Abstract
Modal logics are often criticised for their coarse grain representation of knowledge of possibilities about assertions. That is to say, if two assertions are possible in the current world, their further properties are indistinguishable in the modal formalism even if an agent knows that one of them is true in twice as many possible worlds as compared to the other one. Epistemic logic, that is the logic of knowledge and belief, cannot avoid this shortcomings because it inherits the syntax and semantics of modal logics. In this paper, we develop an extended formalism of modal epistemic logic which will allow an agent to represent its degrees of support about an assertion. The degrees are drawn from qualitative or quantitative dictionaries which are accumulated from agent’s a priori knowledge about the application domain. A possible-world semantics of the logic is developed by using the accessibility hyperelation and the soundness and completeness results are stated. The abstract syntax and semantics are illustrated and motivated by an example from the medical domain.
The author completed this work while working at the Imperial College, University of London. The author would like to thank his colleagues in the RED project, John Fox and Paul Krause of Imperial Cancer Research Fund, for many helpful comments. The project was supported under the DTI/SERC project ITD 4/1/9053: Safety-Critical Systems Initiative.
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References
F. Bacchus. Representing and reasoning with probabilistic knowledge. MIT Press, 1990.
P. Chatalic and C. Froidevaux. Lattice-based graded logic: a multimodal approach. In Proceedings of the Conference Conferenceon Uncertainty in Artificial Intelligence, pages 33–40, 1992.
B. Chellas. Modal Logic. Cambridge University Press, 1980.
P. R. Cohen and H. Levesque. Intention is choice with commitment. Artificial Intelligence, 42, 1990.
S. K. Das. Deductive Databases and Logic Programming. Addison-Wesley, 1992.
S. K. Das. A logical reasoning with preference. Decision Support Systems, 15:19–25, 1995.
S. K. Das, J. Fox, D. Elsdon, and P. Hammond. Decision making and plan management by autonomous agents: theory, implementation and applications. In Proceedings of the International Conference on Autonomous Agents, California, February 1997.
S. K. Das, J. Fox, P. Hammond, and D. Elsdon. A flexible architecture for autonomous agents. to appear in the Journal of Experimental and Theoretical Artificial Intelligence, 1997.
S. K. Das, J. Fox, and P. Krause. A unified framework for hypothetical and practical reasoning (1): theoretical foundations. In D. M. Gabbay and H. J. Ohlbach, editors, Proceedings of the International Conference on Formal and Applied Practical Reasoning, pages 58–72. Springer-Verlag, June 1996.
D. Dubois and H. Prade. Non-standard theories of uncertainty in knowledge representation and reasoning. The Knowledge Engineering Review, 9:399–416, 1994.
R. Fagin and J. Y. Halpern. Belief, awareness and limited reasoning. Artificial Intelligence, 34:39–76, 1988.
J. Fox and S. K. Das. A unified framework for hypothetical and practical reasoning (2): lessons from medical applications. In Proceedings of the International Conference on Formal and Applied Practical Reasoning, pages 73–92. Springer-Verlag, June 1996.
J. Fox, P. J. Krause, and S. Ambler. Arguments, contradictions and practical reasoning. In Proceedings of the European Conference on Artificial Intelligence, August 1992.
P. Hajek, L. Godo, and F. Esteva. Fuzzy logic and probability. In Proceedings of the 11th European Conference on Uncertainty in Artificial Intelligence, pages 237–244, 1995.
J. Halpern and M. Rabin. A logic to reason about likelihood. Artificial Intelligence, 32:379–405, 1987.
J. Y. Halpern and Y. O. Moses. A guide to the modal logics of knowledge and belief. In Proceedings of the 9th International Joint Conference on Artificial Intelligence, pages 480–490, 1985.
J. Hintikka. Knowledge and Belief. Cornell University Press, 1962.
P. Krause and D. Clark. Representing Uncertain Knowledge: An artificial intelligence approach. Intellect, Oxford, 1993.
P. J. Krause, S. J. Ambler, M. Elvang-Goransson, and J. Fox. A logic of argumentation for uncertain reasoning. Computational Intelligence, 11:113–131, 1995.
E. J. Lemmon. An Introduction to Modal Logic. Basil Blackwell, 1977.
J. J. Meyer and W. van der Hoek. Epistemic Logic for AI and Computer Science. Cambridge Tracks in Theoretical Computer Science. Cambridge University Press, 1995.
J.-J. Ch. Meyer, W. van der Hoek, and G. A. W. Vreeswijk. Epistemic logic for computer science: a tutorial (part one). EATCS, 44:242–270, 1991.
N. J. Nilsson. Probabilistic logic. Artificial Intelligence, 28:71–87, 1986.
H. S. Nwana. Software agents: an overview. The Knowledge Engineering Review, 11:205–244, 1996.
A. S. Rao and M. P. Georgeff. Modelling rational agents within a BDI-architecture. In Proceedings of the Conference on Knowledge Representation and Reasoning, pages 473–484, 1991.
N. Wilson and S. Moral. A logical view of probability. In Proceedings of the 11th European Conference on Artificial Intelligence, pages 386–390, 1994.
M. Wooldridge and N. R. Jennings. Intelligent agents: theory and practice. The Knowledge Engineering Review, 10:1–38, 1995.
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Das, S.K. (1998). How much does an agent believe: an extension of modal epistemic logic. In: Hunter, A., Parsons, S. (eds) Applications of Uncertainty Formalisms. Lecture Notes in Computer Science(), vol 1455. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-49426-X_19
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DOI: https://doi.org/10.1007/3-540-49426-X_19
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