CD, the antecedent Ant is that triangle △ABD is congruent to triangle △ACD, and the construction action Cat is to extract the corresponding sides of the congruent triangles;

[0102] The consequent of the second type of rule item, Cns, is that triangles △ABD and △ACD are congruent; the antecedent, Ant, is that line segments AB and AC are equal, angles ∠BAD and ∠CAD are equal, and line segments AD and AD are equal; the construction action, Cat, is to connect point A and point D.

[0103] The consequent of the third type of rule item, Cns, is that line segment BD is equal to line segment CD, the antecedent, Ant, is that point D is the midpoint of line segment BC, and the constructing action, Cat, is to check the relationship between point D and the midpoint of line segment BC.

[0104] S22. Search the rule item in the inference rule base Rul where the rule consequent Cns is consistent with the relation to be proved Gol, and read the rule antecedent Ant and the construction action Cat corresponding to the rule item;

[0105] Specifically: During the search process, the relation type and relation object in the relation to be proved Gol are compared with the rule consequent Cns of each rule item in the inference rule base Rul. When the relation type of the rule consequent Cns is equal and the relation object is line segment BD and line segment CD, the rule item is determined to be consistent with the relation to be proved Gol, and the rule antecedent Ant and the construction action Cat in the rule item are read.

[0106] In this embodiment, the rule item "since triangles △ABD and △ACD are congruent, line segment BD is equal to line segment CD" is read, and the rule item "since point D is the midpoint of line segment BC, line segment BD is equal to line segment CD" is read. This provides two different rule entry points for generating different candidate proof paths Pat in the future.

[0107] It should be noted that when the read rule predecessor Ant does not exist in the geometric relation set Rel, and the rule predecessor Ant is an intermediate geometric relation, the search continues in the inference rule base Rul for rule items that match the rule successor Cns with the intermediate geometric relation, and the rule predecessor Ant and the construction action Cat in the rule items that are searched are read, until the rule predecessor Ant can be compared with the existing relations in the geometric relation set Rel, the relations generated by the construction action Cat, and the relations generated by the rule items in the inference rule base Rul.

[0108] S23. Compare the rule antecedent Ant with the geometric relation set Rel. The rule antecedent Ant that already exists in the geometric relation set Rel is formed into a satisfied condition set Sat. The rule antecedent Ant that does not exist in the geometric relation set Rel but is generated through the construction action Cat and the rule items in the reasoning rule base Rul is formed into a supplementary condition set Lac. At least two candidate proof paths Pat are generated according to the combination of the satisfied condition set Sat, the supplementary condition set Lac and the construction action Cat. The candidate proof path set Pts is formed by the at least two candidate proof paths Pat.

[0109] Specifically: During the comparison process, each condition in the rule antecedent Ant is compared with the geometric relations in the geometric relation set Rel. If the condition in the rule antecedent Ant is that line segment AB is equal to line segment AC, and the geometric relation set Rel already has a geometric relation of the relation type of equality and relation objects of line segment AB and line segment AC, then the condition is added to the set of satisfied conditions Sat.

[0110] If the condition in the antecedent Ant of the rule is that angle ∠BAD and angle ∠CAD are equal, and the geometric relation set Rel already contains a geometric relation of type equality with relation objects angle ∠BAD and angle ∠CAD, then this condition is added to the set of satisfied conditions Sat.

[0111] If the condition in the antecedent Ant of the rule is that line segment AD is equal to line segment AD, and the geometric relation set Rel has not yet recorded line segment AD as a common edge relation, and the construction action Cat is to connect point A and point D to form line segment AD, then the condition set Lac to be supplemented will be added to the condition set Lac.

[0112] Specifically: When generating candidate proof path Pat, the first candidate proof path Pat is "connecting point A and point D, obtaining line segment AD equal to line segment AD, combining line segment AB equal to line segment AC and angle ∠BAD equal to angle ∠CAD, deriving that triangle △ABD is congruent to triangle △ACD, obtaining line segment BD equal to line segment CD". The second candidate proof path Pat is "attempting to call the midpoint definition rule, checking whether point D is the midpoint of line segment BC, and recording the missing condition when point D is not the midpoint of line segment BC". The first and second candidate proof paths Pat together form the candidate proof path set Pts.

[0113] S2 further includes:

[0114] S24. Convert the construction action Cat in the candidate proof path Pat into a standard proof node Stn of the construction class. The standard proof node Stn is a standard node in the standard node sequence Nod. Convert the relationship in the satisfied condition set Sat and the condition set to be supplemented Lac into the standard proof node Stn of the relationship class.

[0115] Specifically: During the node transformation process, the construction action Cat "connecting points A and D" in the first candidate proof path Pat is transformed into a standard proof node Stn of the construction class. The node type Nty of the standard proof node Stn is a construction class. The input relation set Inr includes points A and D existing in the geometric object set Obj. The operation object set Opo includes points A and D. The output relation set Our includes line segment AD and line segment AD being equal to line segment AD. The target relation Tar is the common edge condition for forming triangles △ABD and △ACD. The node number Ord is set according to the proof execution order.

[0116] Specifically: In the process of converting relational nodes, the equality of line segments AB and AC in the condition set Sat is converted into a standard proof node Stn of the relational class. The node type Nty of the standard proof node Stn is a relational class. The input relation set Inr is the equality of line segments AB and AC that already exist in the geometric relation set Rel. The operation object set Opo includes line segments AB and AC. The output relation set Our includes line segments AB and AC. The target relation Tar is the edge equality condition that satisfies the congruence judgment.

[0117] The equality of angles ∠BAD and ∠CAD in the condition set Sat is converted into the standard proof node Stn of the relation class in the same way, and the target relation Tar is the one that satisfies the condition of equal included angles in the congruence determination.

[0118] The action of triggering the rule consequent Cns after the rule antecedent Ant is satisfied is converted into the standard proof node Stn of the rule class;

[0119] Specifically: When the standard proof node Stn of the relation class and the standard proof node Stn of the construction class have output that line segment AB is equal to line segment AC, angle ∠BAD is equal to angle ∠CAD, and line segment AD is equal to line segment AD, the action of triggering the congruence judgment rule will be converted into the standard proof node Stn of the rule class. The node type Nty of this standard proof node Stn is the rule class, the input relation set Inr includes line segment AB is equal to line segment AC, angle ∠BAD is equal to angle ∠CAD, and line segment AD is equal to line segment AD, the operation object set Opo includes triangle △ABD and triangle △ACD, the output relation set Our includes triangle △ABD and triangle △ACD being congruent, and the target relation Tar is to obtain the intermediate conclusion that line segment BD is equal to line segment CD.

[0120] The action of obtaining the relationship to be proved, Gol, is converted into the standard proof node Stn of the conclusion class;

[0121] Specifically: When the standard proof node Stn of the rule class has output that triangles △ABD and △ACD are congruent, the action of obtaining the relation to be proved Gol by the equality of corresponding sides of congruent triangles is converted into a standard proof node Stn of the conclusion class. The node type Nty of this standard proof node Stn is the conclusion class, the input relation set Inr includes triangles △ABD and △ACD being congruent, the operation object set Opo includes line segments BD and CD, the output relation set Our includes line segments BD and CD being equal, and the target relation Tar is the relation to be proved Gol.

[0122] The standard proof nodes Stn are arranged in the order of proof execution to form the standard node sequence Nod; wherein each standard proof node Stn includes a node type Nty, an input relation set Inr, an operation object set Opo, an output relation set Our, a target relation Tar, and a node number Ord.

[0123] Specifically: When forming the standard node sequence Nod, a node number Ord is set for each standard proof node Stn according to the proof execution order. For example, the standard node sequence Nod in the first candidate proof path Pat includes the following in sequence: the relational standard proof node Stn that "reads that line segment AB is equal to line segment AC", the relational standard proof node Stn that "reads that angle ∠BAD is equal to angle ∠CAD", the construction standard proof node Stn that "connects point A and point D", the rule standard proof node Stn that "triggers the triangle congruence determination", and the conclusion standard proof node Stn that "deduces that line segment BD is equal to line segment CD". In this way, each candidate proof path Pat is transformed from a natural language proof process into a standard node sequence Nod with unified fields and a clear order.

[0124] This embodiment does not directly play the proof process of the geometry problem as a natural language step through the above steps. Instead, it first uses the rule items in the reasoning rule base Rul, which consist of rule antecedent Ant, rule consequent Cns, and construction action Cat, to perform reverse matching on the geometric relation set Rel and the relation to be proved Gol. It distinguishes between the satisfied condition set Sat that already exists in the geometric relation set Rel and the condition set Lac that needs to be supplemented by the construction action Cat. Then, it splits each candidate proof path Pat into standard proof nodes Stn of construction class, relation class, rule class, and conclusion class, forming a standard node sequence Nod. Therefore, in real-world auxiliary line proof scenarios, such as proving two triangles are congruent, it can effectively demonstrate the correctness of the proof process. When it is necessary to complete the "SAS" conditions, this embodiment can classify the existing edge equality relationships in the problem into the satisfied condition set Sat, classify the common edge relationships that need to be formed by connecting auxiliary lines into the condition set Lac to be supplemented, and convert "connecting auxiliary lines", "confirming common edges", "triggering the equality rule" and "deriving the target conclusion" into standard proof nodes Stn with node type Nty, input relation set Inr, operation object set Opo, output relation set Our, target relation Tar and node number Ord, respectively. This allows the subsequent sequential comparison, closure calculation and bifurcation point determination of different candidate proof paths Pat to no longer rely on whether the textual expressions are similar, but to be processed based on node data with a unified structure.

[0125] Example 4

[0126] Specifically: S3 includes:

[0127] S31. Select the current standard node Cur in the standard node sequence Nod according to the node number Ord, and form the preceding standard proof node Stn into a set of predecessor nodes Bef.

[0128] Specifically: In the application scenario set in Example 1, for each standard node sequence Nod formed in Example 3, nodes are selected one by one according to the node number Ord. For example, in the first candidate proof path Pat, when the current standard node Cur is the standard proof node Stn of the construction class of "connecting point A and point D", the standard proof nodes Stn of the relationship class of "reading that line segment AB is equal to line segment AC" and "reading that angle ∠BAD is equal to angle ∠CAD" that have a node number Ord earlier than this node are combined to form the preceding node set Bef.

[0129] S32. Read the geometric relationship set Rel in the geometric relationship topology graph Top as the basic relationship;

[0130] Add the output relation set Our of each standard proof node Stn in the preceding node set Bef to the basic relation;

[0131] Specifically: When forming the basic relationship, first read the recorded "line segment AB is equal to line segment AC", "point D belongs to line segment BC", and "angle ∠BAD is equal to angle ∠CAD" from the geometric relationship topology graph Top as the initial content. Then read the output relationship set Our of each standard proof node Stn in the preceding node set Bef. For example, add "line segment AB is equal to line segment AC" and "angle ∠BAD is equal to angle ∠CAD" to the basic relationship so that the basic relationship simultaneously includes the initial relationship of the problem and the path output relationship before the current node.

[0132] S33. When the basic relation after being added satisfies the rule predecessor Ant in the inference rule base Rul, the corresponding rule successor Cns is added to the basic relation. The addition process is repeated until there is no new rule successor Cns that satisfies the addition condition. The basic relation after the addition process is completed is determined as the predecessor relation closure Pre before the current standard node Cur.

[0133] Specifically: During the addition process, each of the basic relations is compared with the rule antecedent Ant in the inference rule base Rul. For example, when the basic relations contain both "line segment AB is equal to line segment AC" and "angle ∠BAD is equal to angle ∠CAD", if the inference rule base Rul contains a rule item with these two relations as the rule antecedent Ant and "AD is the angle bisector of angle ∠BAC" as the rule consequent Cns, then the rule consequent Cns is added to the basic relations.

[0134] After adding, continue rule comparison until no new rule successor Cns is added, and save the basic relationship at this time as the predecessor relationship closure Pre before the current standard node Cur.

[0135] S3 further includes:

[0136] S34. Align the standard node sequences Nod corresponding to at least two candidate proof paths Pat according to the node sequence number Ord, and calculate the preceding relation closure Pre for the current standard node Cur under the same node sequence number Ord.

[0137] Specifically: During the path alignment process, the standard node sequence Nod corresponding to the first candidate proof path Pat and the second candidate proof path Pat are read respectively, and the positions are matched according to the node number Ord. For example, the nodes with node number Ord 1 in the two paths are matched with each other, the nodes with node number Ord 2 are matched with each other, and the nodes with node number Ord 3 are matched with each other.

[0138] When aligned to the position with node ord of 3, calculate the preceding relation closure Pre of the current standard node Cur at that position for both paths, so that subsequent comparisons are based on the geometric relation results before the same sequential position.

[0139] S35. When the relation items in the preceding relation closure Pre corresponding to different candidate proof paths Pat correspond one-to-one, and the relation type and relation object of each corresponding relation item are consistent, and the target relation Tar in the current standard node Cur corresponding to different candidate proof paths Pat are consistent, the preceding relation closure Pre before the current standard node Cur is determined to be equivalent.

[0140] Specifically: When determining whether the preceding relation closure Pre is equivalent, the relation items obtained by the two candidate proof paths Pat before the same node index Ord are compared item by item. For example, if the preceding relation closure Pre of the first path contains a relation item with the same relation type and relation objects of line segments AB and AC, and the preceding relation closure Pre of the second path also contains a relation item with the same relation type and relation objects of line segments AB and AC, then the relation items are consistent.

[0141] Continue comparing relational items such as "angle ∠BAD is equal to angle ∠CAD" and "point D belongs to line segment BC". When the relational type and relational object of all corresponding relational items are consistent, and the current standard node Cur of both paths serves to derive the relation to be proved Gol, the preceding relational closure Pre of the two paths before the current standard node Cur is determined to be equivalent.

[0142] S36. Under the condition that the preceding relation closures Pre corresponding to different candidate proof paths Pat are equivalent, compare the node type Nty, the operation object set Opo, and the output relation set Our corresponding to the current standard node Cur of different candidate proof paths Pat, and determine the current standard node Cur that first appears to have at least one of the following inconsistencies: node type Nty inconsistency, operation object set Opo inconsistency, and output relation set Our inconsistency as the candidate fork point Brk.

[0143] Specifically: When determining the candidate fork point Brk, the current standard node Cur corresponding to the same node index Ord is compared only if the preceding relation closure Pre of the two candidate proof paths Pat is already equivalent. For example, the first path is a constructive node at the position of node index Ord 3. The operation object set Opo includes point A and point D. The output relation set Our includes line segment AD and line segment AD is equal to line segment AD.

[0144] The second path has a rule-type node at node number Ord 3. The operation object set Opo includes point D and line segment BC. The output relation set Our is an empty set, and the fact that the output relation set Our is an empty set indicates that point D is not found to be the midpoint of line segment BC in the current inference relation set Der.

[0145] Since the current standard node Cur of the two paths is inconsistent in at least one of the node type Nty, the operation object set Opo, and the output relation set Our, and this inconsistency first appears at the node index Ord of position 3, the current standard node Cur at this position is determined as the candidate fork point Brk.

[0146] In this embodiment, before determining whether different candidate proof paths Pat have truly begun to separate, the standard proof nodes Stn preceding the current standard node Cur are grouped into a preceding node set Bef, using the current standard node Cur as the boundary. The geometric relation set Rel, the output relation set Our, and the rule consequent Cns derived from the inference rule base Rul are all included in the preceding relation closure Pre. Then, the different standard node sequences Nod are aligned according to the node number Ord. Thus, in the explanation of real-world multi-solution geometry problems, for example, when one candidate proof path Pat emphasizes the equality of edges and another candidate proof path Pat emphasizes the equality of angles, but both have formed the same geometric relation basis before entering the selection of auxiliary lines, this difference in the display order is not mistaken for a difference in proof ideas. Instead, after the preceding relation closure Pre is equivalent, the node type Nty, the operation object set Opo, and the output relation set Our of the current standard node Cur are compared. Thus, the current standard node Cur, where the first substantial difference in proof actions occurs, is identified as the candidate fork point Brk, so that the subsequent branching explanation starts from the position where the proof structure changes.

[0147] Example 5

[0148] Please see Figure 3 Specifically: S4 includes:

[0149] S41. Read the node number Ord corresponding to the candidate fork point Brk as the starting number, and form the current standard node Cur corresponding to the starting number and the standard proof node Stn located after the starting number into a subsequent node set Aft.

[0150] Specifically: In the application scenario set in Example 1, if Example 4 determines that the candidate fork point Brk is located at node number Ord 3, then the current standard node Cur with node number Ord 3 and the standard proof node Stn with node number Ord greater than 3 are combined to form the subsequent node set Aft. For example, the subsequent node set Aft of the first candidate proof path Pat includes "connecting point A and point D", "triggering triangle congruence determination", and "deducing that line segment BD is equal to line segment CD". The subsequent node set Aft of the second candidate proof path Pat includes "attempting to call the midpoint definition rule", "checking whether point D is the midpoint of line segment BC", and "recording missing conditions".

[0151] S42. Take the preceding relation closure Pre before the candidate bifurcation point Brk as the deductive relation set Der, and read the standard proof node Stn in the subsequent node set Aft in sequence according to the node number Ord.

[0152] Specifically: at the start of subsequent deductions, the preceding relation closure Pre, which was formed before the candidate bifurcation point Brk, is copied into the deduction relation set Der. For example, the deduction relation set Der initially includes line segment AB being equal to line segment AC, angle ∠BAD being equal to angle ∠CAD, and point D belonging to line segment BC. Then, the standard proof node Stn in the subsequent node set Aft is read in ascending order of the node number Ord, so that each deduction step is based on the geometric relations added in the previous step.

[0153] S43. When the input relation set Inr of the standard proof node Stn is included in the deduction relation set Der, the output relation set Our of the standard proof node Stn is added to the deduction relation set Der. When the deduction relation set Der after being added satisfies the rule antecedent Ant in the reasoning rule base Rul, the corresponding rule consequent Cns is added to the deduction relation set Der.

[0154] Specifically: during the derivation of the first candidate proof path Pat, when reading the standard proof node Stn of the construction class that "connects points A and D", if points A and D in the input relation set Inr already exist in the geometric object corresponding to the derivation relation set Der, then the line segment AD in the output relation set Our and the line segment AD equal to the line segment AD are added to the derivation relation set Der;

[0155] When continuing to read the standard proof node Stn of the rule class that triggers triangle congruence determination, if the derivation relation set Der already contains line segment AB equal to line segment AC, angle ∠BAD equal to angle ∠CAD, and line segment AD equal to line segment AD, then add triangle △ABD and triangle △ACD to the derivation relation set Der for congruence.

[0156] Repeat the addition process until no new rule consequent Cns that meets the addition conditions is found, and determine the inference relation set Der after the inference is completed as the subsequent relation closure Pos.

[0157] Specifically: After each addition of a new output relation set Our or a new rule consequent Cns to the inference relation set Der, the inference relation set Der is re-compared with the rule antecedent Ant in the reasoning rule base Rul. For example, after triangles △ABD and △ACD are congruent and added to the inference relation set Der, the rule item "corresponding sides of congruent triangles are equal" is triggered and line segments BD and CD are added as equal.

[0158] When no new rule consequent Cns is added after the re-comparison, the current inference relation set Der is saved as the subsequent relation closure Pos corresponding to the first candidate proof path Pat.

[0159] S4 further includes:

[0160] S44. During the subsequent deduction process according to S42 and S43, each time a standard proof node Stn in the subsequent node set Aft is read, the input relation set Inr of the read standard proof node Stn is compared with the currently formed deduction relation set Der, and the relations in the input relation set Inr that are not included in the deduction relation set Der are added to the missing condition set Mis.

[0161] Specifically: During the derivation of the candidate proof path Pat mentioned in the second article, if the standard proof node Stn of the rule class of "attempt to call the midpoint definition rule" is read, the input relation set Inr requires that there is a point D as the midpoint of line segment BC, but there is no point D as the midpoint of line segment BC in the current derivation relation set Der, then the point D as the midpoint of line segment BC is added to the missing condition set Mis.

[0162] S45. After reading the subsequent node set Aft, compare the relationship to be proved Gol with the subsequent relationship closure Pos, and if the relationship to be proved Gol is not in the subsequent relationship closure Pos, add the relationship to be proved Gol to the missing condition set Mis.

[0163] Specifically: After reading the subsequent node set Aft of each candidate proof path Pat, check whether there is a relation item in the corresponding subsequent relation closure Pos that is consistent with the relation to be proved Gol. For example, the relation to be proved Gol is that line segment BD and line segment CD are equal. If there is no relation item in the subsequent relation closure Pos corresponding to a certain candidate proof path Pat that has a relation type of equality and relation objects of line segment BD and line segment CD, then add the equality of line segment BD and line segment CD to the missing condition set Mis corresponding to that candidate proof path Pat.

[0164] S4 further includes:

[0165] S46. Compare the subsequent relation closure Pos and the missing condition set Mis corresponding to different candidate proof paths Pat:

[0166] When there is a relation in the subsequent relation closure Pos corresponding to any candidate proof path Pat, and there is no relation with the same relation type and relation object in the subsequent relation closure Pos corresponding to at least one other candidate proof path Pat, it is determined that different candidate proof paths Pat form different proof results after the candidate bifurcation point Brk;

[0167] Specifically: When comparing the subsequent relation closures Pos, the relation items in the subsequent relation closures Pos corresponding to the first candidate proof path Pat are read item by item, and the relation items with the same relation type and relation object are searched in the subsequent relation closures Pos corresponding to the second candidate proof path Pat. For example, if the subsequent relation closures Pos corresponding to the first candidate proof path Pat contain triangles △ABD and △ACD being congruent, but the subsequent relation closures Pos corresponding to the second candidate proof path Pat do not contain such congruent relation items, then it is determined that the two candidate proof paths Pat form different proof results after the candidate bifurcation point Brk.

[0168] When there is a missing relation in the missing condition set Mis corresponding to any candidate proof path Pat, and there is no missing relation in the missing condition set Mis corresponding to at least one other candidate proof path Pat that has the same relation type and relation object, it is determined that different candidate proof paths Pat form different proof gaps after the candidate bifurcation point Brk;

[0169] Specifically: When comparing the missing condition set Mis, the missing relationships in the missing condition set Mis corresponding to the first candidate proof path Pat are read item by item, and the missing relationships with the same relationship type and relationship object are searched in the missing condition set Mis corresponding to the second candidate proof path Pat. For example, the second candidate proof path Pat is missing point D, which is the midpoint of line segment BC, while the first candidate proof path Pat forms a common edge relationship between line segment AD and line segment AD by connecting point A and point D and continues to trigger the triangle congruence judgment. Then it is determined that the two candidate proof paths Pat form different proof gaps after the candidate bifurcation point Brk.

[0170] When at least one of the following conditions is met—that different proof results or different proof gaps—the candidate bifurcation point Brk is determined as the proof bifurcation point Bpt.

[0171] Specifically: When S46 confirms that the two candidate proof paths Pat form at least one of different proof results and different proof gaps after the candidate fork point Brk, the candidate fork point Brk is saved as the proof fork point Bpt. For example, the position of the constructive node with node number Ord 3 and corresponding to "connection point A and point D" is saved as the proof fork point Bpt, indicating that from this position, the subsequent reasoning content of the different candidate proof paths Pat has produced substantial differences.

[0172] S5 includes:

[0173] S51. Take the standard proof node Stn located before the proof bifurcation point Bpt, and having the same node number Ord, the same node type Nty, the same set of operation objects Opo, and the same set of output relations Our in different candidate proof paths Pat as common standard nodes, and form a common node set Cnd from the common standard nodes. Generate a common pre-explanation segment Com based on the common node set Cnd.

[0174] Specifically: When generating the common node set Cnd, the node index Ord before the proof fork point Bpt is read, for example, the standard proof nodes Stn with node index Ord 1 and node index Ord 2. If both candidate proof paths Pat are nodes that read the relationship between line segment AB and line segment AC at node index Ord 1, and nodes that read the relationship between angle ∠BAD and angle ∠CAD at node index Ord 2, then these two nodes are added to the common node set Cnd as common standard nodes, and the common pre-explanation segment Com is generated accordingly, which first shows the relationship between line segment AB and line segment AC, and then shows the relationship between angle ∠BAD and angle ∠CAD.

[0175] S52. Read the node number Ord corresponding to the proof fork point Bpt, and form a branch node set Bnd from the standard proof nodes Stn in different candidate proof paths Pat starting from the node number Ord corresponding to the proof fork point Bpt. Generate a branch deduction solution segment Bra based on the branch node set Bnd.

[0176] Specifically: When generating the branch node set Bnd, starting from the node index Ord corresponding to the proof fork point Bpt, the standard proof node Stn in different candidate proof paths Pat is read. For example, the branch node set Bnd of the first candidate proof path Pat includes connecting point A and point D, forming a common edge AD, triggering triangle △ABD and triangle △ACD to be congruent, and deducing that line segment BD is equal to line segment CD. The branch node set Bnd of the second candidate proof path Pat includes attempting to call the midpoint definition rule, checking that the missing point D is the midpoint of line segment BC, outputting the missing condition prompt, and generating the branch deduction solution segment Bra accordingly.

[0177] S53. Generate branched dynamic graphic explanation content Dyn in the order of outputting the common pre-explanation segment Com first and the branched derivation explanation segment Bra last.

[0178] Specifically: When outputting the branched dynamic graphic explanation content Dyn, the common pre-explanation segment Com is played first, allowing students to see that the two candidate proof paths Pat depend on the fact that line segments AB and AC are equal, and angles ∠BAD and ∠CAD are equal. Then, the branch derivation explanation segment Bra is played, allowing students to see the process of different auxiliary constructions entering different reasoning chains from the proof bifurcation point Bpt. For example, the left side shows that after connecting points A and D, line segments BD and CD are equal through triangle congruence. The right side shows the missing relationship when the same common edge condition is not formed, thereby generating the complete branched dynamic graphic explanation content Dyn.

[0179] In this embodiment, instead of immediately switching the explanation branch after determining the candidate fork point Brk, the subsequent node set Aft is read starting from the node index Ord corresponding to the candidate fork point Brk. The preceding relation closure Pre is used as the deduction relation set Der for subsequent deduction. During the deduction process, the subsequent relation closure Pos and the missing condition set Mis are simultaneously formed. Then, the proof fork point Bpt is confirmed based on whether the subsequent relation closure Pos and the missing condition set Mis corresponding to different candidate proof paths Pat produce different proof results or different proof gaps. Therefore, in real-world geometric explanation scenarios, for example, a candidate proof path Pat connects auxiliary lines... After obtaining the common edge relation, we can continue to deduce triangle congruence. If another candidate proof path Pat can also enter the subsequent reasoning but lacks the corresponding edge relation that can be used for congruence determination, this embodiment can record this difference in the subsequent relation closure Pos and the missing condition set Mis, and determine the position that truly causes the difference in the subsequent proof as the proof bifurcation point Bpt. Then, the common standard nodes before the proof bifurcation point Bpt are organized into a common pre-explanation segment Com, and the different standard proof nodes from the proof bifurcation point Bpt are organized into a branch deduction explanation segment Bra. This allows the finally generated branched dynamic graphical explanation content Dyn to simultaneously display the differences in subsequent reasoning brought about by the common reasoning basis and different auxiliary constructions.

[0180] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and variations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for generating dynamic graphical explanations based on geometric relationship topological evolution, characterized in that: Includes the following steps: S1. Obtain geometry problem data Inp, and construct a geometric relationship topology graph Top based on the geometry problem data Inp; S1 includes: S11, the geometry problem data Inp includes text data Txt, graphic data Fig, and the relation to be proved Gol; The text data Txt is at least one of the following: the text input of the question and the text content obtained after recognizing the text region in the question image; The graphic data Fig can be at least one of the following: the graphic input of the question and the graphic content obtained by segmenting the graphic region in the question image; The relation to be proved, Gol, is at least one of the following: a conclusion item in the question bank, or a conclusion content extracted from the text data Txt containing a statement with the meaning of the proof. S12. Extract the geometry name and conditional statement from the text data Txt, generate a text object item Tob based on the geometry name, and generate a text relation item Trl based on the conditional statement. Each text object item Tob includes an object name and an object type, and each text relation item Trl includes a relation type and a relation object. Extract graphic annotations, primitive endpoints, and primitive connection results from the graphic data Fig. Generate graphic object items Fob based on the graphic annotations and primitive endpoints. Generate graphic relationship items Frl based on the primitive connection results. Each graphic object item Fob includes an object name and an object type. Each graphic relationship item Frl includes a relationship type and a relationship object. Merge text object items Tob with the same object name and object type with graphic object items Fob into a geometric object. Merge the text relation item Trl, which has the same relation type and relation object, with the graph relation item Frl into a geometric relation; S1. A geometric object set Obj is formed by the geometric objects, and a geometric relation set Rel is formed by the geometric relations. A geometric relation topology graph Top is generated based on the geometric object set Obj, the geometric relation set Rel, and the relation to be proved Gol. S2. A candidate proof path set Pts is generated based on the geometric relation topology graph Top, and each candidate proof path Pat in the candidate proof path set Pts is converted into a standard node sequence Nod. The standard node sequence Nod includes multiple standard nodes arranged in the order of proof execution. S2 includes: S21. Read the geometric relation set Rel and the relation to be proved Gol in the geometric relation topology graph Top, and call the preset inference rule library Rul. The inference rule library Rul includes multiple rule items composed of rule antecedent Ant, rule consequent Cns and construction action Cat. S22. Search the rule item in the inference rule base Rul where the rule consequent Cns is consistent with the relation to be proved Gol, and read the rule antecedent Ant and the construction action Cat corresponding to the rule item; S23. Compare the rule antecedent Ant with the geometric relation set Rel. The rule antecedent Ant that already exists in the geometric relation set Rel is formed into a satisfied condition set Sat. The rule antecedent Ant that does not exist in the geometric relation set Rel but is generated through the construction action Cat and the rule items in the reasoning rule base Rul is formed into a supplementary condition set Lac. At least two candidate proof paths Pat are generated according to the combination of the satisfied condition set Sat, the supplementary condition set Lac and the construction action Cat. The candidate proof path set Pts is formed by the at least two candidate proof paths Pat. S2 further includes: S24. Convert the construction action Cat in the candidate proof path Pat into a standard proof node Stn of the construction class. The standard proof node Stn is a standard node in the standard node sequence Nod. Convert the relationship in the satisfied condition set Sat and the condition set to be supplemented Lac into the standard proof node Stn of the relationship class. The action of triggering the rule consequent Cns after the rule antecedent Ant is satisfied is converted into the standard proof node Stn of the rule class; The action of obtaining the relationship to be proved, Gol, is converted into the standard proof node Stn of the conclusion class; The standard proof nodes Stn are arranged in the order of proof execution to form the standard node sequence Nod; wherein each standard proof node Stn includes a node type Nty, an input relation set Inr, an operation object set Opo, an output relation set Our, a target relation Tar, and a node number Ord; S3. Calculate the preceding relation closure Pre before the current standard node of the standard node sequence Nod for different candidate proof paths Pat. When the relation type and relation object in the preceding relation closure Pre corresponding to different candidate proof paths Pat are consistent, compare the node type, operation object and output relation between the current standard nodes, and determine the current standard node that first produces a difference as the candidate fork point Brk. Read the geometric relation set Rel from the geometric relation topology graph Top as the basic relation; S3 includes S33; S33. When the basic relation after being added satisfies the rule predecessor Ant in the inference rule base Rul, the corresponding rule successor Cns is added to the basic relation. The addition process is repeated until there is no new rule successor Cns that satisfies the addition condition. The basic relation after the addition process is completed is determined as the predecessor relation closure Pre before the current standard node Cur. S4. Taking the candidate bifurcation point Brk as the starting point for further deduction, the subsequent relation closure Pos and the missing condition set Mis corresponding to different candidate proof paths Pat are obtained respectively. When there is a difference between at least one of the subsequent relation closure Pos and the missing condition set Mis, the candidate bifurcation point Brk is determined as the proof bifurcation point Bpt. S4 includes: S41. Read the node number Ord corresponding to the candidate fork point Brk as the starting number, and form the current standard node Cur corresponding to the starting number and the standard proof node Stn located after the starting number into a subsequent node set Aft. S42. Take the preceding relation closure Pre before the candidate bifurcation point Brk as the deductive relation set Der, and read the standard proof node Stn in the subsequent node set Aft in sequence according to the node number Ord. S43. When the input relation set Inr of the standard proof node Stn is included in the deduction relation set Der, the output relation set Our of the standard proof node Stn is added to the deduction relation set Der. When the deduction relation set Der after being added satisfies the rule antecedent Ant in the reasoning rule base Rul, the corresponding rule consequent Cns is added to the deduction relation set Der. Repeat the addition process until no new rule consequent Cns that meets the addition conditions is found, and determine the inference relation set Der after the inference is completed as the subsequent relation closure Pos; S5. Generate a common pre-explanation segment Com based on the standard nodes in the standard node sequence Nod that have the same node type, the same operation object, and the same output relationship before the proof bifurcation point Bpt. Generate a branch deduction explanation segment Bra based on the non-common standard nodes in the standard node sequence Nod after the proof bifurcation point Bpt. Output branched dynamic graphical explanation content Dyn based on the common pre-explanation segment Com and the branch deduction explanation segment Bra.

2. The method for generating dynamic graphics explanations based on geometric relationship topological evolution according to claim 1, characterized in that: S3 includes: S31. Select the current standard node Cur in the standard node sequence Nod according to the node number Ord, and form the preceding standard proof node Stn into a set of predecessor nodes Bef. S32. Add the output relation set Our of each standard proof node Stn in the preceding node set Bef to the basic relation.

3. The method for generating dynamic graphics explanations based on geometric relationship topological evolution according to claim 2, characterized in that: S3 further includes: S34. Align the standard node sequences Nod corresponding to at least two candidate proof paths Pat according to the node sequence number Ord, and calculate the preceding relation closure Pre for the current standard node Cur under the same node sequence number Ord. S35. When the relation items in the preceding relation closure Pre corresponding to different candidate proof paths Pat correspond one-to-one, and the relation type and relation object of each corresponding relation item are consistent, and the target relation Tar in the current standard node Cur corresponding to different candidate proof paths Pat are consistent, the preceding relation closure Pre before the current standard node Cur is determined to be equivalent. S36. Under the condition that the preceding relation closures Pre corresponding to different candidate proof paths Pat are equivalent, compare the node type Nty, the operation object set Opo, and the output relation set Our corresponding to the current standard node Cur of different candidate proof paths Pat, and determine the current standard node Cur that first appears to have at least one of the following inconsistencies: node type Nty inconsistency, operation object set Opo inconsistency, and output relation set Our inconsistency as the candidate fork point Brk.

4. The method for generating dynamic graphical explanations based on geometric relationship topological evolution according to claim 3, characterized in that: S4 further includes: S44. During the subsequent deduction process according to steps S42 and S43, each time a standard proof node Stn in the subsequent node set Aft is read, the input relation set Inr of the read standard proof node Stn is compared with the currently formed deduction relation set Der, and the relations in the input relation set Inr that are not included in the deduction relation set Der are added to the missing condition set Mis. S45. After reading the subsequent node set Aft, compare the relationship to be proved Gol with the subsequent relationship closure Pos, and if the relationship to be proved Gol is not in the subsequent relationship closure Pos, add the relationship to be proved Gol to the missing condition set Mis.

5. The method for generating dynamic graphical explanations based on geometric relationship topological evolution according to claim 4, characterized in that: S4 further includes: S46. Compare the subsequent relation closure Pos and the missing condition set Mis corresponding to different candidate proof paths Pat: When there is a relation in the subsequent relation closure Pos corresponding to any candidate proof path Pat, and there is no relation with the same relation type and relation object in the subsequent relation closure Pos corresponding to at least one other candidate proof path Pat, it is determined that different candidate proof paths Pat form different proof results after the candidate bifurcation point Brk; When there is a missing relation in the missing condition set Mis corresponding to any candidate proof path Pat, and there is no missing relation in the missing condition set Mis corresponding to at least one other candidate proof path Pat that has the same relation type and relation object, it is determined that different candidate proof paths Pat form different proof gaps after the candidate bifurcation point Brk; When at least one of the following conditions is met—that different proof results or different proof gaps—the candidate bifurcation point Brk is determined as the proof bifurcation point Bpt.

6. The method for generating dynamic graphical explanations based on geometric relationship topological evolution according to claim 5, characterized in that: S5 includes: S51. Take the standard proof node Stn located before the proof bifurcation point Bpt, and having the same node number Ord, the same node type Nty, the same set of operation objects Opo, and the same set of output relations Our in different candidate proof paths Pat as common standard nodes, and form a common node set Cnd from the common standard nodes. Generate a common pre-explanation segment Com based on the common node set Cnd. S52. Read the node number Ord corresponding to the proof fork point Bpt, and form a branch node set Bnd from the standard proof nodes Stn in different candidate proof paths Pat starting from the node number Ord corresponding to the proof fork point Bpt. Generate a branch deduction solution segment Bra based on the branch node set Bnd. S53. Generate branched dynamic graphic explanation content Dyn in the order of outputting the common pre-explanation segment Com first and the branched derivation explanation segment Bra last.

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