Temporally Annotated Extended Logic Programs

Anastasia Analyti,Ioannis Pachoulakis

doi:10.14569/ijarai.2012.010704

Anastasia Analyti, Ioannis Pachoulakis

Open Access

https://doi.org/10.14569/ijarai.2012.010704

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Abstract

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.

Highlights

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 [1]
ELP rules are assumed to be valid at the time of their evaluation but no historical information is derived as it is not known if these rules were valid in the past
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

Summary

INTRODUCTION

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 [1]. 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. We provide an algorithm that for an ELP literal or 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. Algorithm 2 FindMaximalIntervals(C,L), where L is an ELP literal or a weakly negated ELP literal over V, first calls algorithm GetIntervals(C, pred(L)) which returns a list IL of maximal intervals i that define pred(L), ordered by start(i) (line 2). This technique has higher complexity and does not provides answer sets in the case that it exists a time point t such that C(t) has no (consistent) answer set

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