Two-sorted Point-Interval Temporal Logics

Authors:
Philippe Balbiani;Valentin Goranko;Guido Sciavicco
Affiliations:
Institut de Recherche, en Informatique de Toulouse, Université Paul Sabatier, Toulouse, France;Department of Informatics and Mathematical Modeling, Technical University of Denmark, Lyngby, Denmark;Department of Computer Engineering, Middle East Technical University, Northern Cyprus Campus, and Department of Information Engineering and Communications, University of Murcia, Murcia, Spain
Venue:
Electronic Notes in Theoretical Computer Science (ENTCS)
Year:
2011

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Abstract

There are two natural and well-studied approaches to temporal ontology and reasoning: point-based and interval-based. Usually, interval-based temporal reasoning deals with points as particular, duration-less intervals. Here we develop explicitly two-sorted point-interval temporal logical framework whereby time instants (points) and time periods (intervals) are considered on a par, and the perspective can shift between them within the formal discourse. We focus on fragments involving only modal operators that correspond to the inter-sort relations between points and intervals. We analyze their expressiveness, comparative to interval-based logics, and the complexity of their satisfiability problems. In particular, we identify some previously not studied and potentially interesting interval logics.