Complete and Terminating Tableau for the Logic of Proper Subinterval Structures Over Dense Orderings

We introduce special pseudo-models for the interval logic of proper subintervals over dense linear orderings. We prove finite model property with respect to such pseudo-models, and using that result we develop a decision procedure based on a sound, complete, and terminating tableau for that logic. The case of proper subintervals is essentially more complicated than the case of strict subintervals, for which we developed a similar tableau-based decision procedure in a recent work.

[1]  A. A. Aaby,et al.  Propositional Temporal Interval Logic is PSPACE Complete , 1988, CADE.

[2]  Kamal Lodaya,et al.  Sharpening the Undecidability of Interval Temporal Logic , 2000, ASIAN.

[3]  Louise E. Moser,et al.  Interval Logics and Their Decision Procedures, Part I: An Interval Logic , 1996, Theor. Comput. Sci..

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

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

[6]  Alexander K. Petrenko,et al.  Electronic Notes in Theoretical Computer Science , 2009 .

[7]  Bresolin Davide,et al.  A tableau-based decision procedure for a branching-time interval temporal logic , 2005 .

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

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

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

[11]  Louise E. Moser,et al.  Interval Logics and Their Decision Procedures. Part II: A Real-Time Interval Logic , 1996, Theor. Comput. Sci..

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

[13]  Dimitar P. Guelev,et al.  Completeness and Decidability of a Fragment of Duration Calculus with Iteration , 1999, ASIAN.

[14]  Davide Bresolin,et al.  A Tableau-Based Decision Procedure for Right Propositional Neighborhood Logic , 2005, TABLEAUX.

[15]  Alan Bundy,et al.  Constructing Induction Rules for Deductive Synthesis Proofs , 2006, CLASE.

[16]  Michael R. Hansen,et al.  Decidability and Undecidability Results for Duration Calculus , 1993, STACS.

[17]  Guido Sciavicco,et al.  Decidability of Interval Temporal Logics over Split-Frames via Granularity , 2002, JELIA.

[18]  Howard Bowman,et al.  A Tableau Method for Interval Temporal Logic with Projection , 1998, TABLEAUX.