Theory of Generalized Annotated Logic Programming and its Applications

Annotated logics were introduced in 43] and later studied in 5, 7, 31, 32]. In 31], annotations were extended to allow variables and functions, and it was argued that such logics can be used to provide a formal semantics for rule-based expert systems with uncertainty. In this paper we continue to investigate the power of this approach. First, we introduce a new semantics for such programs based on ideals of lattices. Subsequently, some proposals for multivalued logic programming 5, 7, 32, 47, 40, 18] as well as some formalisms for temporal reasoning 1, 3, 42] are shown to t into this framework. As an interesting by-product of this investigation, we obtain a new result concerning multivalued logic programming: a model theory for Fitting's bilattice-based logic programming, which until now has not been characterized model-theoretically. This is accompanied by a corresponding proof theory.