Connectionist Representation of Multi-Valued Logic Programs

Hölldobler and Kalinke showed how, given a propositional logic program P , a 3-layer feedforward artificial neural network may be constructed, using only binary threshold units, which can compute the familiar immediate-consequence operator TP associated with P . In this chapter, essentially these results are established for a class of logic programs which can handle many-valued logics, constraints and uncertainty; these programs therefore represent a considerable extension of conventional propositional programs. The work of the chapter basically falls into two parts. In the first of these, the programs considered extend the syntax of conventional logic programs by allowing elements of quite general algebraic structures to be present in clause bodies. Such programs include many-valued logic programs, and semiring-based constraint logic programs. In the second part, the programs considered are bilattice-based annotated logic programs in which body literals are annotated by elements drawn from bilattices. These programs are well-suited to handling uncertainty. Appropriate semantic operators are defined for the programs considered in both parts of the chapter, and it is shown that one may construct artificial neural networks for computing these operators. In fact, in both cases only binary threshold units are used, but it simplifies the treatment conceptually to arrange them in so-called multiplication and addition units in the case of the programs of the first part.