Multi-Valued Logic Programming Semantics: An Algebraic Approach

In 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 descend ing 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