Patrick Blackburn Roskilde University
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  1.  5
    Loredana Afanasiev, Patrick Blackburn, Ioanna Dimitriou, Gaiffe Evan, Goris Maarten & Marx Maarten (forthcoming). Rijke. PDL for Ordered Trees. Journal of Applied Non-Classical Logics.
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  2.  4
    Patrick Blackburn & Maarten De Rijke (forthcoming). Rijke. Zooming in, Zooming Out. Journal of Logic, Language and Information.
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  3.  6
    Patrick Blackburn & Klaus Frovin Jørgensen (forthcoming). Arthur Prior and ‘Now’. Synthese:1-12.
    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 (...)
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  4.  3
    Patrick Blackburn & Klaus Frovin Jørgensen (forthcoming). Reichenbach, Prior and Hybrid Tense Logic. Synthese:1-13.
    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 noted (...)
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  5. M. de Rijke & P. Blackburn (forthcoming). Special Issue on Combining Logics, Volume 37 (2) Of. Notre Dame Journal of Formal Logic.
     
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  6.  54
    Carlos Areces, Patrick Blackburn, Antonia Huertas & María Manzano (2013). Completeness in Hybrid Type Theory. Journal of Philosophical Logic (2-3):1-30.
    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 (...)
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  7.  8
    Carlos Areces, Patrick Blackburn, Antonia Huertas & María Manzano (2012). Hybrid Type Theory: A Quartet in Four Movements. Principia 15 (2):225.
    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, Blackburn, Huertas, e (...)
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  8. Carlos Areces, Patrick Blackburn, Antonia Huertas & María Manzano (2012). Hybrid Type Theory: A Quartet in Four Movements DOI:10.5007/1808-1711.2011v15n2p225. Principia: An International Journal of Epistemology 15 (2).
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  9.  60
    Patrick Blackburn, Johan van Benthem & Frank Wolter (eds.) (2007). Handbook of Modal Logic. Elsevier.
    The Handbook of Modal Logic contains 20 articles, which collectively introduce contemporary modal logic, survey current research, and indicate the way in which the field is developing. The articles survey the field from a wide variety of perspectives: the underling theory is explored in depth, modern computational approaches are treated, and six major applications areas of modal logic (in Mathematics, Computer Science, Artificial Intelligence, Linguistics, Game Theory, and Philosophy) are surveyed. The book contains both well-written expository articles, suitable for beginners (...)
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  10.  19
    P. Blackburn & B. ten Cate (2006). Pure Extensions, Proof Rules, and Hybrid Axiomatics. Studia Logica 84 (2):277 - 322.
    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 which extend automatically to a (...)
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  11.  32
    Patrick Blackburn (2006). Arthur Prior and Hybrid Logic. Synthese 150 (3):329 - 372.
    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.
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  12.  1
    Patrick Blackburn (2006). Arthur Prior and Hybrid Logic. Synthese 150 (3):329-372.
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  13.  19
    Patrick Blackburn & Balder Ten Cate (2006). Pure Extensions, Proof Rules, and Hybrid Axiomatics. Studia Logica 84 (2):277-322.
    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 to the strong Priorean language . We show that hybrid logic offers a genuinely first-order perspective on Kripke semantics: it is possible to define base logics which extend automatically to a wide variety of frame classes and to prove completeness using the Henkin method. In the (...)
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  14.  61
    Loredana Afanasiev, Patrick Blackburn, Ioanna Dimitriou, Bertrand Gaiffe, Evan Goris, Maarten Marx & Maarten de Rijke (2005). PDL for Ordered Trees. Journal of Applied Non-Classical Logics 15 (2):115-135.
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  15.  4
    Patrick Blackburn (2005). Instructions for Authors. Journal of Logic, Language and Information 14 (1):491-496.
  16. Patrick Blackburn (2005). Instructions for Authors. Journal of Logic, Language and Information 14 (1):127-132.
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  17. Patrick Blackburn (2005). Representation and Inference for Natural Language: A First Course in Computational Semantics. Center for the Study of Language and Information.
    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 will be an essential text for computer scientists, linguists, and anyone (...)
     
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  18.  5
    G. Allwein, C. Areces, G. Ben-Avi, R. la BerkBernardi, P. Blackburn, J. Bos, T. Braüner, J. M. Castano & R. Cooper (2004). Index of Authors of Volume 13. Journal of Logic, Language and Information 13 (535):535-535.
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  19. Patrick Blackburn (2004). Modal Logic As Dialogical Logic. Synthese 127 (1):57-93.
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  20.  31
    Patrick Blackburn & Michael Kohlhase (2004). Inference and Computational Semantics. Journal of Logic, Language and Information 13 (2):117-120.
  21. C. Areces, P. Blackburn, M. Marx, S. Cook, A. Kolokolova, T. Coquand, G. Sambin, J. Smith, S. Valentini & P. Dybjer (2003). Ardeshir, M., Ruitenburg, W. And Salehi, S., Intuitionistic. Annals of Pure and Applied Logic 124:301.
     
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  22.  5
    Carlos Areces, Patrick Blackburn & Maarten Marx (2003). Repairing the Interpolation Theorem in Quantified Modal Logic. Annals of Pure and Applied Logic 124 (1-3):287-299.
    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 interpolation property, (...)
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  23. P. Blackburn, C. Ghidini, R. Turner & F. Giunchiglia (eds.) (2003). Proceedings of the Fourth International and Interdisciplinary Conference on Modeling and Using Context (CONTEXT'03), Lecture Notes in Artificial Intelligence, Vol. 2680. Springer.
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  24.  53
    Patrick Blackburn & Johan Bos (2003). Computational Semantics. Theoria 18 (1):27-45.
    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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  25.  15
    Patrick Blackburn & Maarten Marx (2003). Constructive Interpolation in Hybrid Logic. Journal of Symbolic Logic 68 (2):463-480.
    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 (...)
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  26.  7
    P. Blackburn, A. Bochman, T. Clausing, P. Dekker, J. Engelfriet, D. M. Gabbay, F. Giunchiglia, J. M. Goñimenoyo, G. Jäger & T. M. V. Janssen (2002). Index of Authors of Volume 11. Journal of Logic, Language and Information 11 (519):519.
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  27. P. Blackburn, M. De Rijke, Y. Venema & Marcus Kracht (2002). REVIEWS-Modal Logic. Bulletin of Symbolic Logic 8 (2):299-300.
     
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  28.  21
    Patrick Blackburn (2002). Editorial. Journal of Logic, Language and Information 11 (1):1-1.
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  29.  32
    Patrick Blackburn (2002). Modal Logic: Graph. Darst. Cambridge University Press.
    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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  30.  39
    Patrick Blackburn, Maarten de Rijke & Yde Venema (2002). Modal Logic. Cambridge University Press.
    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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  31.  44
    Patrick Blackburn & Maarten Marx (2002). Remarks on Gregory's “Actually” Operator. Journal of Philosophical Logic 31 (3):281-288.
    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" operator with the work of Arthur Prior now known under (...)
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  32.  23
    Carlos Areces, Patrick Blackburn & Maarten Marx (2001). Hybrid Logics: Characterization, Interpolation and Complexity. Journal of Symbolic Logic 66 (3):977-1010.
    Hybrid languages are expansions of propositional modal languages which can refer to (or even quantify over) worlds. The use of strong hybrid languages dates back to at least [Pri67], but recent work (for example [BS98, BT98a, BT99]) has focussed on a more constrained system called $\mathscr{H}(\downarrow, @)$ . We show in detail that $\mathscr{H}(\downarrow, @)$ is modally natural. We begin by studying its expressivity, and provide model theoretic characterizations (via a restricted notion of Ehrenfeucht-Fraisse game, and an enriched notion of (...)
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  33.  63
    Patrick Blackburn (2001). Modal Logic as Dialogical Logic. Synthese 127 (1-2):57 - 93.
    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 dialogical (...)
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  34. Patrick Blackburn (2001). Third International Workshop on Hybrid Logic. Logic Journal of the Igpl 9 (5):735-737.
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  35. Patrick Blackburn, Nick Braisby, Lawrence Cavedon & Atsushi Shimojima (eds.) (2001). Logic, Language and Computation, Volume 3. Center for the Study of Language and Inf.
    With the rise of the internet and the proliferation of technology to gather and organize data, our era has been defined as "the information age." With the prominence of information as a research concept, there has arisen an increasing appreciation of the intertwined nature of fields such as logic, linguistics, and computer science that answer the questions about information and the ways it can be processed. The many research traditions do not agree about the exact nature of information. By bringing (...)
     
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  36. Patrick Blackburn & Maarten Marx Hybrid Logic (2001). Characterization, Interpolation and Complexity, by Carlos Areces, Patrick Blackburn and Maarten Marx. Journal of Symbolic Logic 66 (3):977-1010.
     
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  37.  4
    S. Aguzzoli, V. Akman, A. D. C. Bennett, P. Blackburn, S. Bringsjord, C. Caporale, A. Ciabattoni, B. J. Copeland, S. Demri & D. Dubois (2000). Index of Authors of Volume 9. Journal of Logic, Language, and Information 9 (519):519.
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  38. Varol Akman & Patrick Blackburn (2000). Editorial: Alan Turing and Artificial Intelligence. [REVIEW] Journal of Logic, Language and Information 9 (4):391-395.
    Department of Computer Engineering, Bilkent University, 06533 Ankara, Turkey E-mail: akman@cs.bilkent.edu.tr; http://www.cs.bilkent.edu.tr/?akman..
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  39.  1
    C. Areces, P. Blackburn & M. Marx (2000). The Computational Complexity of Hybrid Temporal Logics. Logic Journal of the Igpl 8 (5):653-679.
    In their simplest form, hybrid languages are propositional modal languages which can refer to states. They were introduced by Arthur Prior, the inventor of tense logic, and played an important role in his work: because they make reference to specific times possible, they remove the most serious obstacle to developing modal approaches to temporal representation and reasoning. However very little is known about the computational complexity of hybrid temporal logics.In this paper we analyze the complexity of the satisfiability problem of (...)
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  40. P. Blackburn (2000). Representation, Reasoning, and Relational Structures: A Hybrid Logic Manifesto. Logic Journal of the Igpl 8 (3):339-365.
    This paper is about the good side of modal logic, the bad side of modal logic, and how hybrid logic takes the good and fixes the bad.In essence, modal logic is a simple formalism for working with relational structures . But modal logic has no mechanism for referring to or reasoning about the individual nodes in such structures, and this lessens its effectiveness as a representation formalism. In their simplest form, hybrid logics are upgraded modal logics in which reference to (...)
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  41.  7
    B. Aldag, G. Antoniou, T. Aoto, P. Blackburn, K. Britz, M. Brown, A. Bundy, R. Cox, M. De Rijke & S. Demri (1999). Index of Authors of Volume 8. Journal of Logic, Language, and Information 8 (485):485.
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  42.  1
    P. Blackburn & M. Tzakova (1999). Hybrid Languages and Temporal Logic. Logic Journal of the Igpl 7 (1):27-54.
    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 (...)
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  43.  32
    Patrick Blackburn (1999). Basic Model Theory, Kees Doets. Journal of Logic, Language and Information 8 (2):258-261.
  44.  4
    Patrick Blackburn (1999). Upcoming Themes. Journal of Logic, Language and Information 8 (2):263-263.
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  45.  1
    P. Blackburn & M. Tzakova (1998). Hybrid Completeness. Logic Journal of the Igpl 6 (4):625-650.
    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 of (...)
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  46. P. Blackburn (1997). Reinhard Muskens, Meaning and Partiality. Journal of Logic Language and Information 6:353-355.
     
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  47.  11
    Patrick Blackburn (1997). Book Review. [REVIEW] Journal of Logic, Language and Information 6 (3):353-355.
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  48.  8
    Patrick Blackburn & Maarten de Rijke (1997). Why Combine Logics? Studia Logica 59 (1):5-27.
    Combining logics has become a rapidly expanding entreprise 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 languages often miss the point. Using (...)
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  49.  19
    Patrick Blackburn & Maarten de Rijke (1997). Zooming in, Zooming Out. Journal of Logic, Language and Information 6 (1):5-31.
    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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  50.  4
    Patrick Blackburn & Wilfried Meyer-Viol (1997). Modal Logic and Model-Theoretic Syntax. In M. de Rijke (ed.), Advances in Intensional Logic. Kluwer 29--60.
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  51.  3
    Patrick Blackburn & Maarten de Rijke (1997). Why Combine Logics? Studia Logica 59 (1):5 - 27.
    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 languages often miss the point. (...)
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  52.  4
    Patrick Blackburn & Maarten de Rijke (1996). Editors' Introduction. Notre Dame Journal of Formal Logic 37 (2):161-166.
    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 are emerging. This introduction notes some prominent ones and relates them to the papers in this (...)
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  53.  17
    Patrick Blackburn, Claire Gardent & Maarten De Rijke (1996). Rich Ontologies for Tense and Aspect. In Jerry Seligman & Dag Westerståhl (eds.), Logic, Language and Computation. Csli Publications, Stanford
  54. Patrick Blackburn & Maarten de Rijke (1996). Special Issue on Combining Logics - Editor's Introduction. Notre Dame Journal of Formal Logic 37 (2):161-166.
     
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  55.  5
    Patrick Blackburn (1995). Introduction: Static and Dynamic Aspects of Syntactic Structure. [REVIEW] Journal of Logic, Language and Information 4 (1):1-4.
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  56.  18
    Patrick Blackburn & Jerry Seligman (1995). Hybrid Languages. Journal of Logic, Language and Information 4 (3):251-272.
    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 force the existence of infinite models and (...)
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  57.  10
    Patrick Blackburn & Yde Venema (1995). Dynamic Squares. Journal of Philosophical Logic 24 (5):469 - 523.
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  58.  26
    Patrick Blackburn (1994). Tense, Temporal Reference, and Tense Logic. Journal of Semantics 11 (1-2):83-101.
    This paper examines extensions of Priorean tense logic in which reference to rimes is possible. The key technical idea is to sort the atomic symbols of Prior's language and to impose different interpretational restrictions on the different sorts. Among the sorts introduced are nominals (which permit Reichenbachian analyses of tense and tense-in-texts to be reconstructed in tense logic) and sorts which mimic temporal indexicals and calendar terms. The possibilities raised by sorting richer systems are briefly discussed.
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  59. Patrick Blackburn, Frank Beckman & Gabriel Falkenberg (1994). _]() Urnal of Semantics. Journal of Semantics 11.
     
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  60.  11
    Patrick Blackburn & Wilfried Meyer-Viol (1994). Linguistics, Logic and Finite Trees. Logic Journal of the IGPL 2 (1):3-29.
    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 given for which completeness is (...)
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  61.  24
    Patrick Blackburn & Edith Spaan (1993). A Modal Perspective on the Computational Complexity of Attribute Value Grammar. Journal of Logic, Language and Information 2 (2):129-169.
    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, and the ability to express recursive constraints. Two main (...)
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  62. P. Blackburn (1992). La Logique de L'Argumentation: Développement Et Perspectives. Philosopher: revue pour tous 12:41-58.
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  63.  6
    Patrick Blackburn (1992). Nominal Tense Logic. Notre Dame Journal of Formal Logic 34 (1):56-83.
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  64. P. Blackburn (1991). La «nouvelle» épistémologie et ses conséquences sur le plan didactique. Philosopher: revue pour tous 11:117-126.
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  65. P. Blackburn (1989). An Evaluation of Ethical Theories. Revue Internationale de Philosophie 43 (170):379-389.
     
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  66.  47
    Patrick Blackburn & Johan van Benthem (1988). Modal Logic: A Semantic Perspective. Ethics 98:501-517.
    . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2 BASIC MODAL LOGIC . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.
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