The semantics of non-monotonic entailment defined using partial interpretations
The logic of preferential entailment is generalized to the case where the preference ordering is a part of the models, so that axioms can make statements about the preference ordering, and thereby constrain it. The following technique is used: An aggregate is a pair 〈Δ, ≪〉, where Δ is a set of partial interpretations, and ≪ is a preference order on the members of Δ. A monadic propositional operator D (for default) is introduced, where Dα is satisfied in a member J of Δ in an aggregate 〈Δ, ≪〉 iff α is satisfied in all ≪-minimal completions of J in Δ. A number of examples of the use of this semantics are discussed, and it is shown that default rules can be expressed in such ways that the conclusions dictated by common sense are obtained.
KeywordsLogical Formula Model Aggregate Default Rule Default Reasoning Entailment Relation
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- [Gab85]Dov Gabbay. Theoretical foundations for non-monotonic reasoning in expert systems. In K.R. Apt, editor, Logics and Models of Concurrent Systems. Springer Verlag, 1985.Google Scholar
- [Gin86]Matthew L. Ginsberg. Multi-valued logics. In Proc. Fifth AAAI, pages 243–247, 1986.Google Scholar
- [Kle52]S. Kleene. Introduction to Metamathematics. Van Nostrand, 1952.Google Scholar
- [Mak88]D. Makinson. General theory of cumulative inference. In Michael Reinfrank, editor, Non-Monotonic Reasoning and Reason Maintenance. Springer, 1988.Google Scholar
- [San72]Erik Sandewall. An approach to the frame problem, and its implementation. In Machine Intelligence, Vol. 7. Edinburgh University Press, 1972.Google Scholar
- [San88a]Erik Sandewall. An approach to non-monotonic entailment. In Z.W. Ras and L. Saitta, editors, Methodologies for Intelligent Systems, II, pages 391–397. North-Holland, 1988.Google Scholar
- [San88b]Erik Sandewall. Non-monotonic entailment for temporal reasoning, part i. Technical report, Department of Computer and Information Science, Linkoeping University, 1988.Google Scholar
- [Sho87]Yoav Shoham. Non-monotonic logics: Meaning and utility. In Proc. Tenth IJCAI, pages 388–393, 1987.Google Scholar
- [Sho88]Yoav Shoham. Reasoning about Change. MIT Press, 1988.Google Scholar
- [TH88]R. Thomason and J. Horty. Logics for inheritance theory. In Michael Reinfrank, editor, Non-Monotonic Reasoning and Reason Maintenance. Springer, 1988.Google Scholar
- [Tur84]Raymond Turner. Logics for Artificial Intelligence. Ellis Horwood, 1984.Google Scholar