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Automatic reasoning method based on maximum contradiction in propositional logic

A propositional logic and automatic reasoning technology, applied in the direction of reasoning methods, etc., can solve the problem that the clause set S is not satisfied, cannot reflect the cooperative logical relationship of multiple clauses, restricts the ability and efficiency of automatic reasoning, etc., and achieves great flexibility and ability. Strong and targeted 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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Examples

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example 1

[0036] Example 1 Let S={C 1 ,C 2 ,C 3 ,C 4 ,C 5 ,C 6} is a clause set in propositional logic, where, C 1 = l 1 ∨ l 2 , C 2 = l 2 ∨ l 3 , C 3 = l 3 ∨ l 4 , C 4 =~l 3 ∨~l 1 , C 5 =~l 4 ∨~l 2 , C 6 =~l 2 ∨~l 3 , l 1 , l 2 , l 3 , l 4 is a propositional variable. Please use the automatic deductive reasoning method based on maximum contradiction separation to determine the attributes of S.

[0037] (1) For the clause set S:

[0038] Step 1: Use variable l 1 , l 2 , l 3 Generate the largest contradiction S(l 1 , l 2 , l 3 ):

[0039] l 1 ∨l 2 ∨l 3

[0040] l 1 ∨ l 2 ∨~l 3

[0041] l 1 ∨~l 2 ∨ l 3

[0042] l 1 ∨~l 2 ∨~l 3

[0043] ~ l 1 ∨l 2 ∨l 3

[0044] ~ l 1 ∨l 2 ∨~l 3

[0045] ~ l 1 ∨~l 2 ∨ l 3

[0046] ~ l 1 ∨~l 2 ∨~l 3

[0047] The second step: according to the clause set S(l 1 , l 2 , l 3 ) with clause C 1 ,C 2 ,C 3 ,C 4 ,C 6 Contradiction C can be obtained 1 - ∧C 2 - ∧C 3 - ∧C 4 - ∧C 6 - ,in, ...

example 2

[0095] Example 2 Let S={C 1 ,C 2 ,C 3 ,C 4 ,C 5 ,C 6} is a clause set in propositional logic, where, C 1 = l 1 ∨ l 2 , C 2 = l 2 ∨ l 3 , C 3 =~l 3 ∨~l 1 , C 4 =~l 2 , C 5 =~l 2 ∨~l 3 , l 1 , l 2 , l 3 is a propositional variable. Please use the automatic deductive reasoning method based on maximum contradiction separation to determine the attributes of S.

[0096] (1) For the clause set S:

[0097] Step 1: Use variable l 2 , l 3 Generate the largest contradiction S(l 2 , l 3 ):

[0098] l 2 ∨ l 3

[0099] l 2 ∨~l 3

[0100] ~ l 2 ∨l 3

[0101] ~ l 2 ∨~l 3

[0102] The second step: according to the clause set S(l 2 , l 3 ) with clause C 2 ,C 3 ,C 4 ,C 5 The contradictory separation formula R=C can be obtained 2 + ∨C 3 + ∨C 4 + ∨C 5 + =~l 1 .

[0103] The third step: From the second step, we know that R≠φ, and there is no artificial stop condition, let C 6 =R=~l 1 , the C 7 Join S to get a new set of clauses S 1 .

[01...

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Abstract

The invention discloses an automatic reasoning method based on a maximum contradiction in propositional logic. The automatic reasoning method comprises the steps of firstly, generating the maximum contradiction by utilizing k variables appearing in a clause set S; secondly, finding out the contradiction by utilizing the maximum contradiction, and after texts in the contradiction are deleted, extracting all remaining texts to form a contradiction separation formula; and finally, judging attributes of the clause set S by utilizing the contradiction separation formula, thereby finishing the reasoning. The method breaks through the limitation that only two clauses can participate in each deduction of a traditional resolution principle; static, bivariate and resolution deduction is developed into dynamic, multivariate and contradiction separation deduction; and the method has stronger pertinency and higher flexibility, and is stronger in capability of judging logical formula attributes.

Description

technical field [0001] The invention belongs to the technical field of automatic reasoning based on logic, and in particular relates to an automatic reasoning method based on maximum contradiction 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 representations. One of the essences of solving these problems is to determine the attributes of the corresponding logical formulas (satisfiability or unsatisfiability ( False)), but because of its abstraction, complexity, and scale, artificial logic reasoning and solution cannot be effectively realized, so it is necessary to automatically determine it with the help of a computer. Automatic reasoning is the process of formalizing the reasoning process into a series of symbols, and using a computer to automatically perform a series of calculations on these s...

Claims

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Application Information

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IPC IPC(8): G06N5/04
CPCG06N5/04G06N5/045
Inventor 徐扬钟小梅刘军何星星陈树伟
Owner SOUTHWEST JIAOTONG UNIV
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