Contradiction separating deductive reasoning based on standard continuation triangle in propositional logic

A propositional logic and triangle technology, applied in the field of automatic verification of system credibility, can solve the problems that the clause set S cannot be satisfied, the ability and efficiency cannot meet the objective needs, and cannot reflect the cooperative logical relationship of multiple clauses, etc., to achieve efficient construction. Effect

Inactive Publication Date: 2018-11-23
SOUTHWEST JIAOTONG UNIV
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AI Technical Summary

Problems solved by technology

Binary resolution selects two clauses with complementary pairs from the clause set S to be determined each time, deletes the complementary pair from the two clauses, and adds the new clauses formed by the disjunction of the remaining words into the atomic sentence set, and repeats as above process, until an empty clause is obtained, it can be determined that the clause set S is unsatisfiable
[0006] Although the automatic reasoning system based on the resolution principle has made many achievements, it is still far from meeting the objective needs in terms of ability and efficiency. Only in the internationally renowned problem bank TPTP in the field of automatic reasoning, there are a large number of the most difficult (Rating 1) problems so far. solve
In the resolution method, because each deduction has and can only have two clauses involved, it cannot reflect the cooperative logical relationship between multiple clauses
The concise and beautiful reasoning mechanism of binary resolution seriously restricts the further improvement of the ability and efficiency of automatic reasoning

Method used

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  • Contradiction separating deductive reasoning based on standard continuation triangle in propositional logic
  • Contradiction separating deductive reasoning based on standard continuation triangle in propositional logic
  • Contradiction separating deductive reasoning based on standard continuation triangle in propositional logic

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Embodiment 1

[0065] According to the above-mentioned deductive reasoning method, the clause set S={C in propositional logic 1 , C 2 , C 3 , C 4 , C 5 , C 6}Follow the above process to reason, specifically:

[0066] For the clause set S={C 1 , C 2 , C 3 , C 4 , C 5 , C 6},in Among them: 1, 2, 3, 4, 5 are proposition variables.

[0067] The following deduction can be obtained by using the multiple dynamic automatic deductive reasoning method based on the separation of contradictory bodies based on the standard continuation triangle:

[0068] Choose C first 1 for D 1 , at D 1 select text 1 as x 1 . Using the continuation of literal 1, select the clause C containing ~1 2 for D 2 . at this time there is a clause and clause

[0069] in D 2 select text 2 as x 2 , using 2-continuation, select the clause C containing ~2 3 for D 3 . at this time there is a clause and clause

[0070] in D 3 Select text 3 as x in 3 , using the 3-continuation, select the clause C...

Embodiment 2

[0075] Embodiment 2 supposes S={C 1 ,C 2 ,C 3 ,C 4},in C 4 =~3. Among them: 1, 2, 3 are proposition variables. The following deduction can be obtained by using the multiple dynamic automatic deductive reasoning method based on the separation of contradictory bodies based on the standard continuation triangle:

[0076] Choose C first 4 for D 1 , at D 1 Select text in ~3 is x 1 . Using literal ~3 continuation, select the clause C containing 3 2 for D 2 . at this time there is a clause and clause

[0077] in D 2 select text 1 as x 2 , using 1 continuation, choose the clause C containing ~1 1 for D 3 . at this time there is a clause and clause

[0078] in D 3 Select text in ~2 is x 3 , using ~2 continuation, select the clause C containing 2 3 for D 4 . at this time there is a clause and clause

[0079] due to D 4 The remaining literal in S is 1, and all the clauses in S are exhausted, so stop the continuation. at this time there is a clause...

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Abstract

The invention provides contradiction separating deductive reasoning based on a standard continuation triangle in propositional logic. The method sequentially comprises the following steps: constructing a standard continuation triangle-based contradiction; forming a contradiction separating formula; according to the characteristics of the contradiction separating formula and clauses, determining the attribute of a clause set; if the clause set is judged to be unsatisfiable or satisfiable, stopping, otherwise, adding the contradiction separating formula to an original clause set to form a new clause set; then constructing and separating the standard continuation triangle-based contradiction until the condition is satisfied and the conclusion of clause set attributes is obtained. The invention can efficiently construct the contradiction, realizes the improvement and popularization of the static and dual resolution deductive reasoning mechanism into a dynamic and multiple deductive reasoning mechanism based on the separation of the contradiction, and is an essential breakthrough in the field of automatic deductive reasoning.

Description

technical field [0001] The invention relates to the technical field of automatic verification of system credibility, in particular to the separation of contradictions and deductive reasoning based on standard continuation triangles in propositional logic. Background technique [0002] A large number of scientific problems in the fields of logic, mathematics, system optimization, artificial intelligence, computer science, etc. can be formalized into logical expressions. False)), but because of its abstraction, complexity, and scale, it is impossible to effectively implement logical reasoning and solving manually, so it needs to be judged by a computer. Automatic reasoning is the process of formalizing the reasoning process through a series of symbols, and making the computer automatically perform a series of calculations on these symbols according to certain rules. It is an intelligent behavior. Advanced logic-based automatic reasoning theories, methods and systems can provi...

Claims

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Application Information

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Patent Type & Authority Applications(China)
IPC IPC(8): G06N5/04
CPCG06N5/04G06N5/045
Inventor 徐扬何星星陈树伟钟小梅刘军
Owner SOUTHWEST JIAOTONG UNIV
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