Paradox separation type-based reverse parallel deductive reasoning method in propositional logic

Abstract

The invention discloses a paradox separation type-based reverse parallel deductive reasoning method in propositional logic. The method comprises the following steps of: constructing a paradox and forming a paradox separation type for a sub-sentence set S in the naming logic; judging whether the S can be satisfied or not according to the paradox separation type; if the S cannot be satisfied, stopping the operation, and otherwise, constructing a reverse deduction sub-sentence set on the basis of the paradox separation type so as to obtain t new sub-sentence sets, and carrying out deductive reasoning; and if the t new sub-sentence sets are deduced to be empty sub-sentences, considering that the S cannot be satisfied, and otherwise, circulating the above steps, and stopping the operation untila judging conclusion of attribute of the S is obtained or a set condition is satisfied. The method is capable of dynamically decomposing paradox separation types to form dynamic reverse deduction targets so as to effectively guide deductive reasoning of the next step, and carrying out parallel processing on decomposed logic formula set attribute judgement so as to effectively improve the deduction efficiency of a paradox separation-based dynamic automatic deductive reasoning system; and the method can be applied to the field of program verification, automated theorem proving and the like.

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 the separation 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 of ...

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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