Intuitionistic basis for non-monotonic logic (original) (raw)

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Abstract

McDermott and Doyle [4] suggested a system, denoted by ⊢, of non-monotonic logic. This notion was intended to formalise non-monotonic reasoning as involved in real situations and in artificial intelligence. McDermott and Doyle also list in their paper several difficulties and problems in their approach. Their semantics seems to be inadequate and there are several counterintuitive results obtained in their system.

McDermott and Doyle base their provability notion ⊢ on the provability notion ⊢ of classical logic. We introduce in this note two logical systems based on the provability notion ⊩ of intuitionistic logic. We show that in the resulting nonmonotonic logic most of the problems disappear. We further show that intuitionistic ⊩ is indeed the reasoning adopted implicitly by available TMS (Truth Maintainance Systems).

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References

1. D.M. Gabbay, Investigations in Modal and Tense Logic with Applications, D. Reidel, 1976.
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2. D.M. Gabbay, Semantical Investigations in Heytings' Intuitionistic Logic, D. Reidel, 1981.
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3. John McCarthy, Circumscription: A form of non-monotonic reasoning, in Artificial Intelligence 13 (1980), pp. 27–39.
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4. D. McDermott and J. Doyle, Non-monotonic logic I, in Artificial Integlligence 13 (1980), pp. 41–72.
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5. R. Reiter, A logic for default reasoning, in Artificial Intelligence 13 (1980), pp. 81–132.
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Authors and Affiliations

1. University of Stuttgart, USA
   Dov M. Gabbay (Project Rohrer)
2. Bar-Ilan University, USA
   Dov M. Gabbay (Project Rohrer)

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D. W. Loveland

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© 1982 Springer-Verlag Berlin Heidelberg

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Gabbay, D.M. (1982). Intuitionistic basis for non-monotonic logic. In: Loveland, D.W. (eds) 6th Conference on Automated Deduction. CADE 1982. Lecture Notes in Computer Science, vol 138. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0000064

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• DOI: https://doi.org/10.1007/BFb0000064
• Published: 07 September 2005
• Publisher Name: Springer, Berlin, Heidelberg
• Print ISBN: 978-3-540-11558-8
• Online ISBN: 978-3-540-39240-8
• eBook Packages: Springer Book Archive

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