negation and minimality in non-horn databases
Two main approaches have been followed in the literature to give a semantics to non-Horn databases. The first one is based on considering the set of rules composing the programs as inference rules and interpreting the negation in the body as failure to prove. The other approach is based on the so-called closed-world assumption and its objective is to define a stronger notion of consequence from a theory than the classical one, where, very roughly, negative information can be inferred whenever its positive counterpart cannot be deduced from the theory. In this work we generalize the semantics for negation in logic programs, putting together the constructive nature of the rule-based deductive databases with the syntax-independence of the closed-world reasoning rules. These generalized semantics are shown to be a well-motivated and well-founded alternative to closed-world assumptions since they enjoy nice semantic and computational properties.
minimal database semantic rules program inference failure object theory informal posit general logic program reasoning computation