Denotational semantics for def”mite programs
Christopher John Hogger · 1990
Abstract The general aim of a denotational semantics in the logic programming context is to attribute to each predicate symbol p in a program P some well-defined relation r. The chosen relation then represents the meaning of pin P-it is what p is considered to denote in this program. Ideally we want to definer for pin the least redundant way, that is, to define the minimal r sufficient for the task. Moreover, we prefer this smallest r to be uniquely minimal, so that the meaning given to p shall be unambiguous. For the case where P is definite these requirements are met by the minimal model MM(P) which, for all n, attributes to the n-ary predicate symbols in P the smallest respective n-ary relations in Hn which jointly determine a model. Every other model would redundantly enlarge the relations’ extensions, thereby rendering them ‘more defined’ than necessary.