Checking Interval Properties of Computations

Model checking is a powerful method widely explored in formal verification. Given a model of a system, e.g. A Kripke structure, and a formula specifying its expected behavior, one can verify whether the system meets the behavior by checking the formula against the model. Classically, system behavior is given as a formula of a temporal logic, such as LTL and the like. These logics are "point-wise" interpreted, as they describe how the system evolves state-by-state. However, there are relevant properties, such as those involving temporal aggregations, which are inherently "interval-based", and thus asking for an interval temporal logic. In this paper, we give a formalization of the model checking problem in an interval logic setting. First, we provide an interpretation of formulas of Halpern and Shoham's interval temporal logic HS over Kripke structures, which allows one to check interval properties of computations. Then, we prove that the model checking problem for HS against Kripke structures is decidable by a suitable small model theorem, and we outline a PSpace decision procedure for the meaningful fragments AAbarBBbar and AAbarEEbar.

[1]  Angelo Montanari,et al.  Checking interval properties of computations , 2014, Acta Informatica.

[2]  Alessio Lomuscio,et al.  Decidability of model checking multi-agent systems against a class of EHS specifications , 2014, ECAI.

[3]  Davide Bresolin,et al.  The dark side of interval temporal logic: marking the undecidability border , 2013, Annals of Mathematics and Artificial Intelligence.

[4]  Davide Bresolin,et al.  What's Decidable about Halpern and Shoham's Interval Logic? The Maximal Fragment ABBL , 2011, 2011 IEEE 26th Annual Symposium on Logic in Computer Science.

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

[6]  Valentin Goranko,et al.  Interval Temporal Logics: a Journey , 2013, Bull. EATCS.

[7]  Edmund M. Clarke,et al.  Design and Synthesis of Synchronization Skeletons Using Branching Time Temporal Logic , 2008, 25 Years of Model Checking.

[8]  D. Gabbay,et al.  Many-Dimensional Modal Logics: Theory and Applications , 2003 .

[9]  Edmund M. Clarke,et al.  Model Checking , 1999, Handbook of Automated Reasoning.

[10]  Yde Venema,et al.  Expressiveness and Completeness of an Interval Tense Logic , 1990, Notre Dame J. Formal Log..

[11]  Pierre Wolper,et al.  An Automata-Theoretic Approach to Automatic Program Verification (Preliminary Report) , 1986, LICS.

[12]  Amir Pnueli.  The Temporal Semantics of Concurrent Programs , 1981, Theor. Comput. Sci..

[13]  Valentin Goranko,et al.  A Road Map of Interval Temporal Logics and Duration Calculi , 2004, J. Appl. Non Class. Logics.

[14]  Alessio Lomuscio,et al.  An Epistemic Halpern-Shoham Logic , 2013, IJCAI.

[15]  Gabriele Puppis,et al.  Maximal Decidable Fragments of Halpern and Shoham's Modal Logic of Intervals , 2010, ICALP.

[16]  Davide Bresolin,et al.  Propositional interval neighborhood logics: Expressiveness, decidability, and undecidable extensions , 2009, Ann. Pure Appl. Log..

[17]  Michael Sipser,et al.  Introduction to the Theory of Computation , 1996, SIGA.

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

[19]  Amir Pnueli,et al.  The temporal logic of programs , 1977, 18th Annual Symposium on Foundations of Computer Science (sfcs 1977).

[20]  Peter Roper,et al.  Intervals and tenses , 1980, J. Philos. Log..

[21]  Jakub Michaliszyn,et al.  The Undecidability of the Logic of Subintervals , 2014, Fundam. Informaticae.

[22]  James F. Allen.  Maintaining knowledge about temporal intervals , 1983, CACM.

[23]  Martin Lange,et al.  Model checking propositional dynamic logic with all extras , 2006, J. Appl. Log..

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

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

[26]  Davide Bresolin,et al.  Tableaux for Logics of Subinterval Structures over Dense Orderings , 2010, J. Log. Comput..

[27]  Dov M. Gabbay,et al.  The Declarative Past and Imperative Future: Executable Temporal Logic for Interactive Systems , 1987, Temporal Logic in Specification.