TOPOLOGY AND THE SEMANTICS OF LOGIC PROGRAMS

Article type: Research Article

Authors: Seda, Anthony Karel

Affiliations: Department of Mathematics, University College, Cork, Ireland, e-mail: stmt8002@iruccvax.ucc.ie

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.

DOI: 10.3233/FI-1995-2443

Journal: Fundamenta Informaticae, vol. 24, no. 4, pp. 359-386, 1995