Equivalent Transformation of the Reasoning Model in Production Zeroth-Order Logic

Reasoning models play an important role in artificial intelligence. One of such models is logic-based production systems. These systems are based on rules, or productions, of the form "if A is true then B is true" where A, B are the elements of logic of a particular order. In this paper propositional logic is under consideration thus A, B are elementary facts or expressions over elementary facts constructed using propositional logic operators. There are two types of logical inference performed in production systems: forward chaining and backward chaining. In the backward chaining the problem of decreasing the number of queries to external sources of information arises. In this work, an approach to solving this problem is proposed in the case of logic-based production systems that use conjunctions and disjunctions in their rules. This approach is based on representing a set of rules and their implications with the help of an additional relation over a distributive lattice (the resulting algebraic system is so-called LP structure). The process of backward chaining is modeled as a solution of a production-logical equation on an LP-structure. The specified algebraic model is reduced equivalently to a simpler model of the form of an LP-structure over an atom-based lattice.