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  1. Alasdair Urquhart (unknown). Review of A.-F. Schmid, Ed., Bertrand Russell, Correspondance Sur la Philosophie, la Logique Et la Politique Avec Louis Couturat. [REVIEW] Russell 22 (2).
     
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  2. Alasdair Urquhart (forthcoming). Mathematical Depth. Philosophia Mathematica:nkv004.
    The first part of the paper is devoted to surveying the remarks that philosophers and mathematicians such as Maddy, Hardy, Gowers, and Zeilberger have made about mathematical depth. The second part is devoted to the question of whether we can make the notion precise by a more formal proof-theoretical approach. The idea of measuring depth by the depth and bushiness of the proof is considered, and compared to the related notion of the depth of a chess combination.
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  3. Alasdair Urquhart (forthcoming). Pavel Pudlák. Logical Foundations of Mathematics and Computational Complexity: A Gentle Introduction. Springer Monographs in Mathematics. Springer, 2013. ISBN: 978-3-319-00118-0 ; 978-3-319-00119-7 . Pp. Xiv + 695. [REVIEW] Philosophia Mathematica:nkv006.
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  4. Alasdair Urquhart (2012). Henry M. Sheffer and Notational Relativity. History and Philosophy of Logic, Vol. 33. Bulletin of Symbolic Logic 18 (3):408-409.
     
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  5. Alasdair Urquhart (2012). REVIEWS-L. Haaparanta (Editor), The Development of Modern Logic. Bulletin of Symbolic Logic 18 (2):268.
  6. Alasdair Urquhart (2012). The Development of Modern Logic. [REVIEW] Bulletin of Symbolic Logic 18 (2):268-270.
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  7. Alasdair Urquhart (2011). Henry M. Sheffer and Notational Relativity. History and Philosophy of Logic 33 (1):33 - 47.
    Henry M. Sheffer is well known to logicians for the discovery (or rather, the rediscovery) of the ?Sheffer stroke? of propositional logic. But what else did Sheffer contribute to logic? He published very little, though he is known to have been carrying on a rather mysterious research program in logic; the only substantial result of this research was the unpublished monograph The General Theory of Notational Relativity. The main aim of this paper is to explain, as far as possible (given (...)
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  8. Alasdair Urquhart (2011). The Depth of Resolution Proofs. Studia Logica 99 (1-3):349-364.
    This paper investigates the depth of resolution proofs, that is to say, the length of the longest path in the proof from an input clause to the conclusion. An abstract characterization of the measure is given, as well as a discussion of its relation to other measures of space complexity for resolution proofs.
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  9. Alasdair Urquhart (2010). Anderson and Belnap's Invitation to Sin. Journal of Philosophical Logic 39 (4):453 - 472.
    Quine has argued that modal logic began with the sin of confusing use and mention. Anderson and Belnap, on the other hand, have offered us a way out through a strategy of nominahzation. This paper reviews the history of Lewis's early work in modal logic, and then proves some results about the system in which "A is necessary" is intepreted as "A is a classical tautology.".
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  10. Alasdair Urquhart (2010). K. Bimbó and JM Dunn: Relational Semantics of Nonclassical Logical Calculi. Bulletin of Symbolic Logic 16 (2).
     
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  11. Alasdair Urquhart (2010). Relational Semantics of Nonclassical Logical Calculi. [REVIEW] Bulletin of Symbolic Logic 16 (2):277-277.
     
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  12. Alasdair Urquhart (2010). Von Neumann, Gödel and Complexity Theory. Bulletin of Symbolic Logic 16 (4):516-530.
    Around 1989, a striking letter written in March 1956 from Kurt Gödel to John von Neumann came to light. It poses some problems about the complexity of algorithms; in particular, it asks a question that can be seen as the first formulation of the P=?NP question. This paper discusses some of the background to this letter, including von Neumann's own ideas on complexity theory. Von Neumann had already raised explicit questions about the complexity of Tarski's decision procedure for elementary algebra (...)
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  13. Alasdair Urquhart & Albert Visser (2010). Decorated Linear Order Types and the Theory of Concatenation. In F. Delon (ed.), Logic Colloquium 2007. Cambridge University Press. 1.
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  14. Alasdair Urquhart (2009). Emil Post. In Dov Gabbay (ed.), The Handbook of the History of Logic. Elsevier. 5--617.
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  15. Alasdair Urquhart (2009). Enumerating Types of Boolean Functions. Bulletin of Symbolic Logic 15 (3):273-299.
    The problem of enumerating the types of Boolean functions under the group of variable permutations and complementations was first stated by Jevons in the 1870s. but not solved in a satisfactory way until the work of Pólya in 1940. This paper explains the details of Pólya's solution, and also the history of the problem from the 1870s to the 1970s.
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  16. Alasdair Urquhart (2009). Logic and Denotation. In Nicholas Griffin & Dale Jacquette (eds.), Russell Vs. Meinong: The Legacy of "on Denoting". Routledge.
     
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  17. Alasdair Urquhart (2009). 2009 North American Annual Meeting of the Association for Symbolic Logic. Bulletin of Symbolic Logic 15 (4):441-464.
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  18. Alasdair Urquhart (2009). Review of John P. Burgess, Philosophical Logic. [REVIEW] Notre Dame Philosophical Reviews 2009 (10).
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  19. T. Aho, A. V. Pietarinen & Alasdair Urquhart (2008). Truth and Games: Essays in Honour of Gabriel Sandu. Bulletin of Symbolic Logic 14 (1):119-121.
  20. Aldo Antonelli, Alasdair Urquhart & Richard Zach (2008). Mathematical Methods in Philosophy Editors' Introduction. Review of Symbolic Logic 1 (2):143-145.
    Mathematics and philosophy have historically enjoyed a mutually beneficial and productive relationship, as a brief review of the work of mathematician–philosophers such as Descartes, Leibniz, Bolzano, Dedekind, Frege, Brouwer, Hilbert, Gödel, and Weyl easily confirms. In the last century, it was especially mathematical logic and research in the foundations of mathematics which, to a significant extent, have been driven by philosophical motivations and carried out by technically minded philosophers. Mathematical logic continues to play an important role in contemporary philosophy, and (...)
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  21. Francis Jeffry Pelletier & Alasdair Urquhart (2008). Synonymous Logics: A Correction. [REVIEW] Journal of Philosophical Logic 37 (1):95 - 100.
    In an earlier paper entitled Synonymous Logics, the authors attempted to show that there are two modal logics so that each is exactly translatable into the other, but they are not translationally equivalent. Unfortunately, there is an error in the proof of this result. The present paper provides a new example of two such logics, and a proof of the result claimed in the earlier paper.
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  22. Alasdair Urquhart (2008). Philosophical Relevance of the Interaction Between Mathematical Physics and Pure Mathematics. In Paolo Mancosu (ed.), The Philosophy of Mathematical Practice. Oup Oxford.
     
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  23. Alasdair Urquhart (2008). The Boundary Between Mathematics and Physics. In Paolo Mancosu (ed.), The Philosophy of Mathematical Practice. Oup Oxford. 407--416.
  24. Alasdair Urquhart (2008). The Unnameable. Canadian Journal of Philosophy 38 (S1):119-135.
    Hans Herzberger as a philosopher and logician has shown deep interest both in the philosophy of Gottlob Frege, and in the topic of the inexpressible and the ineffable. In the fall of 1982, he taught at the University of Toronto, together with André Gombay, a course on Frege's metaphysics, philosophy of language, and foundations of arithmetic. Again, in the fall of 1986, he taught a seminar on the philosophy of language that dealt with 'the limits of discursive symbolism in several (...)
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  25. N. J. Cutland, M. Di Nasso, D. A. Ross & Alasdair Urquhart (2007). REVIEWS-Nonstandard Methods and Applications in Mathematics. Bulletin of Symbolic Logic 13 (3):372-374.
     
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  26. S. Hedman & Alasdair Urquhart (2007). REVIEWS-A First Course in Logic: An Introduction to Model Theory, Proof Theory, Computability, and Complexity. Bulletin of Symbolic Logic 13 (4):538-539.
  27. Alasdair Urquhart (2007). Four Variables Suffice. Australasian Journal of Philosophy 5:66-73.
    What I wish to propose in the present paper is a new form of “career induction” for ambitious young logicians. The basic problem is this: if we look at the n-variable fragments of relevant propositional logics, at what point does undecidability begin? Focus, to be definite, on the logic R. John Slaney showed that the 0-variable fragment of R contains exactly 3088 non-equivalent propositions, and so is clearly decidable. In the opposite direction, I claimed in my paper of 1984 that (...)
     
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  28. Noriko H. Arai, Toniann Pitassi & Alasdair Urquhart (2006). The Complexity of Analytic Tableaux. Journal of Symbolic Logic 71 (3):777 - 790.
    The method of analytic tableaux is employed in many introductory texts and has also been used quite extensively as a basis for automated theorem proving. In this paper, we discuss the complexity of the system as a method for refuting contradictory sets of clauses, and resolve several open questions. We discuss the three forms of analytic tableaux: clausal tableaux, generalized clausal tableaux, and binary tableaux. We resolve the relative complexity of these three forms of tableaux proofs and also resolve the (...)
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  29. B. Russell & Alasdair Urquhart (2005). REVIEWS-Correspondance Avec Louis Couturat (1897-1913). Bulletin of Symbolic Logic 11 (3):442-443.
     
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  30. Alasdair Urquhart (2005). Correspondance Avec Louis Couturat. [REVIEW] Bulletin of Symbolic Logic 11 (3):442-443.
     
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  31. Alasdair Urquhart (2005). Russell Bertrand Correspondance sur la philosophie, la logique et la politique avec Louis Couturat (1897-1913)., Édition et commentaire par Anne-Françoise Schmid. Transcription et notes sur la langue internationale par Tazio Carlevaro. Éditions Kimé, Paris, 2001. 737 pp. [REVIEW] Bulletin of Symbolic Logic 11 (3):442-444.
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  32. Alasdair Urquhart (2005). The Complexity of Propositional Proofs with the Substitution Rule. Logic Journal of the Igpl 13 (3):287-291.
    We prove that for sufficiently large N, there are tautologies of size O that require proofs containing Ω lines in axiomatic systems of propositional logic based on axioms and the rule of substitution for single variables. These tautologies have proofs with O lines in systems with the multiple substitution rule.
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  33. Michael Soltys & Alasdair Urquhart (2004). Matrix Identities and the Pigeonhole Principle. Archive for Mathematical Logic 43 (3):351-357.
    We show that short bounded-depth Frege proofs of matrix identities, such as PQ=I⊃QP=I (over the field of two elements), imply short bounded-depth Frege proofs of the pigeonhole principle. Since the latter principle is known to require exponential-size bounded-depth Frege proofs, it follows that the propositional version of the matrix principle also requires bounded-depth Frege proofs of exponential size.
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  34. Alasdair Urquhart (2004). David Corfield, Towards a Philosophy of Real Mathematics Reviewed By. Philosophy in Review 24 (3):175-177.
  35. Alasdair Urquhart (2004). David Corfield, Towards a Philosophy of Real Mathematics. [REVIEW] Philosophy in Review 24:175-177.
     
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  36. Alasdair Urquhart (2004). Model Theory of Stochastic Processes. [REVIEW] Bulletin of Symbolic Logic 10 (1):110-111.
     
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  37. Alasdair Urquhart (2004). Sergio Fajardo and H. Jerome Keisler. Model Theory of Stochastic Processes, Lecture Notes in Logic, Vol. 14. Association for Symbolic Logic, AK Peters, Ltd., Natick, Massachusetts, 2002, Xii+ 136 Pp. [REVIEW] Bulletin of Symbolic Logic 10 (1):110-112.
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  38. Alasdair Urquhart (2004). The Limits of Abstraction. Journal of Philosophy 101 (11):594-598.
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  39. Luc Lismont, Philippe Mongin, Strong Completeness, Volker Halbach, Hannes Leitgeb, Philip Welch, Francis Jeffry Pelletier, Alasdair Urquhart & Synonymous Logics (2003). Philip G. Calabrese/Operating on Functions with Variable Domains 1–18 Stewart Shapiro/Mechanism, Truth, and Penrose's New Argu-Ment 19–42 Steven E. Boër/Thought-Contents and the Formal Ontology Of. [REVIEW] Journal of Philosophical Logic 32:667-668.
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  40. Francis Jeffry Pelletier & Alasdair Urquhart (2003). Synonymous Logics. Journal of Philosophical Logic 32 (3):259-285.
    This paper discusses the general problem of translation functions between logics, given in axiomatic form, and in particular, the problem of determining when two such logics are "synonymous" or "translationally equivalent." We discuss a proposed formal definition of translational equivalence, show why it is reasonable, and also discuss its relation to earlier definitions in the literature. We also give a simple criterion for showing that two modal logics are not translationally equivalent, and apply this to well-known examples. Some philosophical morals (...)
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  41. Alasdair Urquhart (2003). The Theory of Types. In Nicholas Griffin (ed.), The Cambridge Companion to Bertrand Russell. Cambridge University Press. 286--309.
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  42. Alasdair Urquhart (2002). The Complexity of Linear Logic with Weakening. Bulletin of Symbolic Logic 8 (1):100-101.
     
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  43. Alasdair Urquhart (2001). The Search for Mathematical Roots, 1870-1940. [REVIEW] Russell 21 (1).
     
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  44. Alasdair Urquhart (1999). Beth's Definability Theorem in Relevant Logics. In E. Orłowska (ed.), Logic at Work. Heidelberg. 229--234.
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  45. Alasdair Urquhart (1999). From Berkeley to Bourbaki. Dialogue 38 (03):587-.
    This has been a great century for logic and the foundations of mathematics. Ewald's excellent sourcebook is a welcome addition to the literature on the exciting developments of this and the past two centuries. The richness of the material on which Ewald is drawing is shown by the fact that he has assembled a broad and representative selection without once duplicating anything to be found in the famous sourcebooks of van Heijenoort and Benacerraf/Putnam.
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  46. Alasdair Urquhart (1999). George Boolos, Logic, Logic and Logic Reviewed By. Philosophy in Review 19 (4):244-246.
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  47. Alasdair Urquhart (1999). George Boolos, Logic, Logic and Logic. [REVIEW] Philosophy in Review 19:244-246.
     
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  48. Alasdair Urquhart (1999). Review: Gregory Landini, Russell's Hidden Substitutional Theory. [REVIEW] Journal of Symbolic Logic 64 (3):1370-1371.
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  49. Alasdair Urquhart (1999). The Complexity of Decision Procedures in Relevance Logic II. Journal of Symbolic Logic 64 (4):1774-1802.
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  50. James R. Brown & Alasdair Urquhart (1998). Benacerraf and His Critics Adam Morton and Stephen Stich, Editors Philosophers and Their Critics, Vol. 8 Cambridge, MA: Blackwell Publishers, 1996, Xi + 271 Pp., $54.95. [REVIEW] Dialogue 37 (03):633-.
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