Contradictory-body internal-clause-based inverse parallel deduction reasoning method in first-order logic

Abstract

The invention discloses a contradictory-body internal-clause-based inverse parallel deduction reasoning method in first-order logic. The method sequentially includes: constructing contradictory bodiesfor a clause set S in the first-order logic, forming a contradictory-body separation formula, and according to the contradictory-body separation formula, judging whether deduction reasoning is terminated, wherein if S cannot be met, deduction reasoning is stopped, and otherwise, standard contradictory-body internal-clauses shown in the description are extracted, the obtained t clauses shown in the description are used as a target for respective deduction reasoning on S, if the t clauses can be obtained by deduction, deduction is stopped, and a conclusion that S cannot be met is obtained, andotherwise, the above process is repeated until a determination conclusion of S attributes is obtained or a set condition is met for stopping. Therefore, according to the method, the standard contradictory-body internal-clauses can be dynamically extracted, the dynamic inverse deduction target can be formed, parallel processing on logic formula set attribute determination can be realized, deductionreasoning can be effectively guided, and deduction efficiency of a dynamic automatic deduction reasoning system based on contradictory-body separation can be improved. The method can be applied to the fields of program verification, theorem machine-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 internal clauses 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 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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