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The logic of nonmonotonicity

Artificial Intelligence 41 (3):365-374 (1990)

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  1. Counterfactuals and updates as inverse modalities.Mark Ryan & Pierre-Yves Schobbens - 1997 - Journal of Logic, Language and Information 6 (2):123-146.
    We point out a simple but hitherto ignored link between the theoryof updates, the theory of counterfactuals, and classical modal logic: update is a classicalexistential modality, counterfactual is a classical universalmodality, 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 rules for updates andrules for counterfactuals. Thus, Katsuno and Mendelzons postulatesU1--U8 are translated into counterfactual rules C1--C8(Table VII), and (...)
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  • Revision algebra semantics for conditional logic.John Pais - 1992 - Studia Logica 51 (2):279 - 316.
    The properties of belief revision operators are known to have an informal semantics which relates them to the axioms of conditional logic. The purpose of this paper is to make this connection precise via the model theory of conditional logic. A semantics for conditional logic is presented, which is expressed in terms of algebraic models constructed ultimately out of revision operators. In addition, it is shown that each algebraic model determines both a revision operator and a logic, that are related (...)
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  • Propositional knowledge base revision and minimal change.Hirofumi Katsuno & Alberto O. Mendelzon - 1991 - Artificial Intelligence 52 (3):263-294.
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  • From causal models to counterfactual structures.Joseph Y. Halpern - 2013 - Review of Symbolic Logic 6 (2):305-322.
    Galles & Pearl (l998) claimed that s [possible-worlds] framework.s framework. Recursive models are shown to correspond precisely to a subclass of (possible-world) counterfactual structures. On the other hand, a slight generalization of recursive models, models where all equations have unique solutions, is shown to be incomparable in expressive power to counterfactual structures, despite the fact that the Galles and Pearl arguments should apply to them as well. The problem with the Galles and Pearl argument is identified: an axiom that they (...)
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  • Five faces of minimality.David Makinson - 1993 - Studia Logica 52 (3):339 - 379.
    We discuss similarities and residual differences, within the general semantic framework of minimality, between defeasible inference, belief revision, counterfactual conditionals, updating — and also conditional obligation in deontic logic. Our purpose is not to establish new results, but to bring together existing material to form a clear overall picture.
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  • In All But Finitely Many Possible Worlds: Model-Theoretic Investigations on ‘ Overwhelming Majority ’ Default Conditionals.Costas D. Koutras & Christos Rantsoudis - 2017 - Journal of Logic, Language and Information 26 (2):109-141.
    Defeasible conditionals are statements of the form ‘if A then normally B’. One plausible interpretation introduced in nonmonotonic reasoning dictates that ) is true iff B is true in ‘most’ A-worlds. In this paper, we investigate defeasible conditionals constructed upon a notion of ‘overwhelming majority’, defined as ‘truth in a cofinite subset of \’, the first infinite ordinal. One approach employs the modal logic of the frame \\), used in the temporal logic of discrete linear time. We introduce and investigate (...)
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  • Faithful representation of nonmonotonic patterns of inference.John Pais - 1992 - Minds and Machines 2 (1):27-49.
    Recently, John Bell has proposed that a specific conditional logic, C, be considered as a serious candidate for formally representing and faithfully capturing various (possibly all) formalized notions of nonmonotonic inference. The purpose of the present paper is to develop evaluative criteria for critically assessing such claims. Inference patterns are described in terms of the presence or absence of residual classical monotonicity and intrinsic nonmonotonicity. The concept of a faithful representation is then developed for a formalism purported to encode a (...)
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  • Counterfactuals and Scientific Realism.Michael J. Shaffer - 2012 - London and Basingstoke: Palgrave MacMillan.
    This book is a sustained defense of the compatibility of the presence of idealizations in the sciences and scientific realism. So, the book is essentially a detailed response to the infamous arguments raised by Nancy Cartwright to the effect that idealization and scientific realism are incompatible.
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