Paradox separation-based multi-element dynamic automatic deductive reasoning method in first-order logic

A technology of automatic deduction and reasoning method, applied in the direction of reasoning method, etc., can solve the problems that restrict the ability and efficiency of automatic deduction and reasoning

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

Problems solved by technology

[0005] Even so, the automatic deductive reasoning system based on the resolution principle is still far from meeting the objective needs in terms of ability and efficiency. Only in the internationally renowned problem bank TPTP, there are a large number of the most difficult (Rating 1) problems that have not been solved so far. Among them, the most basic, The most critical reasoning mechanism is binary resolution—in the whole deduction process, each deduction “has, and only two clauses participate in” (although there are methods such as group-reduction deduction, linear-reduction deduction, lock-reduction deduction, etc., but among them Every deduction is still the same), this reasoning mechanism seriously restricts the further improvement of the ability and efficiency of automatic deductive reasoning

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Examples

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example 1

[0035] Example 1 Let S={C 1 ,C 2 ,...,C 5} is a set of clauses in first-order logic, where,

[0036] C 1 =P 1 (f 1 (x 11 ),x 11 ,a 1 ), C 2 =P 1 (a 1 ,x 21 ,x 21 ),

[0037] C 3 =~P 1 (x 31 ,x 32 ,x 35 )∨~P 1 (x 32 ,x 33 ,x 36 )∨~P 1 (x 35 ,x 33 ,x 34 )∨P 1 (x 31 ,x 36 ,x 34 ),

[0038] C 4 =~P 1 (x 41 ,x 42 ,x 45 )∨~P 1 (x 42 ,x 43 ,x 46 )∨~P 1 (x 41 ,x 46 ,x 44 )∨P 1 (x 45 ,x 43 ,x 44 ),

[0039] C 5 =~P 1 (a 2 ,a 1 ,a 2 ),

[0040] a 1 ,a 2 is constant, x 11 ,x 21 ,x 31 ,x 32 ,x 33 ,x 34 ,x 35 ,x 36 ,x 41 ,x 42 ,x 43 ,x 44 ,x 45 ,x 46 is the variable. The attributes of S are judged by the automatic deductive reasoning method based on the separation of contradictions.

[0041] (1) For the clause set S:

[0042] Step 1: For clause C 2 ,C 4 ,C 5 Substitute θ and merge the same text to get the standard contradiction C 2 θ- ∧C 4 θ- ∧C 5 θ- ,in,

[0043] C 2 θ- =P 1 (a 1 ,a 1 ,a 1 ),

[0044...

example 2

[0065] Example 2 Let S={C 1 ,C 2 ,...,C 5} is a set of clauses in first-order logic, where,

[0066] C 1 =P 1 (f 1 (x 11 ),x 11 ,a 1 ), C 2 =P 1 (a 1 ,x 21 ,x 21 ),

[0067] C 3 =~P 1 (x 31 ,x 32 ,x 35 )∨~P 1 (x 32 ,x 33 ,x 36 )∨~P 1 (x 35 ,x 33 ,x 34 )∨P 1 (x 31 ,x 36 ,x 34 ),

[0068] C 4 =~P 1 (x 41 ,x 42 ,x 45 )∨~P 1 (x 42 ,x 43 ,x 46 )∨~P 1 (x 41 ,x 46 ,x 44 )∨P 1 (x 45 ,x 43 ,x 44 ),

[0069] C 5 =~P 1 (a 2 ,a 1 ,a 2 ),

[0070] a 1 ,a 2 is constant, x 11 ,x 21 ,x 31 ,x 32 ,x 33 ,x 34 ,x 35 ,x 36 ,x 41 ,x 42 ,x 43 ,x 44 ,x 45 ,x 46 is the variable. Use the automatic deductive reasoning method based on the separation of contradictions to determine the attributes of S, and the number of separations of contradictions should not exceed 2 times.

[0071] It can be seen from Example 1 that it is unsatisfactory to obtain S after four times of contradiction separation. Obviously, it is impossible to determi...

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Abstract

The invention discloses a paradox separation-based multi-element dynamic automatic deductive reasoning method in first-order logic. The method comprises the following steps of: searching a standard paradox in a sub-sentence set S in the first-order logic; deleting characters occurring in the standard paradox from the residual sub-sentences in the sub-sentence set S; extracting all the residual characters to form a paradox separation type; and finally judging an attribute of the initial sub-sentence set S according to the paradox separation type, and stopping deductive reasoning until a judgingresult is finally obtained. The method is capable of improving and popularizing static and binary deductive reasoning mechanisms into dynamic and multi-element paradox separation-based deductive reasoning mechanisms, can be applied to the field of automatic system credibility verification and automated theorem proving, and has the characteristics of being multi-element, dynamic, parallel, coordinated, oriented, flexible and convenient.

Description

technical field [0001] The invention belongs to the technical field of automatic deductive reasoning based on logic, and in particular relates to a multiple dynamic automatic deductive reasoning method based on the separation of contradictions in first-order 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 analyze the attributes of the corresponding logical formulas (satisfiability or unsatisfiability (constant False)), but because of its abstraction, complexity, and scale, it is impossible to effectively implement logical reasoning and solution artificially, so it needs to be automatically judged by a computer. Automatic reasoning is the process of formalizing the reasoning process through a series of symbols, and making the computer automaticall...

Claims

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Application Information

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