-
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.
-
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
-
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
-
15Modal logic and model-theoretic syntaxIn Maarten de Rijke (ed.), Advances in Intensional Logic, Kluwer Academic Publishers. pp. 29--60. 1997.
-
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
-
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
-
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
-
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
-
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.
-
Special issue on combining logics, volume 37 (2) ofNotre Dame Journal of Formal Logic. forthcoming.
-
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
-
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
-
62Inference and computational semanticsJournal of Logic, Language and Information 13 (2): 117-120. 2004.
-
51Computational SemanticsTheoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 18 (1): 27-45. 2010....
-
67Arthur Prior and Hybrid LogicSynthese 150 (3): 329-372. 2006.Contemporary hybrid logic is based on the idea of using formulas as terms, an idea invented and explored by Arthur Prior in the mid-1960s. But Prior’s own work on hybrid logic remains largely undiscussed. This is unfortunate, since hybridisation played a role that was both central to and problematic for his philosophical views on tense. In this paper I introduce hybrid logic from a contemporary perspective, and then examine the role it played in Prior’s work.
-
124Completeness in Hybrid Type TheoryJournal of Philosophical Logic (2-3): 1-30. 2013.We show that basic hybridization (adding nominals and @ operators) makes it possible to give straightforward Henkin-style completeness proofs even when the modal logic being hybridized is higher-order. The key ideas are to add nominals as expressions of type t, and to extend to arbitrary types the way we interpret $@_i$ in propositional and first-order hybrid logic. This means: interpret $@_i\alpha _a$ , where $\alpha _a$ is an expression of any type $a$ , as an expression of type $a$ that rigid…Read more
-
176Modal Logic: Graph. DarstCambridge University Press. 2001.This modern, advanced textbook reviews modal logic, a field which caught the attention of computer scientists in the late 1970's.
-
18Hybrid completenessLogic Journal of the IGPL 6 (4): 625-650. 1998.In this paper we discuss two hybrid languages, ℒ and ℒ, and provide them with complete axiomatizations. Both languages combine features of modal and classical logic. Like modal languages, they contain modal operators and have a Kripke semantics. Unlike modal languages, in these systems it is possible to 'label' states by using A and ↓ to bind special state variables.This paper explores the consequences of hybridization for completeness. As we shall show, the challenge is to blend the modal idea …Read more
-
29Linguistics, Logic and Finite TreesLogic Journal of the IGPL 2 (1): 3-29. 1994.A modal logic is developed to deal with finite ordered binary trees a they are used in linguistics. A modal language is introduced with operators for the ‘mother of’, ‘first daughter of’ and ‘second daughter of’ relations together with their transitive reflexive closures. The relevant class of tree models is defined and three linguistic applications of this language are discussed: context free grammars, command relations, and trees decorated with feature structures. An axiomatic proof system is …Read more
-
Characterization, Interpolation and Complexity, by Carlos Areces, Patrick Blackburn and Maarten MarxJournal of Symbolic Logic 66 (3): 977-1010. 2001.
-
26Zooming 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.
Areas of Specialization
Logic and Philosophy of Logic |