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Nonmonotonic Reasoning, Preferential Models and Cumulative Logics
, 1990
"... Many systems that exhibit nonmonotonic behavior have been described and studied already in the literature. The general notion of nonmonotonic reasoning, though, has almost always been described only negatively, by the property it does not enjoy, i.e. monotonicity. We study here general patterns of ..."
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Cited by 538 (13 self)
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Many systems that exhibit nonmonotonic behavior have been described and studied already in the literature. The general notion of nonmonotonic reasoning, though, has almost always been described only negatively, by the property it does not enjoy, i.e. monotonicity. We study here general patterns of nonmonotonic reasoning and try to isolate properties that could help us map the field of nonmonotonic reasoning by reference to positive properties. We concentrate on a number of families of nonmonotonic consequence relations, defined in the style of Gentzen [13]. Both prooftheoretic and semantic points of view are developed in parallel. The former point of view was pioneered by D. Gabbay in [10], while the latter has been advocated by Y. Shoham in [38]. Five such families are defined and characterized by representation theorems, relating the two points of view. One of the families of interest, that of preferential relations, turns out to have been studied by E. Adams in [2]. The pr...
Counterfactuals and Updates as Inverse Modalities
 Journal of Logic, Language and Information
, 1997
"... . We point out a simple but hitherto ignored link between the theory of updates and counterfactuals and classical modal logic: update is a classical existential modality, counterfactual is a classical universal modality, and the accessibility relations corresponding to these modalities are inverses. ..."
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Cited by 12 (1 self)
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. We point out a simple but hitherto ignored link between the theory of updates and counterfactuals and classical modal logic: update is a classical existential modality, counterfactual is a classical universal modality, and the accessibility relations corresponding to these modalities are inverses. The Ramsey Rule (often thought esoteric) is simply an axiomatisation of this inverse relationship. We use this fact to translate between postulates for updates and postulates for counterfactuals. Thus, Katsuno/Mendelzon's postulates U1U8 are translated into counterfactual postulates C1C8 (table VII), and many of the familiar counterfactual postulates are translated into postulates for updates (table VIII). Our conclusions are summarised in table V. We also present a syntactic condition which is sufficient to guarantee that a translation from update to counterfactual (or vice versa) is possible. 1. Introduction Background. An intuitive connection between theory change and counterfactuals...
Intertranslating Counterfactuals and Updates
 Proc. ECAI'96
, 1996
"... . We recall that the Ramsey Rule can be seen as axiomatising the relationship of inverse accessibility relations which exists between the notions of update and counterfactual conditional. We use this fact to translate between postulates for updates and postulates for counterfactuals. Thus, Katsuno/ ..."
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Cited by 4 (1 self)
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. We recall that the Ramsey Rule can be seen as axiomatising the relationship of inverse accessibility relations which exists between the notions of update and counterfactual conditional. We use this fact to translate between postulates for updates and postulates for counterfactuals. Thus, Katsuno/Mendelzon's postulates U1U8 are translated into counterfactual postulates C1C8 (theorem 6), and many of the familar counterfactual postulates are translated into postulates for updates (theorem 7). Our conclusions are summarised in table 5. 1 INTRODUCTION It is now known that update, rather than revision, is the correct notion of theory change to fulfil Ramsey's test for the acceptance of counterfactual conditionals [7]. Moreover, in previous work [17] we have shown that Katsuno/Mendelzon's theory of updates is essentially an exercise in multimodal logic: the update operator is an existential modality. And we have shown that the accessibility relation corresponding to this operator is...