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We explore ways in which purely qualitative belief change in the AGM tradition throws light on options in the treatment of conditional probability. First, by helping see why it can be useful to go beyond the ratio rule defining conditional from one-place probability. Second, by clarifying what is at stake in different ways of doing that. Third, by suggesting novel forms of conditional probability corresponding to familiar variants of qualitative belief change, and conversely. Likewise, we explain how recent work on (...) the qualitative part of probabilistic inference leads to a very broad class of 'proto-probability' functions. (shrink)

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We seek a better understanding of why an inferential semantics devised by Tor Sandqvist yields full classical logic, by providing and analysing a direct proof via a suitable maximality construction.

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We define and examine a notion of logical friendliness, which is a broadening of the familiar notion of classical consequence. The concept is studied first in its simplest form, and then in a syntax-independent version, which we call sympathy. We also draw attention to the surprising number of familiar notions and operations with which it makes contact, providing a new light in which they may be seen.

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In this paper dedicated to Carlos Alchourrón, we review an issue that emerged only after his death in 1996, but would have been of great interest to him: To what extent do the formal operations of AGM belief change respect criteria of relevance? A natural criterion was proposed in 1999 by Rohit Parikh, who observed that the AGM model does not always respect it. We discuss the pros and cons of this criterion, and explain how the AGM account may be (...) refined, if we so desire, so that it is always respected. En este trabajo dedicado a Carlos Alchourrón consideramos un problema que surgió recién después de su muerte en 1996 pero que seguramente habría sido de gran interés para él: ¿hasta dónde las operaciones formales sobre el cambio de creencias de AGM respetan el criterio de relevancia? Un criterio natural ha sido propuesto en 1999 por Rohit Parikh quien asimismo observó que el modelo AGM no siempre lo respeta. Nosotros discutimos los pros y los contras de este criterio y explicamos cómo podría refinarse AGM para que, si así lo deseáramos, lo respetara siempre. (shrink)

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We define and examine a notion of logical friendliness, which is a broadening of the familiar notion of classical consequence. The concept is tudied first in its simplest form, and then in a syntax-independent version, which we call sympathy. We also draw attention to the surprising number of familiar notions and operations with which it makes contact, providing a new light in which they may be seen.

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A discussion of the connections and differences between completeness and representation theorems in logic, with examples drawn from classical and modal logic, the logic of friendliness, and nonmonotonic reasoning.

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The concept of relevance between classical propositional formulae, defined in terms of letter-sharing, has been around for a very long time. But it began to take on a fresh life in 1999 when it was reconsidered in the context of the logic of belief change. Two new ideas appeared in independent work of Odinaldo Rodrigues and Rohit Parikh. First, the relation of relevance was considered modulo the belief set under consideration, Second, the belief set was put in a canonical form, (...) known as its finest splitting. In this paper we explain these ideas; relate the approaches of Rodrigues and Parikh to each other; and briefly report some recent results of Kourousias and Makinson on the extent to which AGM belief change operations respect relevance. Finally we suggest a further refinement of the notion of relevance by introducing a parameter that allows one to take epistemic as well as purely logical components into account. -/- A version of this was published in the /Journal of Applied Logic/ (Elsevier). (shrink)

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Reviews the connections between different kinds of nonmonotonic logic and the general idea of varying degrees of belief.

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Discusses the strong points and the limitations of Ajdukiewicz' approach to grammar.

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Relevance logic is ordinarily seen as a subsystem of classical logic under the translation that replaces arrows by horseshoes. If, however, we consider the arrow as an additional connective alongside the horseshoe and other classical connectives, another perspective emerges. Relevance logic, specifically the system R, may be seen as the output of a conservative extension of classical consequence into the language with arrow.

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We investigate introduction and elimination rules for truth-functional connectives, focusing on the general questions of the existence, for a given connective, of at least one such rule that it satisfies, and the uniqueness of a connective with respect to the set of all of them. The answers are straightforward in the context of rules using general set/set sequents of formulae, but rather complex and asymmetric in the restricted (but more often used) context of set/formula sequents, as also in the intermediate (...) set/formula-or-empty context. (shrink)

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Defines and examines a notion of logical friendliness, a broadening of the familiar notion of classical consequence. Also reviews familiar notions and operations with which friendliness makes contact, providing a new light in which they may be seen.

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Relevance logic is ordinarily seen as a subsystem of classical logic under the translation that replaces arrows by horseshoes. If, however, we consider the arrow as an additional connective alongside the horseshoe, then another perspective emerges: the theses of relevance logic, specifically the system R, may also be seen as the output of a conservative extension of the relation of classical consequence. We describe two ways in which this may be done. One is by defining a suitable closure relation out (...) of the set of theses of relevance logic; the other is by adding to the usual natural deduction system for it further rules with ‘projective constraints’, whose application restricts the subsequent application of other rules. The significance of the two constructions is also discussed. (shrink)

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