Journal of Automated Reasoning

, Volume 38, Issue 1–3, pp 173–199

An Optimal Decision Procedure for Right Propositional Neighborhood Logic

  • Davide Bresolin
  • Angelo Montanari
  • Guido Sciavicco
Article

DOI: 10.1007/s10817-006-9051-0

Cite this article as:
Bresolin, D., Montanari, A. & Sciavicco, G. J Autom Reasoning (2007) 38: 173. doi:10.1007/s10817-006-9051-0

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.

Key words

interval temporal logic tableaux-based decision procedures right propositional neighborhood logic 

Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • Davide Bresolin
    • 1
  • Angelo Montanari
    • 1
  • Guido Sciavicco
    • 2
  1. 1.Dipartimento di Matematica e InformaticaUniversità degli Studi di UdineUdineITALY
  2. 2.Department of Information Engineering and Communications, Faculty of InformaticsUniversity of MurciaEspinardo (Murcia)Spain

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