Towards Reasoning in Dynamic Logics with Rewriting Logic: The Petri-PDL Case

Safety is a desired property in software to ensure that no unforeseen scenarios will be achieved and in concurrent systems the variety of scenarios increase with complexity. Dynamic Logics (DL) present a large body of techniques to reason about and certify systems. Modelling and assessing concurrent systems with a formal semantics leads to the possibility of proving that they comply with their specification. Petri nets fulfill these requirements as a formal modelling language comprising a wide body of tools and an intuitive graphical interpretation. Petri-PDL puts together DL with Petri nets, providing a theoretical background to reason about Petri nets, inheriting their properties with all the techniques available for DL. This work presents a prototype implementation, in the Rewriting Logic language Maude, of a bounded model checker for Petri-PDL. The Petri-PDL model checker is formally designed following the representation of Kripke models as rewrite theories defined for the Linear Temporal Logic model checker available in the Maude system.

[1]  Gilles Dowek,et al.  A Calculus for Automatic Verification of Petri Nets Based on Resolution and Dynamic Logics , 2014, LSFA.

[2]  Andrea Vandin,et al.  Towards a Maude Tool for Model Checking Temporal Graph Properties , 2011 .

[3]  José Meseguer,et al.  Specification and proof in membership equational logic , 2000, Theor. Comput. Sci..

[4]  C. A. Petri.  Fundamentals of a Theory of Asynchronous Information Flow , 1962, IFIP Congress.

[5]  Yde Venema,et al.  Dynamic Logic by David Harel, Dexter Kozen and Jerzy Tiuryn. The MIT Press, Cambridge, Massachusetts. Hardback: ISBN 0–262–08289–6, $50, xv + 459 pages , 2002, Theory and Practice of Logic Programming.

[6]  Richard E. Ladner,et al.  Propositional Dynamic Logic of Regular Programs , 1979, J. Comput. Syst. Sci..

[7]  Peter Csaba Ölveczky,et al.  Rewriting Logic as a Unifying Framework for Petri Nets , 2001, Unifying Petri Nets.

[8]  MengChu Zhou,et al.  Petri nets and industrial applications: A tutorial , 1994, IEEE Trans. Ind. Electron..

[9]  José Meseguer,et al.  The Maude LTL Model Checker and Its Implementation , 2003, SPIN.

[10]  Narciso Martí-Oliet,et al.  All About Maude - A High-Performance Logical Framework, How to Specify, Program and Verify Systems in Rewriting Logic , 2007, All About Maude.

[11]  Mario R. F. Benevides,et al.  Propositional dynamic logic for Petri nets , 2014, Log. J. IGPL.

[12]  Mario R. F. Benevides,et al.  Extending Propositional Dynamic Logic for Petri Nets , 2014, LSFA.

[13]  Heikki Tuominen.  Elementary net systems and dynamic logic , 1988, European Workshop on Applications and Theory in Petri Nets.