Go beyond the SCOPE: A Temporal Situation Calculus-Based Software Tool for Time Petri Nets

This paper presents a straightforward and mathematically rigorous software tool for Time Petri Nets (TPN). More precisely, we first build up a formal process ontology of TPNs by extending SCOPE (Situation Calculus Ontology for PEtri nets) with temporal constraints. We then demonstrate that, with this temporal SCOPE, sequential, iterative, or nondeterministic composite sequences of transition firings in TPNs can be further axiomatized through macro-expanding the basic action of transition firing. Finally, it is shown that theorem-proving, i.e., computing the consequences of such an ontology, can be carried out efficiently through logic programming in Prolog. Potential future applications of our approach are also discussed.

[1]  Xing Tan.  SCOPE: A Situation Calculus Ontology of Petri Nets , 2010, FOIS.

[2]  Thomas Chatain,et al.  Time Supervision of Concurrent Systems Using Symbolic Unfoldings of Time Petri Nets , 2005, FORMATS.

[3]  Xing Tan,et al.  On the computational complexity of the reachability problem in UML activity diagrams , 2009, 2009 IEEE International Conference on Intelligent Computing and Intelligent Systems.

[4]  Akhil Kumar,et al.  Process management in supply chains - a new Petri-net based approach , 2004, 37th Annual Hawaii International Conference on System Sciences, 2004. Proceedings of the.

[5]  Javier Esparza,et al.  Implementing LTL model checking with net unfoldings , 2001, SPIN '01.

[6]  John McCarthy,et al.  SOME PHILOSOPHICAL PROBLEMS FROM THE STANDPOINT OF ARTI CIAL INTELLIGENCE , 1987 .

[7]  Andreas Podelski,et al.  ACSAR: Software Model Checking with Transfinite Refinement , 2007, SPIN.

[8]  Michael Leuschel,et al.  Model checking object petri nets in prolog , 2004, PPDP '04.

[9]  Jirí Srba,et al.  Comparing the Expressiveness of Timed Automata and Timed Extensions of Petri Nets , 2008, FORMATS.

[10]  Raymond Reiter,et al.  Knowledge in Action: Logical Foundations for Specifying and Implementing Dynamical Systems , 2001 .

[11]  Andrea Domenici.  Petri nets in logic , 1990 .

[12]  Franca Garzotto,et al.  On the Specification of Real-Time Systems Using Logic Programming , 1987, ESEC.

[13]  Michael Grüninger,et al.  Towards Axiomatizing the Semantics of UML Activity Diagrams: A Situation-Calculus Perspective , 2010, 2010 IEEE/WIC/ACM International Conference on Web Intelligence and Intelligent Agent Technology.