ABSTRACT
This chapter provides a detailed account of the foundations of neural-symbolic integration, and introduces the neural networks and the basic definitions and notation, including the statement of Funahashi’s theorem. It discusses in some detail the so-called core method as a general and well-known approach to neural-symbolic integration. The process of embedding semantic operators of logic programs into neural networks is studied. The chapter takes the issue of the approximate computation of an operator for first-order normal logic programs. Starting with the propositional approximation of the operator, the approximate computation of the operator by sigmoidal networks, radial-basis-function networks, and vector-based networks is studied. The chapter discusses the approximate computation of the least fixed point of the operator for definite normal logic programs. It sketches the construction of neural networks to compute the Fitting-style operator for propositional normal logic programs. Approximate computation for the operators is considered for first-order normal logic programs.
