We propose a notion of an abstract logic. Based on this notion, we define abstract logic programs to be sets of sentences of an abstract logic. When these abstract logics possess certain logical properties (some properties considered are compactness, finitariness, and monotone consequence relations) we show how to develop a fixed-point, model-state-theoretic and proof theoretic semantics for such programs. The work of Melvin Fitting on developing a generalized semantics for multivalued logic programming is extended here to arbitrary abstract logics. We present examples to show how our semantics is robust enough to be applicable to various non-classical logics like temporal logic and multivalued logics, as well as to extensions of classical logic programming such as disjunctive logic programming. We also show how some aspects of the declarative semantics of distributed logic programming, particularly work of Ramanujam, can be incorporated into our framework.
Blair, Howard A.; Brown, Allen Jr.; and Subrahmanian, V. S., "Monotone Logic Programming" (1990). Electrical Engineering and Computer Science Technical Reports. 70.