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Patrick Blackburn
Roskilde University
  1. Modal Logic.Patrick Blackburn, Maarten de Rijke & Yde Venema - 2002 - 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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  2.  85
    Handbook of Modal Logic.Patrick Blackburn, Johan van Benthem & Frank Wolter (eds.) - 2006 - 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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  3.  99
    Arthur Prior and Hybrid Logic.Patrick Blackburn - 2006 - 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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  4.  63
    Hybrid Logics: Characterization, Interpolation and Complexity.Carlos Areces, Patrick Blackburn & Maarten Marx - 2001 - Journal of Symbolic Logic 66 (3):977-1010.
    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-order logic which is invariant for generated (...)
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  5.  50
    Hybrid Languages.Patrick Blackburn & Jerry Seligman - 1995 - 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 have undecidable satisfiability (...)
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  6.  9
    Representation and Inference for Natural Language: A First Course in Computational Semantics.Patrick Blackburn - 2005 - 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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  7.  65
    Modal Logic: A Semantic Perspective.Patrick Blackburn & Johan van Benthem - 1988 - Ethics 98:501-517.
    . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2 BASIC MODAL LOGIC . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.
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  8.  88
    Pure Extensions, Proof Rules, and Hybrid Axiomatics.Patrick Blackburn & Balder Ten Cate - 2006 - 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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  9.  8
    Representation, Reasoning, and Relational Structures: A Hybrid Logic Manifesto.P. Blackburn - 2000 - 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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  10.  22
    Nominal Tense Logic.Patrick Blackburn - 1992 - Notre Dame Journal of Formal Logic 34 (1):56-83.
  11.  18
    The Computational Complexity of Hybrid Temporal Logics.C. Areces, P. Blackburn & M. Marx - 2000 - 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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  12.  41
    Tense, Temporal Reference, and Tense Logic.Patrick Blackburn - 1994 - 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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  13.  17
    Completeness in Hybrid Type Theory.Carlos Areces, Patrick Blackburn, Antonia Huertas & María Manzano - 2014 - Journal of Philosophical Logic 43 (2-3):209-238.
    We show that basic hybridization 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 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}[email protected]_i$\end{document} in propositional and first-order hybrid logic. This means: interpret \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}[email protected]_i\alpha _a$\end{document}, where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} (...)
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  14.  99
    Completeness in Hybrid Type Theory.Carlos Areces, Patrick Blackburn, Antonia Huertas & María Manzano - 2013 - 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 [email protected]_i$ in propositional and first-order hybrid logic. This means: interpret [email protected]_i\alpha _a$ , where $\alpha _a$ is an expression of any type $a$ , as an expression of type $a$ that (...)
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  15.  11
    Hybrid Languages and Temporal Logic.P. Blackburn & M. Tzakova - 1999 - 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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  16.  34
    Repairing the Interpolation Theorem in Quantified Modal Logic.Carlos Areces, Patrick Blackburn & Maarten Marx - 2003 - 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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  17.  50
    Why Combine Logics?Patrick Blackburn & Maarten de Rijke - 1997 - 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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  18.  22
    Linguistics, Logic and Finite Trees.Patrick Blackburn & Wilfried Meyer-Viol - 1994 - 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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  19. Remarks on Gregory's “Actually” Operator.Patrick Blackburn & Maarten Marx - 2002 - 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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  20.  49
    Arthur Prior and ‘Now’.Patrick Blackburn & Klaus Frovin Jørgensen - 2016 - Synthese 193 (11).
    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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  21. Modal Logic As Dialogical Logic.Patrick Blackburn - 2001 - Synthese 127 (1):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 I will show how to lift the dialogical conception to modal proof theory. I argue that this shift (...)
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  22.  74
    A Modal Perspective on the Computational Complexity of Attribute Value Grammar.Patrick Blackburn & Edith Spaan - 1993 - 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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  23.  30
    Reichenbach, Prior and Hybrid Tense Logic.Patrick Blackburn & Klaus Frovin Jørgensen - 2016 - Synthese 193 (11):3677-3689.
    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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  24.  89
    PDL for Ordered Trees.Loredana Afanasiev, Patrick Blackburn, Ioanna Dimitriou, Bertrand Gaiffe, Evan Goris, Maarten Marx & Maarten de Rijke - 2005 - Journal of Applied Non-Classical Logics 15 (2):115-135.
    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 documents, we revisit the language. This renewed interest comes with a (...)
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  25.  8
    Being Deceived: Information Asymmetry in Second‐Order False Belief Tasks.Torben Braüner, Patrick Blackburn & Irina Polyanskaya - 2020 - Topics in Cognitive Science 12 (2):504-534.
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  26.  70
    Hybrid Type Theory: A Quartet in Four Movements.Carlos Areces, Patrick Blackburn, Antonia Huertas & María Manzano - 2011 - Principia: An International Journal of Epistemology 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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  27.  49
    Inference and Computational Semantics.Patrick Blackburn & Michael Kohlhase - 2004 - Journal of Logic, Language and Information 13 (2):117-120.
  28.  40
    Constructive Interpolation in Hybrid Logic.Patrick Blackburn & Maarten Marx - 2003 - 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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  29.  5
    Hybrid Completeness.P. Blackburn & M. Tzakova - 1998 - 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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  30.  28
    Dynamic Squares.Patrick Blackburn & Yde Venema - 1995 - Journal of Philosophical Logic 24 (5):469 - 523.
  31.  16
    Zooming in, Zooming Out.Patrick Blackburn & Maarten De Rijke - 1997 - 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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  32.  49
    Modal Logic: Graph. Darst.Patrick Blackburn - 2002 - 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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  33.  33
    Zooming in, Zooming Out.Patrick Blackburn & Maarten de Rijke - 1997 - 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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  34. Rich Ontologies for Tense and Aspect.Patrick Blackburn, Claire Gardent & Maarten De Rijke - 1996 - In Jerry Seligman & Dag Westerståhl (eds.), Logic, Language and Computation. CSLI Publications.
    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 English present perfect, and progressive aspect, that draws on ideas (...)
     
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  35.  10
    Modal Logic and Model-Theoretic Syntax.Patrick Blackburn & Wilfried Meyer-Viol - 1997 - In M. de Rijke (ed.), Advances in Intensional Logic. Kluwer Academic Publishers. pp. 29--60.
  36.  19
    Introduction: Static and Dynamic Aspects of Syntactic Structure. [REVIEW]Patrick Blackburn - 1995 - Journal of Logic, Language and Information 4 (1):1-4.
  37.  1
    Indexical Hybrid Tense Logic.Patrick Blackburn & Klaus Frovin Jørgensen - 2012 - In Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic. CSLI Publications. pp. 144-160.
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  38.  22
    Index of Authors of Volume 8.B. Aldag, G. Antoniou, T. Aoto, P. Blackburn, K. Britz, M. Brown, A. Bundy, R. Cox, M. De Rijke & S. Demri - 1999 - Journal of Logic, Language, and Information 8 (485):485.
  39.  24
    Rijke. PDL for Ordered Trees.Loredana Afanasiev, Patrick Blackburn, Ioanna Dimitriou, Gaiffe Evan, Goris Maarten & Marx Maarten - forthcoming - Journal of Applied Non-Classical Logics.
  40. Index of Authors of Volume 9.S. Aguzzoli, V. Akman, A. D. C. Bennett, P. Blackburn, S. Bringsjord, C. Caporale, A. Ciabattoni, B. J. Copeland, S. Demri & D. Dubois - 2000 - Journal of Logic, Language, and Information 9 (519):519.
     
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  41. Editorial: Alan Turing and Artificial Intelligence. [REVIEW]Varol Akman & Patrick Blackburn - 2000 - Journal of Logic, Language and Information 9 (4):391-395.
    Department of Computer Engineering, Bilkent University, 06533 Ankara, Turkey E-mail: [email protected]; http://www.cs.bilkent.edu.tr/?akman..
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  42.  20
    Index of Authors of Volume 13.G. Allwein, C. Areces, G. Ben-Avi, R. la BerkBernardi, P. Blackburn, J. Bos, T. Braüner, J. M. Castano & R. Cooper - 2004 - Journal of Logic, Language and Information 13 (535):535-535.
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  43. Ardeshir, M., Ruitenburg, W. And Salehi, S., Intuitionistic.C. Areces, P. Blackburn, M. Marx, S. Cook, A. Kolokolova, T. Coquand, G. Sambin, J. Smith, S. Valentini & P. Dybjer - 2003 - Annals of Pure and Applied Logic 124:301.
  44.  5
    Special Issue on Hybrid Logics.Carlos Areces & Patrick Blackburn - 2010 - Journal of Applied Logic 8 (4):303-304.
  45.  5
    Hybrid Type Theory: A Quartet in Four Movements DOI:10.5007/1808-1711.2011v15n2p225.Carlos Areces, Patrick Blackburn, Antonia Huertas & María Manzano - 2011 - Principia: An International Journal of Epistemology 15 (2):225-247.
    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 (...)
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  46. An Evaluation of Ethical Theories.P. Blackburn - 1989 - Revue Internationale de Philosophie 43 (170):379-389.
     
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  47.  43
    Basic Model Theory, Kees Doets.Patrick Blackburn - 1999 - Journal of Logic, Language and Information 8 (2):258-261.
  48.  18
    Book Review. [REVIEW]Patrick Blackburn - 1997 - Journal of Logic, Language and Information 6 (3):353-355.
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  49. Characterization, Interpolation and Complexity, by Carlos Areces, Patrick Blackburn and Maarten Marx.Patrick Blackburn & Maarten Marx Hybrid Logic - 2001 - Journal of Symbolic Logic 66 (3):977-1010.
     
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  50. Claude Lagadec, La morale de la liberté, ses bases biologiques Reviewed by.Pierre Blackburn - 1986 - Philosophy in Review 6 (9):452-454.
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