A neural implementation of multi-adjoint logic programming

Abstract

A neural net based implementation of propositional [0,1]-valued multi-adjoint logic programming is presented, which is an extension of earlier work on representing logic programs in neural networks carried out in [A.S. d'Avila Garcez et al., Neural-Symbolic Learning Systems: Foundations and Applications, Springer, 2002; S. Hölldobler et al., Appl. Intelligence 11 (1) (1999) 45–58]. Proofs of preservation of semantics are given, this makes the extension to be well-founded. The implementation needs some preprocessing of the initial program to transform it into a homogeneous program; then, transformation rules carry programs into neural networks, where truth-values of rules relate to output of neurons, truth-values of facts represent input, and network functions are determined by a set of general operators; the net outputs the values of propositional variables under its minimal model.