-
16Hybrid Type Theory: A Quartet in Four Movements DOI:10.5007/1808-1711.2011v15n2p225Principia: An International Journal of Epistemology 15 (2): 225-247. 2011.This paper sings a song — a song created by bringing together the work of four great names in the history of logic: Hans Reichenbach, Arthur Prior, Richard Montague, and Leon Henkin. Although the work of the first three of these authors have previously been combined, adding the ideas of Leon Henkin is the addition required to make the combination work at the logical level. But the present paper does not focus on the underlying technicalities rather it focusses on the underlying instruments, and …Read more
-
83Pure Extensions, Proof Rules, and Hybrid AxiomaticsStudia Logica 84 (2): 277-322. 2006.In this paper we argue that hybrid logic is the deductive setting most natural for Kripke semantics. We do so by investigating hybrid axiomatics for a variety of systems, ranging from the basic hybrid language (a decidable system with the same complexity as orthodox propositional modal logic) to the strong Priorean language (which offers full first-order expressivity).We show that hybrid logic offers a genuinely first-order perspective on Kripke semantics: it is possible to define base logics wh…Read more
-
44Why Combine Logics?Studia Logica 59 (1). 1997.Combining logics has become a rapidly expanding enterprise that is inspired mainly by concerns about modularity and the wish to join together tailor made logical tools into more powerful but still manageable ones. A natural question is whether it offers anything new over and above existing standard languages. By analysing a number of applications where combined logics arise, we argue that combined logics are a potentially valuable tool in applied logic, and that endorsements of standard language…Read more
-
32Rich ontologies for tense and aspectIn Jerry Seligman & Dag Westerstahl (eds.), Logic, Language and Computation, Center For the Study of Language and Inf. 1996.In this paper back-and-forth structures are applied to the semantics of natural language. Back-and-forth structures consist of an event structure and an interval structure communicating via a relational link; transitions in the one structure correspond to transitions in the other. Such entities enable us to view temporal constructions (such as tense, aspect, and temporal connectives) as methods of moving systematically between information sources. We illustrate this with a treatment of the Engli…Read more
-
95Hybrid Type Theory: A Quartet in Four MovementsPrincipia: An International Journal of Epistemology 15 (2): 225. 2011.Este artigo canta uma canção — uma canção criada ao unir o trabalho de quatro grandes nomes na história da lógica: Hans Reichenbach, Arthur Prior, Richard Montague, e Leon Henkin. Embora a obra dos primeiros três desses autores tenha sido previamente combinada, acrescentar as ideias de Leon Henkin é o acréscimo requerido para fazer com que essa combinação funcione no nível lógico. Mas o presente trabalho não se concentra nas tecnicalidades subjacentes (que podem ser encontradas em Areces, Blackb…Read more
-
93Modal logic: A semantic perspectiveEthics 98 501-517. 1988.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2 BASIC MODAL LOGIC . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.
-
87Hybrid languagesJournal of Logic, Language and Information 4 (3): 251-272. 1995.Hybrid languages have both modal and first-order characteristics: a Kripke semantics, and explicit variable binding apparatus. This paper motivates the development of hybrid languages, sketches their history, and examines the expressive power of three hybrid binders. We show that all three binders give rise to languages strictly weaker than the corresponding first-order language, that full first-order expressivity can be gained by adding the universal modality, and that all three binders can for…Read more
-
18Editors' IntroductionNotre Dame Journal of Formal Logic 37 (2): 161-166. 1996.The idea of combining logics, structures, and theories has recently been attracting interest in areas as diverse as constraint logic programming, theorem proving, verification, computational linguistics, artificial intelligence and indeed, various branches of logic itself. It would be an exaggeration to claim that these (scattered, and by-and-large independent) investigations have crystallized into an enterprise meriting the title "combined methods"; nonetheless, a number of interesting themes a…Read more
-
69Constructive interpolation in hybrid logicJournal of Symbolic Logic 68 (2): 463-480. 2003.Craig's interpolation lemma (if φ → ψ is valid, then φ → θ and θ → ψ are valid, for θ a formula constructed using only primitive symbols which occur both in φ and ψ) fails for many propositional and first order modal logics. The interpolation property is often regarded as a sign of well-matched syntax and semantics. Hybrid logicians claim that modal logic is missing important syntactic machinery, namely tools for referring to worlds, and that adding such machinery solves many technical problems.…Read more
-
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
-
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
-
25Introduction: Static and dynamic aspects of syntactic structure (review)Journal of Logic, Language and Information 4 (1): 1-4. 1995.
-
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.
-
160Remarks 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
-
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
Areas of Specialization
Logic and Philosophy of Logic |