355 research outputs found

    Default Logic in a Coherent Setting

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    In this talk - based on the results of a forthcoming paper (Coletti, Scozzafava and Vantaggi 2002), presented also by one of us at the Conference on "Non Classical Logic, Approximate Reasoning and Soft-Computing" (Anacapri, Italy, 2001) - we discuss the problem of representing default rules by means of a suitable coherent conditional probability, defined on a family of conditional events. An event is singled-out (in our approach) by a proposition, that is a statement that can be either true or false; a conditional event is consequently defined by means of two propositions and is a 3-valued entity, the third value being (in this context) a conditional probability

    Notes on contraposing conditionals

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    The contraposing conditional 'If A then C' is defined by the conjunction of A > C and ~C > ~A, where > is a conditional of the kind studied by Stalnaker, Lewis and others. This idea has recently been explored, under the name 'evidential conditional', in a sequence of papers by Crupi and Iacona and Raidl, and it has been found of independent interest by Booth and Chandler. I discuss various properties of these conditionals and compare them to the 'difference-making conditionals' studied by Rott, which are defined by the conjunction of A > C and not ~A > C. I raise some doubts about Crupi and Iacona's claim that contraposition captures the idea of evidence or support

    Notes on contraposing conditionals

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    The contraposing conditional 'If A then C' is defined by the conjunction of A > C and ~C > ~A, where > is a conditional of the kind studied by Stalnaker, Lewis and others. This idea has recently been explored, under the name 'evidential conditional', in a sequence of papers by Crupi and Iacona and Raidl, and it has been found of independent interest by Booth and Chandler. I discuss various properties of these conditionals and compare them to the 'difference-making conditionals' studied by Rott, which are defined by the conjunction of A > C and not ~A > C. I raise some doubts about Crupi and Iacona's claim that contraposition captures the idea of evidence or support

    Cognitive constraints, contraction consistency, and the satisficing criterion

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    © 2007, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0

    Three ways of being non-material

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    This paper presents a novel unified account of three distinct non-material interpretations of "if... then...": the suppositional interpretation, the evidential interpretation, and the strict interpretation. We will spell out and compare these three interpretations within a single formal framework which rests on fairly uncontroversial assumptions, in that it requires nothing but propositional logic and the probability calculus. As we will show, each of the three intrerpretations exhibits specific logical features that deserve separate consideration. In particular, the evidential interpretation as we understand it — a precise and well defined version of it which has never been explored before — significantly differs both from the suppositional interpretation and from the strict interpretation

    Satisficing behavior with a secondary criterion

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    Using the techniques of revealed preference analysis, we study a two-stage model of choice behavior. In the first stage, the decision maker maximizes a menu-dependent binary relation encoding preferences that are imperfectly perceived. In the second, a menu-independent binary relation is maximized over the subset of alternatives that survive the first stage. This structure can support various interpretations, including those of salience effects, positive action, and surface characteristics. We characterize the model behaviorally both in ordinal form and in terms of the corresponding numerical representations

    Axiomatic Foundations for Satisficing Behavior

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    A theory of decision making is proposed that supplies an axiomatic basis for the concept of "satisficing" postulated by Herbert Simon. After a detailed review of classical results that characterize several varieties of preference-maximizing choice behavior, the axiomatization proceeds by weakening the inter-menu contraction consistency condition involved in these characterizations. This exercise is shown to be logically equivalent to dropping the usual cognitive assumption that the decision maker fully perceives his preferences among available alternatives, and requiring instead merely that his ability to perceive a given preference be weakly decreasing with respect to the relative complexity (indicated by set inclusion) of the choice problem at hand. A version of Simon's hypothesis then emerges when the notion of "perceived preference" is endowed with sufficiently strong ordering properties, and the axiomatization leads as well to a constraint on the form of satisficing that the decision maker may legitimately employ.
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