Isomorphism of predicate formulas in artificil intelligence problems

The notion of isomorphism of elementary conjunctions of atomic predicate formulas was introduced by the author for solving some AI problems formulated in the predicate calculus language. Two elementary conjunctions are isomorphic if they coincide up to the names of their arguments and the order of literals. This notion specifies such an equivalence relation between formulas that they determine the same relation between the elements of the investigated object. This notion allows you to formulate and solve a number of problems, such as
– “setting a metric in the space of elementary conjunctions of predicate formulas”, which is important, for example, when solving the problem of clustering;
– construction of a “multilevel description of classes in a recognition problem”, which significantly reduces its computational complexity while its multiple solutions;
– construction of “logical databases”, taking into account the relationship between elements of such bases;
– construction of “logic ontologies”;
– formation a “predicate network”, in which, in contrast to the classical artificial neural network, its configuration (the number of layers and the number of cells in a layer) can change after additional training;
– formation of a “fuzzy predicate networ” that allows to recognize new, absent in the training set, objects and to calculate the“degree of confidenc” in the correctness of recognition in the process of its implementation. Brief descriptions of solutions to these problems (with links to complete solutions) are provided in this article.