Abstract
In this paper, we consider provenance and temporally annotated logic rules (pt-logic rules, for short), which are definite logic programming rules associated with the name of the source that they originate and the temporal interval during which they are valid. A collection of pt-logic rules form a provenance and temporally annotated logic program P, called pt-logic program, for short. We develop a model theory for P and define its maximally temporal entailments of the form A:<S, ti>, indicating that atom A is derived from a set of sources S and holds at a maximal temporal interval ti, according to S. We define a consequence operator that derives exactly the maximally temporal entailments of P for a set of sources. We show that the complexity of the considered entailment is EXPTIME-complete.
Highlights
Definite logic programming rules traditionally are not associated with the name of the source from which they originate and the temporal interval during which are valid
We consider definite logic programming rules associated with a source name and a validity temporal interval, called provenance and temporally annotated logic rules, or pt-logic rules for short
In [6], we extend extended logic programming rules [6] with their validity temporal intervals
Summary
Definite logic programming rules traditionally are not associated with the name of the source (provenance information) from which they originate and the temporal interval during which are valid. We consider definite logic programming rules associated with a source name and a validity temporal interval, called provenance and temporally annotated logic rules, or pt-logic rules for short. The models of pt-logic programs P are defined, as well as, the simple entailments and temporally maximal entailments of P. A set of three operators are defined which are applied on pt-atoms such that the closure of their composition derives the minimal model of P. The rest of the paper is organized as follows: In Section II, we define pt-logic rules, pt-logic programs, pt-atoms, and the instantiation of a pt-logic program.
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