Abstract

We introduce topologies on spaces of interpretations which extend and generalise the query and positive query topologies of Batarekh and Subrahmanian. We study continuity in these topologies of the immediate consequence map associated with any normal logic program and provide necessary and sufficient conditions for continuity to hold. We relate these ideas to (i) computational power of programs; (ii) canonical programs; (iii) the declarative semantics of definite programs; (iv) Maher's down continuous programs; (v) the decency thesis of Jaffar, Lassez and Maher, and (vi) compactness of sets of fixed points and models. 1 Introduction The classical approach to the study of fixed point semantics of definite logic programs P utilises two main facts: (1) The set I J L of all interpretations of the underlying language L based on a given preinterpretation J forms a complete lattice under the partial order of set inclusion. (2) The immediate consequence map T P defined on I J L is latti...

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