Algorithms of Isomorphism of Elementary Conjunctions Checking

Abstract When solving artificial intelligence problems related to the study of complex structured objects, a convenient tool for describing such objects is the language of predicate calculus. The paper presents two algorithms for checking the isomorphism of pairs of elementary conjunctions of predicate formulas (they coincide up to variable names and the order of conjunctive terms). The first of the algorithms checks elementary conjunctions containing a single predicate symbol for isomorphism. Furthermore, if the formulas are isomorphic, it finds a one-to-one correspondence between the arguments of these formulas. If all predicates are binary, the proposed algorithm is an algorithm for checking two directed graphs for isomorphism. The second algorithm checks elementary conjunctions containing multiple predicate symbols for isomorphism. Estimates of their time complexity are given for both algorithms.