New Semantic Tools for Logic Programming

The paper is a general overview of our approach to the semantics of logic programs. We introduce new notions and modify the classical semantics, i.e. we use new tools to model those logic programs aspects which really capture their operational semantics, and are therefore useful for defining program equivalences and for semantics-based program analysis. The approach leads to the introduction of extended interpretations which are more expressive than Herbrand interpretations. The semantics in terms of extended interpretations can be obtained as a result of both an operational and a fixpoint construction. It can also be characterized from the modeltheoretic viewpoint, by defining a set of extended models which contains standard Herbrand models. The original construction for positive programs is shown to be applicable to other classes of logic programs, such as constraint logic programs, open programs and general programs. Different extensions are also shown capable to handle higher order constructs such as those used to compute sets of solutions.

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