Foundations of logic programming; (2nd extended ed.)
Foundations of logic programming; (2nd extended ed.)
Modal provability foundations for negation by failure
Proceedings of the international workshop on Extensions of logic programming
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In this paper, We define an annotated logic AL for NF and CWA based on the set of truth values(annotations) in such a way that the structure is the 4-valued complete lattice(Lattice-4) and each annotation corresponds to each state in logic program derivation. We also propose two kinds of annotated completion formulas, which can be the declarative annotated semantics for NF and CWA as well as Clark's completion. Furthermore, we take a multi-agent system having a contradiction between each agent's world as a simple example and show how the annotated completion deals with such inconsistency.