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Abstract

In the last decade the concept of context has been extensivelyexploited in many research areas, e.g., distributed artificialintelligence, multi agent systems, distributed databases, informationintegration, cognitive science, and epistemology. Three alternative approaches to the formalization of the notion ofcontext have been proposed: Giunchiglia and Serafini's Multi LanguageSystems (ML systems), McCarthy's modal logics of contexts, andGabbay's Labelled Deductive Systems.Previous papers have argued in favor of ML systems with respect to theother approaches. Our aim in this paper is to support these arguments froma theoretical perspective. We provide a very general definition of ML systems, which covers allthe ML systems used in the literature, and we develop a proof theoryfor an important subclass of them: the MR systems. We prove variousimportant results; among other things, we prove a normal form theorem,the sub-formula property, and the decidability of an importantinstance of the class of the MR systems. The paper concludes with a detailed comparison among the alternativeapproaches.

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References

  • Akman, V. and Surav, M., 1996, “Steps toward formalizing context, ” AI Magazine 17, 55–72.

    Google Scholar 

  • Akman, V., Bouquet, P., Thomason, R., and Young, R., eds., 2001, Modeling and Using Context, Proceedings of CONTEXT'2001 – Third International and Interdisciplinary Conference on Modeling and Using Context (Dundee, Scotland, 27–30 July 2001), Lecture Notes in Artificial Intelligence, Vol. 2116, Berlin: Springer Verlag.

  • Avron, A., 1987, “Simple consequence relations, ” LFCS Report Series, Laboratory for the Foundations of Computer Science, Computer Science Department, University of Edinburgh.

  • Benerecetti, M., Bouquet, P., and Ghidini, C., 1998a, “Formalizing belief reports – The approach and a case study, ” pp. 62–75 in Proceedings AIMSA'98, cn8th International Conference on Artificial Intelligence, Methodology, Systems, and Applications, Sozopol, Bulgaria, F. Giunchiglia, ed., Lecture Notes in Artificial Intelligence, Vol. 1480, Berlin: Springer-Verlag.

    Google Scholar 

  • Benerecetti, M., Giunchiglia, F., and Serafini, L., 1998b, “Model checking multiagent systems, ” Journal of Logic and Computation, Special Issue on Computational & Logical Aspects of Multi-Agent Systems 8, 401–423.

    Google Scholar 

  • Benerecetti, M., Giunchiglia, E., Serafini, L., and Villafiorita, A., 1999, “Formal specification of beliefs in multi-agent systems, ” International Journal of Intelligent Systems 14, 1021–1040.

    Google Scholar 

  • Benerecetti, M., Bouquet, P., and Ghidini, C., 2000, “'Contextual reasoning distilled, ” Journal of Theoretical and Experimental Artificial Intelligence 12, 279–305.

    Google Scholar 

  • Bonzon, P., Cavalcanti, M., and Nossum, R., eds., 2000, Formal Aspects of Context, Applied Logic Series, Dordrecht: Kluwer Academic Publishers.

  • Bouquet, P. and Giunchiglia, F., 1995, “Reasoning about theory adequacy. A new solution to the qualification problem, ” Fundamenta Informaticae 23, 247–262.

    Google Scholar 

  • Bouquet, P. and Serafini, L., 2001, “Two formalizations of context: A comparison, ” pp. 87–101 in Modeling and Using Context, Proceedings of CONTEXT'2001Third International and Interdisciplinary Conference on Modeling and Using Context (Dundee, Scotland, 27–30 July 2001), V. Akman, P. Bouquet, R. Thomason, and R. Young, eds., Berlin: Springer-Verlag.

    Google Scholar 

  • Bouquet, P., Serafini, L., Brezillon, P., Benerecetti, M., and Castellani, F., eds., 1999, Modelling and Using Context, Proceedings of CONTEXT'99Second International and Interdisciplinary Conference onModelling and Using Context (Trento, Italy, 9–11 September 1999), Lecture Notes in Artificial Intelligence, Vol. 1688, Berlin: Springer-Verlag.

    Google Scholar 

  • Bowen, K. and Kowalski, R., 1982, “Amalgamating language and meta-language in logic programming, ” pp. 153–173 in Logic Programming, S. Tärnlund, ed., New York: Academic Press.

    Google Scholar 

  • Buvač, S. and Mason, I.A., 1993, “Propositional logic of context, ” pp. 412–419 in Proceedings of the 11th National Conference on Artificial Intelligence, R. Fikes and W. Lehnert, eds., Menlo Park, CA: AAAI Press

    Google Scholar 

  • Cimatti, A. and Serafini, L., 1996, “Multi-agent reasoning with belief contexts II: Elaboration tolerance, ” pp. 57–64 in Proceedings of the 1st International Conference on Multi-Agent Systems (ICMAS-95), V. Lesser, ed., Menlo Park, CA: AAAI Press.

    Google Scholar 

  • Clarke, Jr., E.M., Grumberg, O., and Peled, D.A., 1999, Model Checking, Cambridge, MA: MIT Press.

    Google Scholar 

  • Criscuolo, G., Giunchiglia, F., and Serafini, L., 2001a, “A foundation for metareasoning, Part I: The proof theory, ” Journal of Logic and Computation, to appear. Also ITC-IRST Technical Report 0003-38, ITC-IRST, Trento, Italy.

  • Criscuolo, G., Giunchiglia, F., and Serafini, L., 2001b, “A foundation for metareasoning, Part II: The model theory, ” Journal of Logic and Computation, to appear. Also ITC-IRST Technical Report 0010-07, ITC-IRST, Trento, Italy.

  • Dichev, C., 1993, “Theory relations and context dependencies, ” pp. 266–272 in Proceedings of the 6th Australian Joint Conference on Artificial Intelligence (AI-93), Melbourne, P. Jorrand and V. Sgurev, eds., Singapore: World Scientific.

    Google Scholar 

  • Dinsmore, J., 1991, Partitioned Representations, Dordrecht: Kluwer Academic Publishers.

    Google Scholar 

  • Fagin, R. and Halpern, J., 1988, “Belief, awareness, and limited reasoning, ” Artificial Intelligence 34, 39–76.

    Google Scholar 

  • Fisher, M. and Ghidini, C., 1999, “Programming resource-bounded deliberative agents, ” pp. 200–206 in Proceedings of the Sixteenth International Joint Conference on Artificial Intelligence (IJCAI'99), San Mateo, CA: Morgan Kaufmann Publishers.

    Google Scholar 

  • Gabbay, D.M., 1996, Labelled Deductive Systems; Principles and Applications. Vol. 1: Introduction,Oxford Logic Guides, Vol. 33, Oxford: Oxford University Press.

    Google Scholar 

  • Ghidini, C. and Giunchiglia, F., 2001, “Local models semantics, or contextual reasoning = locality + compatibility, ” Artificial Intelligence 127, 221–259.

    Google Scholar 

  • Giunchiglia, E. and Giunchiglia, F., 2001, “Ideal and real belief about belief, ” Journal of Logic and Computation 11, 157–192.

    Google Scholar 

  • Giunchiglia, F., 1993, “Contextual reasoning, ” Epistemologia, Special Issue on I Linguaggi e le Macchine XVI, 345–364.

  • Giunchiglia, F. and Bouquet, P., 1998, “A context-based framework for mental representation, ” pp. 392–397 in Proceedings of the Twentieth Annual Meeting of the Cognitive Science Society – CogSci'98, Madison, WI, M.A. Gernsbacher and S.J. Derry, eds., Mahwah, NJ: Lawrence Erlbaum Publishers.

    Google Scholar 

  • Giunchiglia, F. and Serafini, L., 1994, ‘Multilanguage Hierarchical Logics’ (or: how we can do without modal logics), ” Artificial Intelligence 65, 29–70.

    Google Scholar 

  • Giunchiglia, F. and Traverso, P., 1996, “A metatheory of a mechanized object theory, ” Artificial Intelligence 80, 197–241.

    Google Scholar 

  • Giunchiglia, F., Serafini, L., and Simpson, A., 1992, “Hierarchical meta-logics: Intuitions, proof theory and semantics, ” pp. 235–249 in Proceedings of META-92, Workshop on Metaprogramming in Logic, Uppsala, Sweden, A. Pettorossi, ed., Berlin: Springer-Verlag.

    Google Scholar 

  • Giunchiglia, F., Serafini, L., Giunchiglia, E., and Frixione, M., 1993, “Non-omniscient belief as context-based reasoning, ” pp. 548–554 in Proceedings of the 13th International Joint Conference on Artificial Intelligence, Chambery, France, R. Bajcsy, ed., San Mateo, CA: Morgan Kaufmann Publishers.

    Google Scholar 

  • Masini, A., 1992, “2-sequent calculus: A proof theory of modalities, ” Annals of Pure and Applied Logic 58, 229–246.

    Google Scholar 

  • McCarthy, J., 1979, “Ascribing mental qualities to machines, ” pp. 161–195 in Philosophical Perspectives in Artificial Intelligence, M. Ringle, ed., New York: Science and Humanities Press. Also pp. 93–118 in Formalizing Common Sense: Papers by John McCarthy, V. Lifschitz, ed.,Norwood, NJ: Ablex Publishers, 1990.

    Google Scholar 

  • McCarthy, J., 1993, “Notes on formalizing context, ” pp. 555–560 in Proceedings of the 13th International Joint Conference on Artificial Intelligence, Chambery, France, R. Bajcsy, ed., San Mateo,CA: Morgan Kaufmann Publishers.

    Google Scholar 

  • McCarthy, J. and Buvač, S., 1998, “Formalizing context (Expanded notes), ” pp. 13–50 in Computing Natural Language, A. Aliseda, R. van Glabbeek, and D. Westerståhl, Vol. 81 of CSLI Lecture Notes, Vol. 81, Stanford, CA: Center for the Study of Language and Information, Stanford University.

    Google Scholar 

  • Mylopoulos, J. and Motschnig-Pitrik, R., 1995, “Partitioning information bases with contexts, ” pp. 44–54 in Third International Conference on Cooperative Information Systems, Vienna, S. Laufmann, S. Spaccapietra, and T. Yokoi, eds., Toronto: University of Toronto Press.

    Google Scholar 

  • Noriega, P. and Sierra, C., 1996, “Towards layered dialogical agents, ” pp. 173–188 in Proceedings of the Third International Workshop on Agent Theories, Architectures, and Languages (ATAL-96),ECAI-96, Budapest, Hungary, J.P. Müller, M.J. Wooldridge, and N.R. Jennings, eds., Lecture Notes in Artificial Intelligence, Vol. 1193, Berlin: Springer-Verlag.

    Google Scholar 

  • Parsons, S., Sierra, C., and Jennings, N., 1998, “Agents that reason and negotiate by arguing, ” Journal of Logic and Computation 8, 261–292.

    Google Scholar 

  • Penco, C., 1999, “Objective and cognitive contexts, ” pp. 270–283 Modelling and Using Context, Proceedings of CONTEXT'99Second International and Interdisciplinary Conference on Modelling and Using Context (Trento, Italy, 9–11 September 1999), Lecture Notes in Artificial Intelligence,Vol. 1688, Bouquet, P., Serafini, L., Brezillon, P., Benerecetti, M., and Castellani, F., eds., Berlin: Springer-Verlag.

    Google Scholar 

  • Prawitz, D., 1965, Natural Deduction – A Proof Theoretical Study, Stockholm: Almquist and Wiksell.

    Google Scholar 

  • Russo, A., 1996, “Modal logics as labelled deductive systems, ” Ph.D. Thesis, Imperial College of Science, Technology and Medicine, University of London, London, U.K.

  • Sabater, J., Sierra, C., Parsons, S., and Jennings, N., 2001, “Engineering executable agents using multi-context systems, ” Journal of Logic andComputation, to appear. Draft available at http://www.ecs.soton.ac.uk/nrj/download-files/jlc01a.ps

  • Serafini, L. and Ghidini, C., 2000, “Using wrapper agents to answer queries in distributed information systems, ” pp. 331–340 in Advances in Information Systems – Proceedings of the First International Conference, ADVIS 2000, T. Yakhno, ed., Lecture Notes in Computer Science, Vol. 1909, Berlin: Springer-Verlag.

    Google Scholar 

  • Sharma, N., 1995, “On formalising and reasoning with contexts, ” Technical Report Technical Report 352, Department of Computer Science, The University of Queensland, Australia.

  • Subrahmanian, V., 1994, “Amalgamating knowledge bases, ” ACM Trans. Database Systems 19, 291–331.

    Google Scholar 

  • Weyhrauch, R., 1980, “Prolegomena to a theory of mechanized formal reasoning, ” Artificial Intelligence 13, 133–176.

    Google Scholar 

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Serafini, L., Giunchiglia, F. ML Systems: A Proof Theory for Contexts. Journal of Logic, Language and Information 11, 471–518 (2002). https://doi.org/10.1023/A:1019967901393

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