Reverse parallel deductive inference method based on paradox internal clauses in propositional logic

Abstract

The invention discloses a reverse parallel deductive inference method based on paradox internal clauses in propositional logic. The method comprises the steps that a paradox is constructed for a clause set S in the propositional logic, and a paradox separation formula is formed; whether deductive inference is terminated is judged according to the paradox separation formula, wherein if the paradoxseparation formula is null, the process is stopped, and the conclusion that S cannot be met is obtained; or otherwise, the paradox internal clauses (shown in the description) are extracted, and the obtained t clauses (shown in the description) are used as targets to perform deductive inference on S respectively, wherein if the t clauses can be deduced, the process is stopped, and the conclusion that S cannot be met is obtained; or otherwise, the process is circulated till a determination conclusion of S properties is obtained or set conditions are met, and then the process is stopped. Throughthe method, the paradox internal clauses can be dynamically extracted to form dynamic reverse deductive targets, parallel processing is performed on the properties of a decomposed logic formula set, and the efficiency of a dynamic automatic deductive inference system based on paradox separation is effectively improved; and the method can be applied to the fields of program verification, theorem machine proving, etc.

Description

technical field [0001] The invention belongs to the technical field of automatic deductive reasoning based on logic, and relates to a reverse parallel deductive reasoning method based on internal clauses of contradictions 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 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 automatically perform a series o...

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

[0005] 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 reasoning mechanism of binary resolution seriously restricts the further improvement of the ability and efficiency of automatic reasoning

At the same time, due to the limitation of the binary reasoning mechanism, the binary resolution method lacks the effective guidance and control of the next step of deductive reasoning by dynamically using the deductive results of each step, and it is difficult to parallelize the deductive task decomposition.

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