Set-theoretic formalisms of knowledge representation

Abstract

The classification problem for knowledge representation formalisms is considered. It is based on invariants of knowledge composition operation and relation of knowledge inclusion. The variety of applied knowledge formalisms uses the specified invariants implicitly. Multiple specifications of composition and inclusion for almost all such formalisms may take place. That fact implies possibility of formal systems with different semantic properties and computational complexity of different knowledge processing algorithms. Therefore the recognized empirical classification of formalisms based on sets of rules semantic networks, and logical formulaes doesn't imply productive classification of the formal systems for simulating the content of a given subject area knowledge space. Every formalism, that is included into formalism with sets as form of knowledge presentation and sets’ union and inclusion for knowledge composition and inclusion, is called a set-theoretic knowledge presentation formalisms. Set-theoretic formalisms are simpler than formalisms of rule based systems and formalism of learning spaces. The finite system of axioms that characterize class of set-theoretic formalism is introduced. The example of formalism with non-commutative operation of composition of knowledge representations is proposed. Such formalism isn't comparable with set-theoretic formalisms. Therefore set-theoretic formalisms aren't minimal in knowledge representation formalisms inclusion. The adaptations of inference rules for set-theoretic knowledge formalisms are defined. These rules realize deductive process on systems of knowledge represented by sets.