Temporally Annotated Extended Logic Programs

Extended logic programs (ELPs) are a set of logic rules with strong negation  allowed in the bodies or head of the rules and weak negation ~ allowed in the bodies of the rules. ELPs enable for various forms of reasoning that cannot be achieved by definite logic programs. Answer Set Programming provides a widely acceptable semantics for ELPs. However, ELPs do not provide information regarding the temporal intervals that derived ELP literals or weakly negated ELP literals are valid. In this paper, we associate ELP rules with their validity temporal interval, resulting in a temporally annotated logic program. A ground temporal literal has the form L:i, where L is a ground ELP literal or weakly negated ELP literal and i is a temporal interval. We define (simple) entailment and maximal entailment of a ground temporal literal L:i from a temporally annotated logic program C. Both kinds of entailment are based on Answer Set Programming. Additionally, we provide an algorithm that for an ELP literal or a weakly negated ELP literal L returns a list with all temporal intervals i such that a temporally annotated logic program C maximally entails L:i. Based on this algorithm, the answer of various kinds of temporal queries can be provided. KeywordsExtended logic programs; validity temporal intervals; temporal inference; query answering.