Restricted access logics for inconsistent information

  • Dov Gabbay
  • Anthony Hunter
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 747)


For practical reasoning with classically inconsistent information, desiderata for an appropriate logic L could include (1) it is an extension of classical logic — in the sense that all classical tautologies are theorems of L, and (2) contradictions do not trivialize L — in the sense that ex falso quodlibet does not hold. Two ways of realizing the second desideratum, for any database that may be inconsistent, include (A) take weaker than classical proof rules, but use all the data, or (B) take all the classical proof rules, but restrict the access of the data to the proof rules. The problem with adopting option (A) is that desideratum (1) is then not realizable. In this paper, we pursue option (B) by adding extra conditions on the proof rules to stop certain subsets of the data using the classical proof rules. To facilitate the presentation, we use the approach of Labelled Deductive Systems — formulae are labelled, and proof rules defined to manipulate both the formulae and the labels. The extra conditions on the proof rules are then defined in terms of the labels. This gives us a class of logics, called restricted access logics, that meet the desiderata above.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Anderson A and Belnap N (1975) Entailment: The Logic of Relevance and Necessity, Princeton University PressGoogle Scholar
  2. Besnard P (1991) Paraconsistent logic approach to knowledge representation, in de Glas M, and Gabbay D, Proceedings of the First World Conference on Fundamentals of Artificial Intelligence. AngkorGoogle Scholar
  3. Batens D (1980) Paraconsistent extensional propositional logics, Logique et Analyse, 90–91, 195–234Google Scholar
  4. Cadoli M and Schaerf M (1991) Approximate entailment, in Trends in Artificial Intelligence, Lecture Notes in Computer Science, 549, SpringerGoogle Scholar
  5. da Costa N C (1974) On the theory of inconsistent formal systems, Notre Dame Journal of Formal Logic, 15, 497–510Google Scholar
  6. Finkelstein A, Gabbay D, Hunter A, Kramer J, and Nuseibeh B (1993) Inconsistency handling in multi-perspective specifications, in Proceedings of the Fourth European Software Engineering Conference, Lecture Notes in Computer Science, SpringerGoogle Scholar
  7. Gabbay D (1991) Labelled Deductive System, Technical Report, Centrum fur Informations und Sprachverarbeitung, Universitat MunchenGoogle Scholar
  8. Gabbay D and Hunter A (1991) Making inconsistency respectable, Part 1, in Jorrand Ph. and Keleman J, Fundamentals of Artificial Intelligence Research, Lecture Notes in Artificial Intelligence, 535, SpringerGoogle Scholar
  9. Gabbay D and Hunter A (1992) Making inconsistency respectable, Part 2, in Proceedings of ECSQARU'93, Lecture Notes in Computer Science, SpringerGoogle Scholar
  10. Martins J and Shapiro S (1988) A model of belief revision, Artificial Intelligence, 35, 25–80Google Scholar
  11. Raggio A (1978) in Arrunda A, da Costa N C, and Chuaqui R, Mathematical Logic, Proceedings of the First Brazilian Conference, Marcel DefabierGoogle Scholar
  12. Resher N and Manor R (1970) On inference from inconsistent premises, Theory and Decision, 1, 179–219Google Scholar
  13. Tennant N (1987) Natural deduction and sequent calculus for intuitionisitc relevant logic, Journal of Symbolic Logic, 52, 665–680Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Dov Gabbay
    • 1
  • Anthony Hunter
    • 1
  1. 1.Department of ComputingImperial CollegeLondonUK

Personalised recommendations