Abstract
We introduce a class of Petri nets, simple logic Petri nets (SLPN), that are based on logical expressions. We show how this type of nets can be efficiently mapped into logic programs with negation: the corresponding answer sets describe interleaved executions of the underlying nets (Theorem 1). The absence of an answer set indicates a deadlock situation. We also show how to correctly model and specify AgentSpeak agents and multi-agent systems with SLPN’s (Theorem 2). Both theorems allow us to solve the task of model checking AgentSpeak multi-agent systems by computing answer sets of the obtained logic program with any ASP system.
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Baral, C.: Knowledge Representation, Reasoning and Declarative Problem Solving. Cambridge University Press (2003) ISBN 0521818028
Bordini, R.H., Fisher, M., Pardavila, C., Wooldridge, M.: Model checking Agentspeak. In: AAMAS ’03: Proceedings of the second international joint conference on Autonomous agents and multiagent systems, pp. 409–416. New York, NY, USA. ACM Press (2003)
Bordini, R.H., Fisher, M., Visser, W., Wooldridge, M.: Model checking rational agents. IEEE Intell. Syst. 19(5), 46–52 (2004)
Bordini, R.H., Fisher, M., Visser, W., Wooldridge, M.: Verifying multi-agent programs by model checking. Autonom. Agents Multi-Agent Syst. 12(2), 239–256 (2006)
Brewka, G., Dix, J.: Knowledge representation with extended logic programs. In: Gabbay, D., Guenthner, F. (eds.) Handbook of Philosophical Logic, vol. 12, chapter 1, pp. 1–85. Reidel Publ., 2nd edn., 2005. Shortened version also appeared In: Dix, Pereira, Przymusinski (eds.) Logic Programming and Knowledge Representation, Springer LNAI 1471, pp. 1–55 (1998)
Clarke, E.M., Grumberg, O., Peled, D.A.: Model Checking. The MIT Press (2000) ISBN 0262032708
Dix, J., Furbach, U., Niemelä, I.: Nonmonotonic reasoning: towards efficient calculi and implementations. In: Voronkov, A., Robinson, A., (eds.) Handbook of Automated Reasoning, pp. 1121–1234. Elsevier-Science-Press (2001)
Dix, J., Kuter, U., Nau, D.: Planning in answer set programming using ordered task decomposition. In: Artemov, S., Barringer, H., d’Avila Garcez, A.S., Lamb, L.C., Woods, J. (eds.) We Will Show Them: Essays in Honour of Dov Gabbay, vol. 1, pp. 521–577. King’s College Publications, London (2005)
Grahlmann, B., Best, E.: PEP—more than a Petri net tool. In: Margaria, T., Steffen, B. (eds.) Tools and Algorithms for the Construction and Analysis of Systems, vol. 1055 of Lecture Notes in Computer Science, pp. 397–401. Springer Verlag (1996)
Hamez, A., Hillah, L., Kordon, F., Linard, A., Paviot-Adet, E., Renault, X., Thierry-Mieg, Y.: New features in CPN-AMI 3: focusing on the analysis of complex distributed systems. In: ACSD, pp. 273–275. IEEE Computer Society (2006)
Heljanko, K., Niemelä, I.: Petri net analysis and nonmonotonic reasoning. In: Husberg, N., Janhunen, T., Niemelä, I. (eds.) Leksa Notes in Computer Science—Festschrift in Honour of Professor Leo Ojala, pp. 7–19, Espoo, Finland, October 2000. Helsinki University of Technology, Laboratory for Theoretical Computer Science (2000)
Heljanko, K., Niemelä, I.: Bounded LTL model checking with stable models. CoRR, cs.LO/0305040 (2003)
Holzmann, G.J.: The model checker SPIN. Softw. Eng. 23(5), 279–295 (1997)
Kindler, E., Weber, M.: The petri net kernel—an infrastructure for building petri net tools. Int. J. Softw. Tools Technol. Trans. 3(4), 486–497 (2001)
Leone, N., Pfeifer, G., Faber, W., Eiter, T., Gottlob, G., Perri, S., Scarcello, F.: The dlv system for knowledge representation and reasoning. ACM Trans. Comput. Logic 7(3), 499–562 (2006)
Lichtenstein, O., Pnueli, A.: Checking that finite state concurrent programs satisfy their linear specification. In: POPL, pp. 97–107 (1985)
Murata, T., Subrahmanian, V.S., Wakayama, T.: A petri net model for reasoning in the presence of inconsistency. IEEE Trans. Knowledge Data Eng. 3(3), 281–292 (1991)
Murata, T., Zhang, D.: A predicate-transition net model for parallel interpretation of logic programs. IEEE Trans. Softw. Eng. 14(4), 481–497 (1988)
Sterling, L., Shapiro, E.: The Art of Prolog: Advanced Programming Techniques. MIT Press, Cambridge, MA, USA (1986)
Syrjänen, T., Niemelä, I.: The smodels system. In: Eiter, T., Faber, W., Truszczynski, W. (eds.) LPNMR, vol. 2173 of Lecture Notes in Computer Science, pp. 434–438. Springer (2001)
Visser, W., Havelund, K., Brat, G.P., Park, S.: Model checking programs. In: ASE, pp. 3–12 (2000)
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This article is dedicated to Jack Minker, the doyen of the area of Deductive Databases. The second author was very much inspired by Jack’s famous book from 1987 and decided to pursue a scientific career in computer science not least because of this book and Jack’s support through the years.
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Behrens, T.M., Dix, J. Model checking multi-agent systems with logic based Petri nets. Ann Math Artif Intell 51, 81–121 (2007). https://doi.org/10.1007/s10472-008-9092-7
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DOI: https://doi.org/10.1007/s10472-008-9092-7