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Nonmonotonic Proof Systems : Algebraic Foundations

Wybrane pełne teksty z tego czasopisma
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Języki publikacji
EN
Abstrakty
EN
A general framework for the algebraization of a category of nonmonotonic logics has been suggested. This method has been applied to the systems of Gabbay, and to Cumulative, Preferential and Ranked systems. The minimal logics required to serve as the base logics for the above systems are investigated. MAK triples and KLM triples are formed in ways similar to MAK models and KLM models but now on the algebraic structures for the nonmonotonic systems, thereby a new type of semantics is given to these systems.
Wydawca
Rocznik
Strony
39--65
Opis fizyczny
Bibliogr. 24 poz.
Twórcy
autor
  • Department of Mathematics, Siksha Bhavana, Visva Вharati, Santiniketan, West Bengal, India
  • Department of Pure Mathematics, University of Calcutta, Kolkata, India
Bibliografia
  • [1] Gabbay, D.: Theoretical foundations for nonmonotonic reasoning in expert systems, in: Logics and Models of Concurrent Systems, (K.Apt.Ed), Springer-Verlag, Berlin, 1985.
  • [2] Lehmman, D., Magidor, M.: What does a conditional knowledge base entail? Artificial Intelligence, 55. 1992, 1-60.
  • [3] Makinson, D.: General theory of cumulative inference, in: Non-monotonic reasoning, (M.Reinfranck.Ed), 346. Lecture Notes in Artificial Intelligence, Springer Verlag. Berlin. 1989, 1-18.
  • [4] Makinson, D.: General Pattern in non-monotonic reasoning, in: Hand book of logic in Artificial Intelligence & Logic Programming, (D.Gabbay.Ed), Vol.3, Oxford University Press, 1994.
  • [5] McDermott, D. : Non-monotonic logic II, Journal of ACM. 29. 1982, 33-57.
  • [61 Poole, D : A logical system for default reasoning, in: Proceedings of Non-monotonic Reasoning Workshop. NY, 1984, 373-384.
  • [7] Adams, E.W. : The Logic of conditionals, (Reidel, Dordrecht), Netherlands, 1975.
  • [8] Gratzer, G. : Lattice Theory, Freeman, San Fransisco, CA. 1971.
  • [9] Rasiowa, H., Sikorski, R. : The Mathematics of Metamathematics Państwowe Wydawnictwo Naukowe, Warszawa. 1963.
  • [l0] Dix, J., Makinson, D. : A note on the relationship between KLM and MAK models for non-monotonic inference operation, ./. Logic Language Inference 1. 1992. 131-140.
  • [11] Bell, J.E..Slomson, A.B. : Models and Ultraproducts : an introduction. North Holland. 1971.
  • [12] McCarthy, J.: Circumscription - a form of non-monotonic reasoning, Artificial Intelligence, 39. 1980, 27-39.
  • [13] Georgatos, K. : Ordering based representations of rational inference, in: Logics in Artificial Intelligence (JELIA’96), 1126 (J.J. Alferes,L.M. Pereira and E.Orłowska, Eds), Springer-Verlag, Berlin, 1996, 176-191.
  • [14] Georgatos, K. : Entrenchment relations: a uniform approach to non-monotonic inference, in: Proceedings of International Joint Conference on Qualitative and Quantitative Reasoning, (D.Gabbay et al.Eds). Lecture Notes in Computer Science, 1244. Springer. Berlin, 1997. 282-297.
  • [15] Georgatos, K. : To preference via entrenchment. Annals of Pure and Applied Logic, 96, 1999. 141-155.
  • [16] Gardenfors, P., Makinson, D. : Nonmonotonic inference based on expectations. Artificial Intelligence, 65. 1994,197-245.
  • [17] Hajek, P. : Metamathematics of Fuzzy Logic, Kluwer Academic Publishers, 1998.
  • [18] Moore, R.C. : Possible world semantics for autoepistemic logic, Technical Note 337. SRI Artificial Intelligence Centre. Menlo Park, California, 1984.
  • [19] Moore, R.C. : Semantical considerations on nonmonotonic logic, Artificial Intelligence, 25. 1985. 75-94.
  • [20] Reiter, R. : A logic for default reasoning. Artificial Intelligence, 13, 1980, 81-132.
  • [21] Benferhat, S.. Dubois, D.. Prade, H. : Nonmonotonic reasoning, conditional objects and possibility theory. Artificial Intelligence, 92, 1997, 259-276.
  • [22] Kraus, S., Lehmann. D., Magidor. M.: Nonmonotonic reasoning, preferential models and cumulative logics, Artificial Intelligence, 44. 1990, 167-207.
  • [23] Marek, V.W., Truszczyński, M. : Nonmonotonic Logic : Context-Dependent Reasoning, Springer-Verlag, 1993.
  • [24] Moinard, Y. : Linking Makinson and Kraus-Lehmann-Magidor preferential entailments, in: Proceedings of 9th Intl. Workshop on Non-Monotonic Reasoning, 2002.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BUS2-0005-0002
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