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53Beth definability, interpolation and language splittingSynthese 179 (2). 2011.Both the Beth definability theorem and Craig's lemma (interpolation theorem from now on) deal with the issue of the entanglement of one language L1 with another language L2, that is to say, information transfer—or the lack of such transfer—between the two languages. The notion of splitting we study below looks into this issue. We briefly relate our own results in this area as well as the results of other researchers like Kourousias and Makinson, and Peppas, Chopra and Foo.Section 3 does contain …Read more
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41Topological reasoning and the logic of knowledgeAnnals of Pure and Applied Logic 78 (1-3): 73-110. 1996.We present a bimodal logic suitable for formalizing reasoning about points and sets, and also states of the world and views about them. The most natural interpretation of the logic is in subset spaces , and we obtain complete axiomatizations for the sentences which hold in these interpretations. In addition, we axiomatize the validities of the smaller class of topological spaces in a system we call topologic . We also prove decidability for these two systems. Our results on topologic relate earl…Read more
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112Social SoftwareSynthese 132 (3): 187-211. 2002.We suggest that the issue of constructing andverifying social procedures, which we suggestively call socialsoftware, be pursued as systematically as computer software is pursued by computer scientists. Certain complications do arise withsocial software which do not arise with computer software, but thesimilarities are nonetheless strong, and tools already exist which wouldenable us to start work on this important project. We give a variety ofsuggestive examples and indicate some theoretical work…Read more
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19Review: Ronald Fagin, Joseph Y. Halpern, Yoram Moses, Moshe Y. Vardi, Reasoning about Knowledge (review)Journal of Symbolic Logic 62 (4): 1484-1487. 1997.
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30Gems of theoretical computer science, Uwe schöning and Randall PruimJournal of Logic, Language and Information 9 (1): 131-132. 2000.
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62Probabilistic conditionals are almost monotonicReview of Symbolic Logic 1 (1): 73-80. 2008.One interpretation of the conditional If P then Q is as saying that the probability of Q given P is high. This is an interpretation suggested by Adams (1966) and pursued more recently by Edgington (1995). Of course, this probabilistic conditional is nonmonotonic, that is, if the probability of Q given P is high, and R implies P, it need not follow that the probability of Q given R is high. If we were confident of concluding Q from the fact that we knew P, and we have stronger information R, we c…Read more
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91Vague predicates and language gamesTheoria 11 (3): 97-107. 1996.Attempts to give a Logic or Semantics for vague predicates and to defuse the Sorites paradoxes have been largely a failure. We point out yet another problem with these predicates which has not been remarked on before,namely that different people do and must use these predicates in individually different ways. Thus even if there were a semantics for vague predicates, people would not be able to share it. To explain the occurrence nonetheless of these troublesome predicates in language, we propose…Read more
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128Sentences, belief and logical omniscience, or what does deduction tell us?Review of Symbolic Logic 1 (4): 459-476. 2008.We propose a model for belief which is free of presuppositions. Current models for belief suffer from two difficulties. One is the well known problem of logical omniscience which tends to follow from most models. But a more important one is the fact that most models do not even attempt to answer the question what it means for someone to believe something, and just what it is that is believed. We provide a flexible model which allows us to give meaning to beliefs in general contexts, including th…Read more
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4Review: Georg Kreisel, William W. Tait, Finite Definability of Number-Theoretic Functions and Parametric Completeness of Equational Calculi (review)Journal of Symbolic Logic 32 (2): 270-271. 1967.
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Philosophy of Language |
Logic and Philosophy of Logic |