| S. Krauss, D. Lehmann, and M. Magidor. Nonmonotonic Reasoning, Preferential Models and Cumulative Logics. Arti cial Intelligence, 44:167-207, 1990. |
.... An) A . Rational Monotony in Gentzen style is If j6 : A1 An) for all A1 ; An 2 , then j A implies [ j A . 3 if added, will cause the inference relation collapsing to a monotonic one, such as Monotonicity, Transitivity and Contraposition (see [Kraus et al. 90] Freund et al. 92] were proposed for special nonmonotonic inference relation, such as If j A; then [ j A or [ j :A (Determinacy Preservation) see [Makinson 93] If j A and , then j A (Antitonicity) see [Kaluzhny and Lehmann 95] The underlying intuition of those rules is a long story 2 , but ....
M. Freund, D. J. Lehmann, P. Morris: Rationality, Transitivity, and Contraposition. Articial Intelligence 52(2), 1992, 191-203.
....operations that are not rational (not even on singletons) The following provides a handy characterization of rational operations. It is closely related to the di erent equivalent rules of restricted transitivity shown to be equivalent to Rational Monotonicity (in the nitary framework) in [7]. The following theorem provides a characterization of rational operations. Theorem 21 An operation C is rational i it is supraclassical, left absorbing and satis es C(X) Cn(X; C(Y ) for any X;Y L such that Y C(X) and X is consistent with C(Y ) Proof : For the only if part, suppose C ....
Michael Freund, Daniel Lehmann, and Paul Morris. Rationality, transitivity, and contraposition. Arti cial Intelligence, 52(2):191-203, December 1991. Research Note.
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S. Krauss, D. Lehmann, and M. Magidor. Nonmonotonic Reasoning, Preferential Models and Cumulative Logics. Arti cial Intelligence, 44:167-207, 1990.
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