Logic programming semantics: techniques and applications

It is generally agreed that providing a precise formal semantics for a programming language is helpful in fully understanding the language. This is especially true in the case of logic-programming-like languages for which the underlying logic provides a well-defined but insufficient semantic basis. Indeed, in addition to the usual model-theoretic semantics of the logic, proof-theoretic deduction plays a crucial role in understanding logic programs. Moreover, for specific implementations of logic programming, e.g. PROLOG, the notion of deduction strategy is also important. In this thesis, we provide semantics for two types of logic programming languages and develop applications of these semantics. First, we propose a semantics of PROLOG programs that we use as the basis of a proof method for termination properties of PROLOG programs. Second, we turn to the temporal logic programming language TEMPLOG of Abadi and Manna, develop its declarative semantics, and then use this semantics to prove a completeness result for a fragment of temporal logic and to study TEMPLOG's expressiveness. In our PROLOG semantics, a program is viewed as a function mapping a goal to a finite or infinite sequence of answer substitutions. The meaning of a program is then given by the least solution of a system of functional equations associated with the program. These equations are taken as axioms in a first-order theory in which various program properties, especially termination or non-termination properties, can be proved. The method extends to PROLOG programs with extra-logical features such as cut. For TEMPLOG, we provide two equivalent formulations of the declarative semantics: in terms of a minimal temporal Herbrand model and in terms of a least fixpoint. Using these semantics, we are able to prove that TEMPLOG is a fragment of temporal logic that admits a complete proof system. The fixpoint semantics also enables us to study TEMPLOG's expressiveness. For this, we focus on the propositional fragment of TEMPLOG. We prove that propositional TEMPLOG has essentially the expressiveness of finite automata or regular languages, and that its extension with stratified negation has the expressiveness of Buchi automata or $\omega$-regular languages.