Implication connectives for logics with right weakening

  • Philippe Besnard
  • Yves Moinard
Part of the Lecture Notes in Computer Science book series (LNCS, volume 945)


We study non-monotonic inference relations, focusing on the properties of the underlying monotonic consequence relation. This sheds new light on the general properties that may or may not be satisfied by a nonmonotonic relation. We let the underlying consequence relation to be any monotonic logic, indicating under what precise conditions it gives rise to a non-monotonic inference relation that obeys major principles such as right weakening and the rule of detachment. We begin to explore the border line that non-monotonic relations cannot cross if they are to enjoy these properties. This work may be considered either as a constructive opposition, or as a complement, to the previous work about the general properties of nonmonotonic inference relations.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [AB75]
    A.R. Anderson and N.D. Jr. Belnap. Entailment: The Logic of Relevance and Necessity. Princeton University Press, 1975.Google Scholar
  2. [Bes88]
    Philippe Besnard. Axiomatizations in the metatheory of nonmonotonic inference systems. In 7th Conf. of the Canadian Society for Computational Studies of Intelligence (CSCSI), pages 117–124, Edmonton, Morgan-Kaufmann, June 1988.Google Scholar
  3. [Del88]
    James P. Delgrande. An approach to default reasoning based on a first-order conditional logic: Revised report. Artificial Intelligence, 36:63–90, 1988.Google Scholar
  4. [FLM91]
    Michael Freund, Daniel Lehmann, and Paul Morris. Rationality, Transitivity, and Contraposition. Artificial Intelligence, 52:191–203, 1991.Google Scholar
  5. [Fre90]
    Michael Freund. Supracompact inference operations. In Nonmonotonic Inductive Logic, in LNAI 543, pages 59–73, Karlsruhe, Springer-Verlag, December 1990.Google Scholar
  6. [Gab82]
    Dov M. Gabbay. Intuitionistic bases for nonmonotonic logic. In D.W. Loveland, editor, LNCS 138, pages 260–273. Springer-Verlag, 1982.Google Scholar
  7. [Gab85]
    D.M. Gabbay. Theoretical foundations for nonmonotonic reasoning in expert systems. In K.R. Apt, editor, Proc. Logics and Models of Concurrent Systems, NATO ASI Series F, volume 13, page xxx. Springer Verlag, 1985.Google Scholar
  8. [Gen33]
    G. Gentzen. Untersuchungen über das logische Schliessen. Mathematische Zeitschrift, 39:176–210, 405–431, 1933. Trad. française publiée aux Presses Universitaires de France, Paris, 1955 English translation in Collected papers of Gerhard Gentzen (Szabo ed.), North Holland, Amsterdam, 1969.Google Scholar
  9. [Her94]
    Heinrich Herre. Compactness Properties of Nonmonotonic Inference Operations. Proc. of JELIA'94. In Logic in Artificial Intelligence, LNAI 838, pages 19–33, York, Springer-Verlag, September 1994.Google Scholar
  10. [KLM90]
    Sarit Kraus, Daniel Lehmann, and Menachem Magidor. Nonmonotonic reasoning, preferential models and cumulative logics. Artificial Intelligence, 44:167–207, 1990.Google Scholar
  11. [Mak88]
    David Makinson. General theory of cumulative inference. In Non-Monotonic Reasoning, in LNAI-346, pages 1–18. Springer-Verlag, June 1988.Google Scholar
  12. [PB91]
    T. Pequeno and A. Buschbaum. The logic of epistemic inconsistency. In Proc. 2nd Conf. on Principles of Knowledge Representation and Reasoning, pages 435–460, Toronto, 1991.Google Scholar
  13. [RB80]
    N. Rescher and R. Brandom. The Logic of Inconsistency. Blackwell, 1980.Google Scholar
  14. [Tar30]
    A. Tarski. Über einige fundamentale Begriffe der Metamathematik. C.R. Soc. Sciences et Lettres de Varsovie, 23, cl. III:22–29, 1930. Trad. française parue dans Logique, sémantique, métamathématique, tome 1, Tarski, A., Armand Collin publ., Paris 1972. English translation in Logic, Semantics, Metamathematics. Papers from 1923–1938 (Woodger ed.), Clarendon Press, Oxford, 1956.Google Scholar
  15. [Tur84]
    Raymond Turner. Logics for artificial intelligence. Hellis Horwood Ltd, 1984.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Philippe Besnard
    • 1
  • Yves Moinard
    • 1
  1. 1.IRISARennes CedexFrance

Personalised recommendations