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J. Lambek [14]Joachim Lambek [10]Jim Lambek [1]
  1. Joachim Lambek (2012). Logic and Grammar. Studia Logica 100 (4):667-681.
    Grammar can be formulated as a kind of substructural propositional logic. In support of this claim, we survey bare Gentzen style deductive systems and two kinds of non-commutative linear logic: intuitionistic and compact bilinear logic. We also glance at their categorical refinements.
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  2. Joachim Lambek (2010). Exploring Feature Agreement in French with Parallel Pregroup Computations. Journal of Logic, Language and Information 19 (1):75-88.
    One way of coping with agreement of features in French is to perform two parallel computations, one in the free pregroup of syntactic types, the other in that of feature types. Technically speaking, this amounts to working in the direct product of two free pregroups.
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  3. J. Lambek (2008). Pregroup Grammars and Chomsky's Earliest Examples. Journal of Logic, Language and Information 17 (2):141-160.
    Pregroups are partially ordered monoids in which each element has two “adjoints”. Pregroup grammars provide a computational approach to natural languages by assigning to each word in the mental dictionary a type, namely an element of the pregroup freely generated by a partially ordered set of basic types. In this expository article, the attempt is made to introduce linguists to a pregroup grammar of English by looking at Chomsky’s earliest examples.
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  4. J. Lambek (2007). From Word to Sentence: A Pregroup Analysis of the Object Pronoun Who ( M ). [REVIEW] Journal of Logic, Language and Information 16 (3):303-323.
    We explore a computational algebraic approach to grammar via pregroups, that is, partially ordered monoids in which each element has both a left and a right adjoint. Grammatical judgements are formed with the help of calculations on types. These are elements of the free pregroup generated by a partially ordered set of basic types, which are assigned to words, here of English. We concentrate on the object pronoun who(m).
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  5. Joachim Lambek (2007). Should Pregroup Grammars Be Adorned with Additional Operations? Studia Logica 87 (2-3):343 - 358.
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  6. Joachim Lambek (2007). Should Pregroup Grammars Be Adorned with Additional Operations? To Michael Moortgat on His First Half Century. Studia Logica 87 (2/3):343 - 358.
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  7. Joachim Lambek & Philip Scott (2005). An Exactification of the Monoid of Primitive Recursive Functions. Studia Logica 81 (1):1 - 18.
    We study the monoid of primitive recursive functions and investigate a onestep construction of a kind of exact completion, which resembles that of the familiar category of modest sets, except that the partial equivalence relations which serve as objects are recursively enumerable. As usual, these constructions involve the splitting of symmetric idempotents.
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  8. J. Lambek (2004). What is the World of Mathematics? Annals of Pure and Applied Logic 126 (1-3):149-158.
    It may be argued that the language of mathematics is about the category\nof sets, although the definite article requires some justification.\nAs possible worlds of mathematics we may admit all models of type\ntheory, by which we mean all local toposes. For an intuitionist,\nthere is a distinguished local topos, namely the so-called free topos,\nwhich may be constructed as the Tarski–Lindenbaum category of intuitionistic\ntype theory. However, for a classical mathematician, to pick a distinguished\nmodel may be as difficult as to define the notion of (...)
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  9. Jim Lambek (2004). To Saunders Mac Lane on His G0th Birthdag. In Thomas Ehrhard (ed.), Linear Logic in Computer Science. Cambridge University Press. 316--325.
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  10. Claudia Casadio & Joachim Lambek (2002). A Tale of Four Grammars. Studia Logica 71 (3):315-329.
    In this paper we consider the relations existing between four deductive systems that have been called categorial grammars and have relevant connections with linguistic investigations: the syntactic calculus, bilinear logic, compact bilinear logic and Curry''s semantic calculus.
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  11. Joachim Lambek (1999). Bilinear Logic and Grishin Algebras. In E. Orłowska (ed.), Logic at Work. Heidelberg. 604--612.
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  12. J. Lambek (1998). Review: Kosta Dosen, Deductive Completeness. [REVIEW] Journal of Symbolic Logic 63 (3):1185-1186.
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  13. J. Lambek (1997). An Extension of the Formulas-as-Types Paradigm. Dialogue 36 (01):33-.
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  14. J. Lambek (1997). Dedicated to the Memory of Alonzo Church. Bulletin of Symbolic Logic 3 (3).
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  15. J. Lambek (1997). Programs, Grammars and Arguments: A Personal View of Some Connections Between Computation, Language and Logic. Bulletin of Symbolic Logic 3 (3):312-328.
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  16. J. Lambek (1995). Bilinear Logic in Algebra and Linguistics 0). In Jean-Yves Girard, Yves Lafont & Laurent Regnier (eds.), Advances in Linear Logic. Cambridge University Press. 222--43.
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  17. Joachim Lambek (1994). What is a Deductive System? In Dov M. Gabbay (ed.), What is a Logical System? Oxford University Press.
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  18. J. Lambek (1992). Review: Michael Moortgat, Categorical Investigations. Logical and Linguistic Aspects of the Lambek Calculus. [REVIEW] Journal of Symbolic Logic 57 (3):1143-1146.
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  19. Jocelyne Couture & Joachim Lambek (1991). Philosophical Reflections on the Foundations of Mathematics. Erkenntnis 34 (2):187 - 209.
    This article was written jointly by a philosopher and a mathematician. It has two aims: to acquaint mathematicians with some of the philosophical questions at the foundations of their subject and to familiarize philosophers with some of the answers to these questions which have recently been obtained by mathematicians. In particular, we argue that, if these recent findings are borne in mind, four different basic philosophical positions, logicism, formalism, platonism and intuitionism, if stated with some moderation, are in fact reconcilable, (...)
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  20. J. Lambek (1989). On Some Connections Between Logic and Category Theory. Studia Logica 48 (3):269 - 278.
    Categories may be viewed as deductive systems or as algebraic theories. We are primarily interested in the interplay between these two views and trace it through a number of structured categories and their internal languages, bearing in mind their relevance to the foundations of mathematics. We see this as a common thread running through the six contributions to this issue of Studia Logica.
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  21. J. Lambek & P. J. Scott (1983). New Proofs of Some Intuitionistic Principles. Mathematical Logic Quarterly 29 (10):493-504.
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  22. J. Lambek & P. J. Scott (1981). Intuitionist Type Theory and Foundations. Journal of Philosophical Logic 10 (1):101 - 115.
    A version of intuitionistic type theory is presented here in which all logical symbols are defined in terms of equality. This language is used to construct the so-called free topos with natural number object. It is argued that the free topos may be regarded as the universe of mathematics from an intuitionist's point of view.
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  23. J. Lambek (1974). Functional Completeness of Cartesian Categories. Annals of Mathematical Logic 6 (3-4):259-292.
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  24. J. Lambek (1965). Review: Yehoshua Bar-Hillel, Language and Information. [REVIEW] Journal of Symbolic Logic 30 (3):382-385.
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  25. Joachim Lambek (1962). Review: Robert B. Lees, The Grammar of English Nominalizations. [REVIEW] Journal of Symbolic Logic 27 (2):212-213.
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