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  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. Joachim Lambek (2007). Should Pregroup Grammars Be Adorned with Additional Operations? Studia Logica 87 (2-3):343 - 358.
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  4. 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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  5. 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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  6. 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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  7. Joachim Lambek (1999). Bilinear Logic and Grishin Algebras. In E. Orłowska (ed.), Logic at Work. Heidelberg. 604--612.
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  8. 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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  9. 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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  10. 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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