Logic Programming on a Topological Bilattice¹

Article type: Research Article

Authors: Fitting, Melvin^{a; b}

Affiliations: [a] Department of Mathematics and Computer Science: Herbert H. Lehman College (CUNY), Bronx, NY 10468 | [b] Department of Computer Science: Department of Philosophy: The Graduate School and University Center (CUNY), 33 West 42 Street, New York, NY 10036, Bitnet MLFLC@CUNYVM

Note: [1] Research supported in part by NSF grant CCR-8702307 and by PSC–CUNY grant 667295.

Abstract: We investigate the semantics of logic programming using a generalized space of truth values. These truth values may be thought of as evidences for and against – possibly incomplete or contradictory. The truth value spaces we use essentially have the structure of M. Ginsberg’s bilattices, and arise from topological spaces. The simplest example is a four-valued logic, previously investigated by N. Belnap. The theory of this special case properly contains that developed in earlier research by the author, on logic programming using Kleene’s three-valued logic.

DOI: 10.3233/FI-1988-11206

Journal: Fundamenta Informaticae, vol. 11, no. 2, pp. 209-218, 1988