Multi-valued logic programming semantics an algebraic approach

AbstractIn this paper we introduce the notion of join-irreducibility in the context of bilattices and present a procedural semantics for bilattice based logic programs which uses, as its basis, the join-irreducible elements of the knowledge part of the bilattice. The join-irreducible elements in a bilattice represent the “primitive bits” of information present within the system. In bilattices which have the descending chain property in their knowledge ordering, these elements provide a small representative set completely characterizing the bilattice. The overall complexity of the inference systems based on such bilattices can thus be reduced by restricting attention to the join-irreducible elements