Some modal logics associated to the reasoning of intelligent agents
Main Article Content
Keywords
agent, reasoner, belief, modal logic, logical omniscience, doxastic logic, epistemic logic, kripke models
Abstract
The hierarchies of systems SCR–nT4, SCR–nT5 and SCR–nD45 with n > 3 are presented. In these systems the belief notion is formalized in the sense of justified belief, of knowledge and of conviction respectively, giving systems of doxastic and epistemic logics as a result where the problem of the logical omniscience can be partially controlled. The systems are characterized with Kripke-style semantics. In these semantics, the length of the possible world chains is restricted in function of reasoner’s type. Moreover, the depth of a model corresponds to the maxim length of the possible world chains that they figure in the model, being that the models of depth n are associated to the deductive systems SCR-nT4, SCR-nT5 and SCR-nD45.
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References
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[2] Manuel Sierra. Caracterización semántica de la jerarquía SCR–n. Revista Boletín de Matemáticas, ISSN 0120–0380, XIV(2), 110–128 (2007).
[3] M. N. Huhns, N. Jacobs, T. Ksiezyk,W. M. Shen, M. R. Singh and P. E. Cannata. Integrating enterprise information models in Camot. In Proceedings of the International Conference on Intelligent and Cooperative Information Systems. ISBN 0–8186–3135–X, 32–43 (1992). Rotterdam, The Netherlands.
[4] Yoav Shoham. Agent Oriented Programming in Knowledge Representation and Reasoning Under Uncertainty: Logic at Work (Lecture Notes in Computer Science), ISBN 3540580956, Editors: Michael Masuch and Laszlo Polos, 123–130 (1993).
[5] Y. Shoham. Agent–oriented programming, Technical Report STAN–CS–1335–90, Computer Science Department. Stanford University, Stanford, CA 94305, 1990.
[6] D. C. Dennett. The Intentional Stance. ISBN 0–262–04093–X. The MIT Press. 1987. Cambridge, MA.
[7] P. R. Cohen and H. J. Levesque. Rational interaction as the basis for communication. In Intentions in Communication, Edited by Philip R. Cohen, Jerry Morgan and Martha E. Pollack, ISBN 978–0–262–03150–9. The MIT Press, Cambridge, MA, 1990.
[8] Michael John Wooldridge. The Logical Modelling of Computational Multi–Agent Systems. PhD thesis, Department of Computation, UMIST, Manchester, UK. (Also available as Technical Report MMU–DOC–94–01). Department of Computing, Manchester Metropolitan University., Chester St., Manchester, UK, 1992.
[9] K. A. Konolige. A deduction model of belief. Pitman Publishing: London and Morgan Kaufmann. San Mateo, CA, 1986.
[10] Brian F. Chellas. Modal logic: an introduction, ISBN 978–0521295154. Cambridge University Press, Cambridge, 1980.
[11] Jaakko Hintikka. Knowledge and Belief. Cornell University Press, lthaca, NY, 1962.
[12] Saul Kripke. Semantical analysis of modal logic. Zeitschrift f¨ur Mathematische Logik und Grundlagen der Mathematik, 9, 1963.
[13] Wolfgang Lenzen. Recent work in epistemic logic. Acta Philosophica Fennica, 30(1), 1978.
[14] Max Freund. Lógica epistémica. Enciclopedia iberoamericana de filosofía, ISBN 84–8164–045–X, 7, Editorial Trotta S. A., Madrid, 1995.