Abstract
The field of nonmonotonic logic, sixteen years old now, is devoted to solve the problem of reasoning under incomplete knowledge, whose good understanding is essential to the construction of AI as a science and whose relevance reaches far beyond AI applications. During these years, many insights have been accumulated in the form of desirable properties the proposed formalisms should exhibit and of criticisms on the available solutions. This paper takes advantage on this experience to derive from them a sort of canon to be imposed to nonmonotonic formalisms. This canon is translated as a set of etiquette rules guiding knowledge representation into theories framed within the Inconsistent Default Logic, IDL. It is then established the important result that IDL produces a unique extension for a theory constructed according to these rules. This result calls forth IDL as an interesting alternative to credulous common sense reasoning formalization fulfilling many desired properties.
research partially sponsored by PICD/CAPES and CNPq.
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References
Brewka, G. ‘Cumulative Default Logic: in defense of nonmonotonic inference rules'. Artificial Intelligence, 50(2):183–205, July, 1991.
da Costa, N.C.A. ‘On the Theory of Inconsistent Formal Systems.’ Notre Dame Journal of Formal Logic, 15. 1974. pp.497–510.
Delgrande, J.P. & Jackson, W.K. ‘Default Logic revisited'. In: Proc. of the 2nd KR'91, J.A. Allen, R.Fikes and E.Sandewall, editors, pp.118–27. San Mateo, CA, Apr. 1991. Morgan Kaufmann Publishers Inc..
Etherington, D.W. ‘Formalizing Nonmonotonic Reasoning Systems'. Artificial Intelligence, 31:41–85, 1987.
Hanks, S. & McDermott, D. ‘Nonmonotonic Logic and Temporal Projection.’ Artificial Intelligence, 33:27–39, 1980.
Lukaszewicz, W. ‘Considerations on default logic — an alternative approach'. Computational Intelligence, 4:1–16, 1988.
Martins, A.T.C. & Pequeno, T. ‘A Meta Axiomatics for the Inconsistent Default Logic'. Journal of the IGPL. Oxford University Press. Submitted.
Martins, A.T.C. 'sequent Calculi for the Logic of Epistemic Inconsistency and for the Inconsistent Default Logic'. Qualification Exam. DI-UFPE. To be submitted.
McCarthy, J. ‘Circumscription — a form of nonmonotonic reasoning'. Artificial Intelligence, 28:89–116, 1986.
Pequeno, M. ‘Defeasible Logic with Exception First'. PhD Thesis, Imperial College, London. 1994.
Pequeno, T.H.C. ‘A Logic for Inconsistent Nonmonotonic Reasoning.’ Technical Report 90/6. Department of Computing, Imperial College. London. 1990.
Pequeno, T.H.C. & Buchsbaum, A.R. ‘The Logic of Epistemic Inconsistency'. In: Proc. of the 2nd KR'91. J.A. Allen, R.Fikes and E.Sandewall, editors, pp 453–60. San Mateo, CA, Apr. 1991. Morgan Kaufmann Publishers Inc..
Pollock, J.L. ‘Defeasible Reasoning'. Cognitive Science, 11:481–518, 1987.
Reiter, R. ‘A Logic of Default Reasoning.’ Artificial Intelligence, 13:81–132, 1980.
Schaub, T. ‘Assertional Default Theories: a semantical view'. In: Proc. of the 2nd KR'91, J.A.Allen, R.Fikes and E.Sandewall, editors, pp. 496–506, San Mateo, CA, Apr. 1991. Morgan Kaufmann Publishers Inc..
Zaverucha, G. ‘A Prioritized Contextual Default Logic: Curing Anomalous Extensions with a Simple Abnormality Default Theory'. In: Proc. KI-94, Nebel and Dreschler-Fischer, eds, Saarbrucken, LNAI 861 (Springer 1994) 260–271.
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© 1996 Springer-Verlag Berlin Heidelberg
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Martins, A.T.C., Pequeno, M., Pequeno, T. (1996). Well-behaved IDL theories. In: Borges, D.L., Kaestner, C.A.A. (eds) Advances in Artificial Intelligence. SBIA 1996. Lecture Notes in Computer Science, vol 1159. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61859-7_2
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DOI: https://doi.org/10.1007/3-540-61859-7_2
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