Abstract
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.
Preview
Unable to display preview. Download preview PDF.
References
Anderson A and Belnap N (1975) Entailment: The Logic of Relevance and Necessity, Princeton University Press
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. Angkor
Batens D (1980) Paraconsistent extensional propositional logics, Logique et Analyse, 90–91, 195–234
Cadoli M and Schaerf M (1991) Approximate entailment, in Trends in Artificial Intelligence, Lecture Notes in Computer Science, 549, Springer
da Costa N C (1974) On the theory of inconsistent formal systems, Notre Dame Journal of Formal Logic, 15, 497–510
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, Springer
Gabbay D (1991) Labelled Deductive System, Technical Report, Centrum fur Informations und Sprachverarbeitung, Universitat Munchen
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, Springer
Gabbay D and Hunter A (1992) Making inconsistency respectable, Part 2, in Proceedings of ECSQARU'93, Lecture Notes in Computer Science, Springer
Martins J and Shapiro S (1988) A model of belief revision, Artificial Intelligence, 35, 25–80
Raggio A (1978) in Arrunda A, da Costa N C, and Chuaqui R, Mathematical Logic, Proceedings of the First Brazilian Conference, Marcel Defabier
Resher N and Manor R (1970) On inference from inconsistent premises, Theory and Decision, 1, 179–219
Tennant N (1987) Natural deduction and sequent calculus for intuitionisitc relevant logic, Journal of Symbolic Logic, 52, 665–680
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1993 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Gabbay, D., Hunter, A. (1993). Restricted access logics for inconsistent information. In: Clarke, M., Kruse, R., Moral, S. (eds) Symbolic and Quantitative Approaches to Reasoning and Uncertainty. ECSQARU 1993. Lecture Notes in Computer Science, vol 747. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0028193
Download citation
DOI: https://doi.org/10.1007/BFb0028193
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-57395-1
Online ISBN: 978-3-540-48130-0
eBook Packages: Springer Book Archive