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1988 Volume 3
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RESEARCH ARTICLE   Open Access    

Default non-monotonic logic

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  • Abstract: This paper is a review of certain non-monotonic logics, which I call default non-monotonic logics. These are logics which exploit failure to prove. How each logic uses this basic idea is explained, and examples given. The emphasis is on leading ideas explained through examples: technical detail is avoided. Four non-monotonic logics are discussed: Reiter's default logic, McCarthy's circumscription, McDermott's modal non-monotonic logic, and Clarks's completed database. The first two are treated in some detail. The recent Hanks-McDermott criticism of non-monotonic logic is discussed, and some conclusions drawn about the prospects for non-monotonic logic. Recommendations for further reading are given.
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  • Barendregt H1981. Lambda Calculus, North Holland, Amsterdam.

    Google Scholar

    Barwise J and Etchmendy J, 1987. Truth and the Liar, Oxford.

    Google Scholar

    Barwise J and Perry J, 1983. Situations and Attitudes, MIT Press.

    Google Scholar

    Bossu G and Siegal P, 1985. “Saturation, non-monotonic reasoning and the closed world assumption”, Artificial Intelligence (25) 13–64.

    Google Scholar

    Boolos G and Jeffrey R, 1982. Computability & Logic, Cambridge.

    Google Scholar

    Blair H A, 1982. “The recursion-theorectic complexity of the semantics of predicate logic as a programming language,” Information and Control (54) 25–47.

    Google Scholar

    Bridge J, 1977. Beginning model theory, Oxford Logic Guides, Oxford.

    Google Scholar

    Bundy A, 1983. The Computer Modelling of Mathematical Reasoning, Academic Press, London.

    Google Scholar

    Chang C C and Keisler H J, 1976. Model Theory, North-Holland.

    Google Scholar

    Clark K L, 1978. “Negation as failure,” In: Gallaire & Minker op cit 293.

    Google Scholar

    Cohen P, 1987. “The control of reasoning under uncertainty: a discussion of some programs,” The Knowledge Engineering Review (2) 6–25.

    Google Scholar

    Davis M, 1980. “The mathematics of non-monotonic reasoning,” Artificial Intelligence (13) 73–80.

    Google Scholar

    Etherington D, Mercer R and Reiter R, 1985. “On the adequacy of predicate circumscription for closed world reasoning,” Computational Intelligence (1) (1985) 11–15.

    Google Scholar

    Fitting M, 1985. “A Kripke-Kleene semantics for logic programs,” Journal of Logic Programming (4) 295–312.

    Google Scholar

    Fitting M, 1986. “Notes on the mathematical aspects of Kripke's theory of truth,” Notre Dame Journal of Formal Logic (27) 75–88.

    Google Scholar

    Flannagan T, 1986. “The consistency of negation as failure,” Journal of Logic Programming (3) 93–115.

    Google Scholar

    Gabbay D, 1982. “Intuitionistic bases for non-monotonic logic,” In: Proc. Conference on Automated Deduction Springer Lecture Notes in Computer Science (6) 260–273.

    Google Scholar

    Gallaire H and Minker J, (Ed.), 1978. Logic and Databases, Plenum Press, New York.

    Google Scholar

    Gibbins P, 1988. Logic with Prolog (Oxford).

    Google Scholar

    Hanks S and McDermott D, 1987. “Nonmonotonic logic and temporal projection,” Artificial Intelligence (33) 379–412.

    Google Scholar

    Hilpinen R, (ed.), 1981. New Studies in Deontic Logic, North Holland, Amsterdam.

    Google Scholar

    Hughes G E and Cresswell M, 1968. An Introduction to Modal Logic, Methuen, London.

    Google Scholar

    Jaffar J, Lassez J-L and Lloyd J W, 1983. “Completeness of the negation as failure rule,” Proceedings of the 8th IJCAI, Karlsruhe, 500–506.

    Google Scholar

    Konolige K, 1988. “On the relation between default and autoepistemic logic,” Artificial Intelligence (35) 343–382.

    Google Scholar

    Kunen K, 1987. “Negation in logic programming,” Journal of Logic Programming (4) 289–308.

    Google Scholar

    Kyburg H, 1970. Probability and Inductive Logic, Macmillan, London.

    Google Scholar

    Lifschitz V, 1985a. “Closed world data bases and circumscription,” Artificial Intelligence (27) 229–335.

    Google Scholar

    Lifschitz V, 1985b. “Pointwise circumscription: preliminary report,” Proc. IJCAI-85, Los Angeles, Ca., 406–10.

    Google Scholar

    Lifschitz V, 1986. “On the satisfiability of circumscription,” Artificial Intelligence (28) 17–28.

    Google Scholar

    Lloyd J W, 1984. Foundations Of Logic Programming, Springer-Verlag, Berlin.

    Google Scholar

    McCarthy J, 1980. “Circumscription—a form of non-monotonic reasoning,” Artificial Intelligence (13) 27–39.

    Google Scholar

    McCarthy J, 1986. “Applications of circumscription to formalising common-sense knowledge,” Artificial Intelligence (28) 89–116.

    Google Scholar

    McDermott D V and Doyle J, 1980. “Non-monotonic logic I,” Artificial Intelligence (13) 41–72.

    Google Scholar

    McDermot D V, 1983. “Non-monotonic logic II,” JACM (29) 33–57.

    Google Scholar

    McDermott D V, 1982. “A temporal logic for reasoning about processes and plans,” Cognitive Sci. (6) 101–155.

    Google Scholar

    Mendelson E, 1987. Introduction to Mathematical Logic (3rd Edition), Wadsworth, California.

    Google Scholar

    Minsky M, 1975. “A framework for representing knowledge,” Winston P (Ed.), The Psychology of Computer VisionMcGraw Hill, New York.

    Google Scholar

    Mill J S, 1843. A System Of Logic.

    Google Scholar

    Moore R C, 1985. “Semantic considerations on non-monotonic logic,” Artificial Intelligence (25) 75–94.

    Google Scholar

    Mott P L, 1987. “A theorem on the consistency of circumscription,” Artificial Intelligence (31) 87–98.

    Google Scholar

    Nute D, 1988. “LDR: a logic for defeasible reasoning,” ACMC Research Report 01–0013, University of Georgia.

    Google Scholar

    Perlis D and Minker J, 1986. “Completeness results for circumscription,” Artificial Intelligence (28) 29–42.

    Google Scholar

    Popper K R, 1972. Objective Knowledge, OUP, London.

    Google Scholar

    Raphael B, 1971. “The frame problem in problem solving systems,” In: Findler N V & Meltzer B (Eds.), AI and Heuristic Programming, Edinburgh U P, Edinburgh.

    Google Scholar

    Reiter R, 1980a. “A logic for default reasoning,” Artificial Intelligence (13) 81–132.

    Google Scholar

    Reiter R, 1980b. “Equality and domain closure in first order data bases,” JACM (27) 235–249.

    Google Scholar

    Reiter R, 1978. “On closed world data bases,” In: Gallaire & Minker, op cit 55–77.

    Google Scholar

    Reiter R, 1978b. “Deductive question answering on relational databases,” In: Gallaire and Minker, op cit 149–177.

    Google Scholar

    Reiter R and Crisculo G. 1983. “Some representational issues in default reasoning,” Int. J. of Computat. Maths (9) 1–13.

    Google Scholar

    Rescher N and Urquhart A, 1971. Temporal Logic, Springer Verlag, Berlin.

    Google Scholar

    Robbin J W, 1969. Mathematical Logic, Benjamin, New York.

    Google Scholar

    Schlipf J, 1987a. “Decidability and definability with circumscription,” Annals of Pure and Applied Logic (35) 173–191.

    Google Scholar

    Schlipf J, 1987b. “When is closed world reasoning tractable?” Department of Computer Science, University of Cincinati, Ohio 45221–0008, USA.

    Google Scholar

    Shepherdson J, 1984. “Negation as failure: a comparison of Clark's completed database and Reiter's closed world assumption,” Journal of Logic Programming (1) 51–79.

    Google Scholar

    Shepherdson J, 1985. “Negation as failure II,” Journal of Logic Programming (2) 185–202.

    Google Scholar

    Shortliffe E, 1976. Computer-Based Medical Consultations: MYCIN, Elsevier, New York.

    Google Scholar

    Smets Ph, Mamdani E H, Dubois D and Prade H, 1988. Non-Standard Logics for Automated Reasoning, Academic Press, London.

    Google Scholar

    Swinburne R (Ed), 1974. The Justification of Induction, Oxford.

    Google Scholar

    Tarski A, 1944. “The semantic conception of truth” Philosophy & Phenomenological Research4341–376.

    Google Scholar

    Tarski A, 1969a. Logic, Semantics, Metamathematics, Woodger J H, (Ed.), Oxford.

    Google Scholar

    Tarski A, 1969b. “Truth and proof,” Scientific American194 (6).

    Google Scholar

    Turner R, 1984. Logics for Artificial Intelligence, Ellis Horwood, New York.

    Google Scholar

    Van Benthem J, 1983. The Logic of Time, Reidel, Dordrecht.

    Google Scholar

    Van Dalen D, 1985. Logic and Structure, Springer, Berlin.

    Google Scholar

    Van Gelder A, Ross K and Schlipf J S, 1988. “Unfounded sets and well-founded semantics for general logic programs,” 7th ACM Principles of Database Systems.

    Google Scholar

    Wojcik M, 1987. “Methods of automatic reasoning using non-monotonic logics—examples of implementation”, Polish Academy of Sciences, ICS Report 610, Warsaw.

    Google Scholar

  • Cite this article

    Peter Mott. 1988. Default non-monotonic logic. The Knowledge Engineering Review. 3:4586 doi: 10.1017/S0269888900004586
    Peter Mott. 1988. Default non-monotonic logic. The Knowledge Engineering Review. 3:4586 doi: 10.1017/S0269888900004586

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RESEARCH ARTICLE   Open Access    

Default non-monotonic logic

The Knowledge Engineering Review  3 Article number: 10.1017/S0269888900004586  (1988)  |  Cite this article

Abstract: Abstract: This paper is a review of certain non-monotonic logics, which I call default non-monotonic logics. These are logics which exploit failure to prove. How each logic uses this basic idea is explained, and examples given. The emphasis is on leading ideas explained through examples: technical detail is avoided. Four non-monotonic logics are discussed: Reiter's default logic, McCarthy's circumscription, McDermott's modal non-monotonic logic, and Clarks's completed database. The first two are treated in some detail. The recent Hanks-McDermott criticism of non-monotonic logic is discussed, and some conclusions drawn about the prospects for non-monotonic logic. Recommendations for further reading are given.

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    Peter Mott. 1988. Default non-monotonic logic. The Knowledge Engineering Review. 3:4586 doi: 10.1017/S0269888900004586
    Peter Mott. 1988. Default non-monotonic logic. The Knowledge Engineering Review. 3:4586 doi: 10.1017/S0269888900004586
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