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15Patrick Blackburn and Johan Bos, Representation and Inference for Natural Language: CSLI Publications, Stanford 2005, pp. xi+348, US$ 30.00, ISBN 1-57586-496-7 (paperback) (review)Studia Logica 85 (3): 413-418. 2007.
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49Hybrid Logics: Characterization, Interpolation and ComplexityJournal of Symbolic Logic 66 (3): 977-1010. 2001.Hybrid languages are expansions of propositional modal languages which can refer to worlds. The use of strong hybrid languages dates back to at least [Pri67], but recent work has focussed on a more constrained system called $\mathscr{H}$. We show in detail that $\mathscr{H}$ is modally natural. We begin by studying its expressivity, and provide model theoretic characterizations and a syntactic characterization. The key result to emerge is that $\mathscr{H}$ corresponds to the fragment of first-o…Read more
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17Remarks on Gregory's “Actually” OperatorJournal of Philosophical Logic 31 (3): 281-288. 2002.In this note we show that the classical modal technology of Sahlqvist formulas gives quick proofs of the completeness theorems in [8] (D. Gregory, Completeness and decidability results for some propositional modal logics containing “actually” operators, Journal of Philosophical Logic 30(1): 57–78, 2001) and vastly generalizes them. Moreover, as a corollary, interpolation theorems for the logics considered in [8] are obtained. We then compare Gregory's modal language enriched with an “actually” o…Read more
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97A modal perspective on the computational complexity of attribute value grammarJournal of Logic, Language and Information 2 (2): 129-169. 1993.Many of the formalisms used in Attribute Value grammar are notational variants of languages of propositional modal logic, and testing whether two Attribute Value Structures unify amounts to testing for modal satisfiability. In this paper we put this observation to work. We study the complexity of the satisfiability problem for nine modal languages which mirror different aspects of AVS description formalisms, including the ability to express re-entrancy, the ability to express generalisations, an…Read more
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120PDL for ordered treesJournal of Applied Non-Classical Logics 15 (2): 115-135. 2005.This paper is about a special version of PDL, proposed by Marcus Kracht, for reasoning about sibling ordered trees. It has four basic programs corresponding to the child, parent, left- and right-sibling relations in such trees. The original motivation for this language is rooted in the field of model-theoretic syntax. Motivated by recent developments in the area of semi-structured data, and, especially, in the field of query languages for XML (eXtensible Markup Language) documents, we revisit th…Read more
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25Introduction: Static and dynamic aspects of syntactic structure (review)Journal of Logic, Language and Information 4 (1): 1-4. 1995.
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51Zooming in, zooming outJournal of Logic, Language and Information 6 (1): 5-31. 1997.This is an exploratory paper about combining logics, combining theories and combining structures. Typically when one applies logic to such areas as computer science, artificial intelligence or linguistics, one encounters hybrid ontologies. The aim of this paper is to identify plausible strategies for coping with ontological richness.
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53Repairing the interpolation theorem in quantified modal logicAnnals of Pure and Applied Logic 124 (1-3): 287-299. 2003.Quantified hybrid logic is quantified modal logic extended with apparatus for naming states and asserting that a formula is true at a named state. While interpolation and Beth's definability theorem fail in a number of well-known quantified modal logics , their counterparts in quantified hybrid logic have these properties. These are special cases of the main result of the paper: the quantified hybrid logic of any class of frames definable in the bounded fragment of first-order logic has the inte…Read more
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161Remarks on Gregory's “actually” operatorJournal of Philosophical Logic 31 (3): 281-288. 2002.In this note we show that the classical modal technology of Sahlqvist formulas gives quick proofs of the completeness theorems in [8] (D. Gregory, Completeness and decidability results for some propositional modal logics containing "actually" operators, Journal of Philosophical Logic 30(1): 57-78, 2001) and vastly generalizes them. Moreover, as a corollary, interpolation theorems for the logics considered in [8] are obtained. We then compare Gregory's modal language enriched with an "actually" o…Read more
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15Modal logic and model-theoretic syntaxIn Maarten de Rijke (ed.), Advances in Intensional Logic, Kluwer Academic Publishers. pp. 29--60. 1997.
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21Hybrid languages and temporal logicLogic Journal of the IGPL 7 (1): 27-54. 1999.Hybridization is a method invented by Arthur Prior for extending the expressive power of modal languages. Although developed in interesting ways by Robert Bull, and by the Sofia school , the method remains little known. In our view this has deprived temporal logic of a valuable tool.The aim of the paper is to explain why hybridization is useful in temporal logic. We make two major points, the first technical, the second conceptual. First, we show that hybridization gives rise to well-behaved log…Read more
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231Computational semanticsTheoria 18 (1): 27-45. 2003.In this article we discuss what constitutes a good choice of semantic representation, compare different approaches of constructing semantic representations for fragments of natural language, and give an overview of recent methods for employing inference engines for natural language understanding tasks
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68Arthur Prior and ‘Now’Synthese 193 (11). 2016.On the 4th of December 1967, Hans Kamp sent his UCLA seminar notes on the logic of ‘now’ to Arthur N. Prior. Kamp’s two-dimensional analysis stimulated Prior to an intense burst of creativity in which he sought to integrate Kamp’s work into tense logic using a one-dimensional approach. Prior’s search led him through the work of Castañeda, and back to his own work on hybrid logic: the first made temporal reference philosophically respectable, the second made it technically feasible in a modal fra…Read more
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30Representation and inference for natural language: a first course in computational semanticsCenter for the Study of Language and Information. 2005.How can computers distinguish the coherent from the unintelligible, recognize new information in a sentence, or draw inferences from a natural language passage? Computational semantics is an exciting new field that seeks answers to these questions, and this volume is the first textbook wholly devoted to this growing subdiscipline. The book explains the underlying theoretical issues and fundamental techniques for computing semantic representations for fragments of natural language. This volume wi…Read more
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60Modal logicCambridge University Press. 2001.This modern, advanced textbook reviews modal logic, a field which caught the attention of computer scientists in the late 1970's.
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Special issue on combining logics, volume 37 (2) ofNotre Dame Journal of Formal Logic. forthcoming.
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64Reichenbach, Prior and hybrid tense logicSynthese 193 (11): 3677-3689. 2016.In this paper we argue that Prior and Reichenbach are best viewed as allies, not antagonists. We do so by combining the central insights of Prior and Reichenbach in the framework of hybrid tense logic. This overcomes a well-known defect of Reichenbach’s tense schema, namely that it gives multiple representations to sentences in the future perfect and the future-in-the-past. It also makes it easy to define an iterative schema for tense that allows for multiple points of reference, a possibility n…Read more
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65Modal Logic As Dialogical LogicSynthese 127 (1-2): 57-93. 2001.The title reflects my conviction that, viewed semantically,modal logic is fundamentally dialogical; this conviction is based on the key role played by the notion of bisimulation in modal model theory. But this dialogical conception of modal logic does not seem to apply to modal proof theory, which is notoriously messy. Nonetheless, by making use of ideas which trace back to Arthur Prior (notably the use of nominals, special proposition symbols which ‘name’ worlds) I will show how to lift the dia…Read more
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63Inference and computational semanticsJournal of Logic, Language and Information 13 (2): 117-120. 2004.
Areas of Specialization
Logic and Philosophy of Logic |