Optimal Tableaux for Right Propositional Neighborhood Logic over Linear Orders

The study of interval temporal logics on linear orders is a meaningful research area in computer science and artificial intelligence. Unfortunately, even when restricted to propositional languages, most interval logics turn out to be undecidable. Decidability has been usually recovered by imposing severe syntactic and/or semantic restrictions. In the last years, tableau-based decision procedures have been obtained for logics of the temporal neighborhood and logics of the subinterval relation over specificclasses of temporal structures. In this paper, we develop an optimal NEXPTIME tableau-based decision procedure for the future fragment of Propositional Neighborhood Logic over the wholeclass of linearly ordered domains.

[1]  Martin Otto,et al.  Two variable first-order logic over ordered domains , 2001, Journal of Symbolic Logic.

[2]  Davide Bresolin,et al.  On Decidability and Expressiveness of Propositional Interval Neighborhood Logics , 2007, LFCS.

[3]  Davide Bresolin,et al.  An Optimal Decision Procedure for Right Propositional Neighborhood Logic , 2006, Journal of Automated Reasoning.

[4]  Benjamin Charles Moszkowski.  Reasoning about Digital Circuits , 1983 .

[5]  Valentin Goranko,et al.  A general tableau method for propositional interval temporal logics: Theory and implementation , 2006, J. Appl. Log..

[6]  Yoav Shoham,et al.  A propositional modal logic of time intervals , 1991, JACM.

[7]  Anil Nerode,et al.  Logical Foundations of Computer Science, International Symposium, LFCS 2009, Deerfield Beach, FL, USA, January 3-6, 2009. Proceedings , 1994, LFCS.

[8]  Howard Bowman,et al.  A Decision Procedure and Complete Axiomatization of Finite Interval Temporal Logic with Projection , 2003, J. Log. Comput..

[9]  Roy Dyckhoff.  Automated Reasoning with Analytic Tableaux and Related Methods , 2000, Lecture Notes in Computer Science.

[10]  Davide Bresolin,et al.  Tableau Systems for Logics of Subinterval Structures over Dense Orderings , 2007, TABLEAUX.

[11]  Davide Bresolin,et al.  An Optimal Tableau-Based Decision Algorithm for Propositional Neighborhood Logic , 2007, STACS.

[12]  Amir Pnueli,et al.  Compositionality: The Significant Difference , 1999, Lecture Notes in Computer Science.

[13]  Michael R. Hansen,et al.  An Adequate First Order Interval Logic , 1997, COMPOS.

[14]  Yde Venema,et al.  A Modal Logic for Chopping Intervals , 1991, J. Log. Comput..