Order:
Disambiguations
J. Lambek [18]Joachim Lambek [14]Jim Lambek [2]
  1.  39
    The Mathematics of Sentence Structure.Joachim Lambek - 1958 - Journal of Symbolic Logic 65 (3):154-170.
    Direct download  
     
    Export citation  
     
    Bookmark   159 citations  
  2.  66
    Introduction to Higher Order Categorical Logic.J. Lambek & P. J. Scott - 1989 - Journal of Symbolic Logic 54 (3):1113-1114.
  3.  34
    Functional completeness of cartesian categories.J. Lambek - 1974 - Annals of Mathematical Logic 6 (3):259.
  4.  15
    Introduction to Higher Order Categorical Logic.Joachim Lambek & Philip J. Scott - 1986 - Cambridge University Press.
    In this book the authors reconcile two different viewpoints of the foundations of mathematics, namely mathematical logic and category theory. In Part I, they show that typed lambda-calculi, a formulation of higher order logic, and cartesian closed categories are essentially the same. In Part II, it is demonstrated that another formulation of higher order logic is closely related to topos theory. Part III is devoted to recursive functions. Numerous applications of the close relationship between traditional logic and the algebraic language (...)
    No categories
    Direct download  
     
    Export citation  
     
    Bookmark   9 citations  
  5.  50
    A tale of four grammars.Claudia Casadio & Joachim Lambek - 2002 - 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.
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   8 citations  
  6.  85
    Philosophical reflections on the foundations of mathematics.Jocelyne Couture & Joachim Lambek - 1991 - 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, (...)
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   4 citations  
  7.  24
    What is the world of mathematics?J. Lambek - 2004 - 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 (...)
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   4 citations  
  8.  33
    Should Pregroup Grammars be Adorned with Additional Operations?Joachim Lambek - 2007 - Studia Logica 87 (2-3):343-358.
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  9.  7
    The Heritage of Thales.W. S. Anglin & J. Lambek - 1998 - Springer Verlag.
    The authors' novel approach to some interesting mathematical concepts - not normally taught in other courses - places them in a historical and philosophical setting. Although primarily intended for mathematics undergraduates, the book will also appeal to students in the sciences, humanities and education with a strong interest in this subject. The first part proceeds from about 1800 BC to 1800 AD, discussing, for example, the Renaissance method for solving cubic and quartic equations and providing rigorous elementary proof that certain (...)
    Direct download  
     
    Export citation  
     
    Bookmark   3 citations  
  10.  30
    Exploring feature agreement in French with parallel pregroup computations.Joachim Lambek - 2010 - 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.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  11.  14
    Bilinear logic in algebra and linguistics 0).J. Lambek - 1995 - In Jean-Yves Girard, Yves Lafont & Laurent Regnier (eds.), Advances in Linear Logic. Cambridge University Press. pp. 222--43.
    Direct download  
     
    Export citation  
     
    Bookmark   2 citations  
  12.  80
    Intuitionist type theory and foundations.J. Lambek & P. J. Scott - 1981 - 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.
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  13.  13
    New proofs of some intuitionistic principles.J. Lambek & P. J. Scott - 1983 - Mathematical Logic Quarterly 29 (10):493-504.
  14. On some connections between logic and category theory.J. Lambek - 1989 - 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.
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  15.  41
    What is a deductive system?Joachim Lambek - 1994 - In Dov M. Gabbay (ed.), What is a Logical System? Oxford University Press.
  16.  58
    Logic and Grammar.Joachim Lambek - 2012 - 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.
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  17.  18
    Categories and types in logic, language, and physics: essays dedicated to Jim Lambek on the occasion of his 90th birthday.C. Casadio, Bob Coecke, Michael Moortgat, Philip Scott & Jim Lambek (eds.) - 2014 - New York: Springer.
    For more than 60 years, Jim Lambek has been a profoundly inspirational mathematician, with groundbreaking contributions to algebra, category theory, linguistics, theoretical physics, logic and proof theory. This Festschrift was put together on the occasion of his 90th birthday. The papers in it give a good picture of the multiple research areas where the impact of Jim Lambek's work can be felt. The volume includes contributions by prominent researchers and by their students, showing how Jim Lambek's ideas keep inspiring upcoming (...)
    Direct download  
     
    Export citation  
     
    Bookmark  
  18.  17
    An Extension of the Formulas-as-Types Paradigm.J. Lambek - 1997 - Dialogue 36 (1):33-.
    RésuméUn paradigme en vogue en informatique théorique exploite l'analogie entre les formules et les types et traite une deduction Al… An→ B comme une opération plurisortale. On propose ici d'étendre cette analogie aux déductions de la forme Al… An→, où la place à droite de la flèche est vide. D'un point de vue logique, une telle déduction constitue une réfutation de la conjonction desformules qui se trouvent à gauche de la flèche. On défend l'idée qu'ilfaut, selon ce paradigme étendu, interpréter (...)
    Direct download (6 more)  
     
    Export citation  
     
    Bookmark  
  19.  39
    An Exactification of the Monoid of Primitive Recursive Functions.Joachim Lambek & Philip Scott - 2005 - 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.
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark  
  20. Bilinear logic and Grishin algebras.Joachim Lambek - 1999 - In E. Orłowska (ed.), Logic at Work. Heidelberg. pp. 604--612.
  21. Dedicated to the memory of Alonzo Church.J. Lambek - 1997 - Bulletin of Symbolic Logic 3 (3).
  22.  13
    Kosta Došen. Deductive completeness. The bulletin of symbolic logic, vol. 2 , pp. 243–283.J. Lambek - 1998 - Journal of Symbolic Logic 63 (3):1185-1186.
  23.  70
    Programs, grammars and arguments: A personal view of some connections between computation, language and logic.J. Lambek - 1997 - Bulletin of Symbolic Logic 3 (3):312-328.
    As an undergraduate I was taught to multiply two numbers with the help of log tables, using the formulaHaving graduated to teach calculus to Engineers, I learned that log tables were to be replaced by slide rules. It was then that Imade the fateful decision that there was no need for me to learn how to use this tedious device, as I could always rely on the students to perform the necessary computations. In the course of time, slide rules were (...)
    Direct download (8 more)  
     
    Export citation  
     
    Bookmark  
  24.  48
    Pregroup Grammars and Chomsky’s Earliest Examples.J. Lambek - 2008 - 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.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  25.  22
    Should Pregroup Grammars Be Adorned with Additional Operations? To Michael Moortgat on His First Half Century.Joachim Lambek - 2007 - Studia Logica 87 (2-3):343 - 358.
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark  
  26. To Saunders Mac Lane on his g0th birthdag.Jim Lambek - 2004 - In Thomas Ehrhard (ed.), Linear logic in computer science. New York: Cambridge University Press. pp. 316--325.
     
    Export citation  
     
    Bookmark  
  27.  17
    An Informal Arithmetical Approach to Computability and Computation.How to Program an Infinite Abacus.Ann M. Singleterry, Z. A. Melzak & Joachim Lambek - 1966 - Journal of Symbolic Logic 31 (3):514.
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark  
  28.  39
    From word to sentence: A pregroup analysis of the object pronoun who ( M ). [REVIEW]J. Lambek - 2007 - 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).
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  29.  31
    Moortgat Michael. Categorical investigations. Logical and linguistic aspects of the Lambek calculus. Groningen-Amsterdam studies in semantics, no. 9. Foris Publications, Dordrecht and Providence 1988, xiii + 285 pp. [REVIEW]J. Lambek - 1992 - Journal of Symbolic Logic 57 (3):1143-1146.
  30. Review: Kosta Dosen, Deductive Completeness. [REVIEW]J. Lambek - 1998 - Journal of Symbolic Logic 63 (3):1185-1186.
  31.  22
    Review: Robert B. Lees, The Grammar of English Nominalizations. [REVIEW]Joachim Lambek - 1962 - Journal of Symbolic Logic 27 (2):212-213.
  32.  16
    Reviews. Robert B. Lees. The grammar of English nominalizations. Publication twelve of the Indiana University Research Center in Anthropology, Folklore, and Linguistics; also Part II of the International journal of American linguistics, vol. 26 no. 3 , xxvi + 205 pp. [REVIEW]Joachim Lambek - 1962 - Journal of Symbolic Logic 27 (2):212-213.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  33. Review: Yehoshua Bar-Hillel, Language and Information. [REVIEW]J. Lambek - 1965 - Journal of Symbolic Logic 30 (3):382-385.
  34.  32
    Yehoshua Bar-Hillel. Preface. Language and information, Selected essays on their theory and application, by Yehoshua Bar-Hillel, Addison-Wesley Publishing Company, Inc., Reading, Mass., Palo Alto, London, and The Jerusalem Academic Press Ltd., Jerusalem, Israel, 1964, pp. vii–viii. - Yehoshua Bar-Hillel. Introduction. Language and information, Selected essays on their theory and application, by Yehoshua Bar-Hillel, Addison-Wesley Publishing Company, Inc., Reading, Mass., Palo Alto, London, and The Jerusalem Academic Press Ltd., Jerusalem, Israel, 1964, pp. 1–16. - Yehoshua Bar-Hillel. On syntactical categories. A reprint of XV 220. Language and information, Selected essays on their theory and application, by Yehoshua Bar-Hillel, Addison-Wesley Publishing Company, Inc., Reading, Mass., Palo Alto, London, and The Jerusalem Academic Press Ltd., Jerusalem, Israel, 1964, pp. 19–37. - Yehoshua Bar-Hillel. Logical syntax and semantics. A reprint of XX 290. Language and information, Selected e. [REVIEW]J. Lambek - 1965 - Journal of Symbolic Logic 30 (3):382-385.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark