An Optimal Decision Procedure for Right Propositional Neighborhood Logic

Authors:
Davide Bresolin;Angelo Montanari;Guido Sciavicco
Affiliations:
Dipartimento di Matematica e Informatica, Università degli Studi di Udine, Udine, ITALY 33100;Dipartimento di Matematica e Informatica, Università degli Studi di Udine, Udine, ITALY 33100;Department of Information Engineering and Communications, Faculty of Informatics, University of Murcia, Espinardo (Murcia), Spain 30100
Venue:
Journal of Automated Reasoning
Year:
2007

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Abstract

Propositional interval temporal logics are quite expressive temporal logics that allow one to naturally express statements that refer to time intervals. Unfortunately, most such logics turn out to be (highly) undecidable. In order to get decidability, severe syntactic or semantic restrictions have been imposed to interval-based temporal logics to reduce them to point-based ones. The problem of identifying expressive enough, yet decidable, new interval logics or fragments of existing ones that are genuinely interval-based is still largely unexplored. In this paper, we focus our attention on interval logics of temporal neighborhood. We address the decision problem for the future fragment of Neighborhood Logic (Right Propositional Neighborhood Logic, RPNL for short), and we positively solve it by showing that the satisfiability problem for RPNL over natural numbers is NEXPTIME-complete. Then, we develop a sound and complete tableau-based decision procedure, and we prove its optimality.