36 found
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  1. Jonathan P. Seldin (1986). On the Proof Theory of the Intermediate Logic MH. Journal of Symbolic Logic 51 (3):626-647.
    A natural deduction formulation is given for the intermediate logic called MH by Gabbay in [4]. Proof-theoretic methods are used to show that every deduction can be normalized, that MH is the weakest intermediate logic for which the Glivenko theorem holds, and that the Craig-Lyndon interpolation theorem holds for it.
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  2.  18
    Jonathan P. Seldin (1989). Normalization and Excluded Middle. I. Studia Logica 48 (2):193 - 217.
    The usual rule used to obtain natural deduction formulations of classical logic from intuitionistic logic, namely.
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  3.  3
    Jonathan P. Seldin (1997). On the Proof Theory of Coquand's Calculus of Constructions. Annals of Pure and Applied Logic 83 (1):23-101.
  4.  23
    Jonathan P. Seldin (1973). Equality in F21. Journal of Symbolic Logic 38 (4):571 - 575.
  5.  2
    Jonathan P. Seldin (1979). Progress Report on Generalized Functionality. Annals of Mathematical Logic 17 (1-2):29-59.
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  6.  2
    Jonathan P. Seldin (1977). A Sequent Calculus for Type Assignment. Journal of Symbolic Logic 42 (1):11-28.
  7.  13
    Jonathan P. Seldin (2011). Curry's Formalism as Structuralism. Logica Universalis 5 (1):91-100.
    In 1939, Curry proposed a philosophy of mathematics he called formalism. He made this proposal in two works originally written then, although one of them was not published until 1951. These are the two philosophical works for which Curry is known, and they have left a false impression of his views. In this article, I propose to clarify Curry’s views by referring to some of his later writings on the subject. I claim that Curry’s philosophy was not what is now (...)
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  8.  1
    Fairouz Kamareddine, Jonathan P. Seldin & J. B. Wells (2016). Bridging Curry and Church's Typing Style. Journal of Applied Logic 18:42-70.
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  9.  24
    Jonathan P. Seldin (2000). On the Role of Implication in Formal Logic. Journal of Symbolic Logic 65 (3):1076-1114.
    Evidence is given that implication (and its special case, negation) carry the logical strength of a system of formal logic. This is done by proving normalization and cut elimination for a system based on combinatory logic or λ-calculus with logical constants for and, or, all, and exists, but with none for either implication or negation. The proof is strictly finitary, showing that this system is very weak. The results can be extended to a "classical" version of the system. They can (...)
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  10.  4
    Jonathan P. Seldin (1975). Arithmetic as a Study of Formal Systems. Notre Dame Journal of Formal Logic 16 (4):449-464.
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  11.  1
    Jonathan P. Seldin (1977). The ${\Bf Q}$-Consistency of ${\Cal F}_{22}$. Notre Dame Journal of Formal Logic 18 (1):117-127.
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  12.  2
    Jonathan P. Seldin (1978). A Sequent Calculus Formulation of Type Assignment with Equality Rules for the \Ambdaβ-Calculus. Journal of Symbolic Logic 43 (4):643-649.
  13.  1
    Jonathan P. Seldin (1975). Böhm Corrado and Gross Wolf. Introduction to the CUCH. Automata Theory, Edited by Caianiello E. R., Academic Press, New York and London 1966, Pp. 35–65. Reprinted in Pubblicazioni dell'Istituto Nazionale Per le Applicazioni Del Calcolo, Ser. 11 No. 669, Rome 1966.Böhm C.. The CUCH as a Formal and Description Language. Formal Language Description Languages for Computer Programming, Proceedings of the IFIP Working Conference on Formal Language Description Languages, Edited by Steel T. B. Jr., North-Holland Publishing Company, Amsterdam 1966, Pp. 179–197. [REVIEW] Journal of Symbolic Logic 40 (1):81-83.
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  14.  5
    M. W. Bunder & Jonathan P. Seldin (1978). Some Anomalies in Fitch's System QD. Journal of Symbolic Logic 43 (2):247-249.
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  15.  14
    Martin W. Bunder, J. Roger Hindley & Jonathan P. Seldin (1989). On Adding (Ξ) to Weak Equality in Combinatory Logic. Journal of Symbolic Logic 54 (2):590-607.
    Because the main difference between combinatory weak equality and λβ-equality is that the rule \begin{equation*}\tag{\xi} X = Y \vdash \lambda x.X = \lambda x.Y\end{equation*} is valid for the latter but not the former, it is easy to assume that another way of defining combinatory β-equality is to add rule (ξ) to the postulates for weak equality. However, to make this true, one must choose the definition of combinatory abstraction in (ξ) very carefully. If one tries to use one of the (...)
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  16.  2
    Jonathan P. Seldin (1968). Note on Definitional Reductions. Notre Dame Journal of Formal Logic 9 (1):4-6.
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  17.  2
    Jonathan P. Seldin (1975). Review: Corrado Bohm, Wolf Gross, E. R. Caianiello, Introduction to the CUCH; C. Bohm, T. B. Steel, The CUCH as a Formal and Description Language. [REVIEW] Journal of Symbolic Logic 40 (1):81-83.
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  18.  2
    Jonathan P. Seldin (2009). The Logic of Church and Curry. In Dov Gabbay (ed.), The Handbook of the History of Logic. Elsevier 5--819.
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  19.  1
    Jonathan P. Seldin (1970). Review: Maarten Wicher Visser Bunder, Set Theory Based on Combinatory Logic. [REVIEW] Journal of Symbolic Logic 35 (1):147-148.
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  20.  1
    Jonathan P. Seldin (1999). Review: Jean-Pierre Ginisti, La Logique Combinatoire. [REVIEW] Journal of Symbolic Logic 64 (4):1833-1834.
  21.  1
    Jonathan P. Seldin (1980). A Second Corrigendum to My Paper: ``Note on Definitional Reductions''. Notre Dame Journal of Formal Logic 21 (4):728-728.
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  22.  1
    Jonathan P. Seldin (1970). Review: Edward J. Cogan, A Formalization of the Theory of Sets From the Point of View of Combinatory Logic; Rainer Titgemeyer, Uber Einen Widerspruch in Cogans Darstellung der Mengenlehre. [REVIEW] Journal of Symbolic Logic 35 (1):147-147.
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  23. M. W. Bunder & Jonathan P. Seldin (2004). Variants of the Basic Calculus of Constructions. Journal of Applied Logic 2 (2):191-217.
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  24. Jonathan P. Seldin (1969). Corrigendum to My Paper: ``Note on Definitional Reductions''. Notre Dame Journal of Formal Logic 10 (4):412-412.
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  25. Jonathan P. Seldin, Edward J. Cogan & Rainer Titgemeyer (1970). A Formalization of the Theory of Sets From the Point of View of Combinatory Logic.Uber Einen Widerspruch in Cogans Darstellung der Mengenlehre. Journal of Symbolic Logic 35 (1):147.
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  26. Jonathan P. Seldin (1970). Bunder Maarten Wicher Visser. Set Theory Based on Combinatory Logic. Dissertation Amsterdam 1969, 80 Pp. + 3 Pp. Of Corrections. [REVIEW] Journal of Symbolic Logic 35 (1):147-148.
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  27. Jonathan P. Seldin (1970). Cogan Edward J.. A Formalization of the Theory of Sets From the Point of View of Combinatory Logic. Zeitschrift Für Mathematische Logik Und Grundlagen der Mathematik, Vol. 1 , Pp. 198–240.Titgemeyer Rainer. Über Einen Widerspruch in Cogans Darstellung der Mengenlehre. Zeitschrift Für Mathematische Logik Und Grundlagen der Mathematik, Vol. 7 , Pp. 161–163. [REVIEW] Journal of Symbolic Logic 35 (1):147.
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  28. Jonathan P. Seldin (1975). De Bruijn N. G.. Lambda Calculus Notation with Nameless Dummies, a Tool for Automatic Formula Manipulation, with Application to the Church-Rosser Theorem. Koninklyke Nederlandse Akademie van Wetenschappen, Proceedings, Ser. A Vol. 75 , Pp. 381–392; Also Indagationes Mathematicae, Vol. 34 , Pp. 381–392. [REVIEW] Journal of Symbolic Logic 40 (3):470.
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  29. Jonathan P. Seldin (1973). Equality In. Journal of Symbolic Logic 38 (4):571-575.
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  30. Jonathan P. Seldin (1973). Equality in $Mathscr{F}_{21}$. Journal of Symbolic Logic 38 (4):571-575.
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  31. Jonathan P. Seldin (1999). Ginisti Jean-Pierre. La Logique Combinatoire. Qui Sais-Je? No. 3205. Presses Universitaires de France, Paris 1997, 127 Pp. [REVIEW] Journal of Symbolic Logic 64 (4):1833-1834.
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  32. Jonathan P. Seldin (2004). Interpreting HOL in the Calculus of Constructions. Journal of Applied Logic 2 (2):173-189.
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  33. Jonathan P. Seldin (1973). Kearns John T.. Combinatory Logic with Discriminators. Journal of Symbolic Logic 38 (2):339-340.
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  34. Jonathan P. Seldin (1973). Review: John T. Kearns, Combinatory Logic with Discriminators. [REVIEW] Journal of Symbolic Logic 38 (2):339-340.
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  35. Jonathan P. Seldin (1975). Review: N. G. De Bruijn, Lambda Calculus Notation with Nameless Dummies, a Tool for Automatic Formula Manipulation, with Application to the Church-Rosser Theorem. [REVIEW] Journal of Symbolic Logic 40 (3):470-470.
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  36. Jonathan P. Seldin & Maarten Wicher Visser Bunder (1970). Set Theory Based on Combinatory Logic. Journal of Symbolic Logic 35 (1):147.
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