Results for 'Cirquent calculus'

941 found
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  1.  23
    Elementary-base cirquent calculus II: Choice quantifiers.Giorgi Japaridze - forthcoming - Logic Journal of the IGPL.
    Cirquent calculus is a novel proof theory permitting component-sharing between logical expressions. Using it, the predecessor article ‘Elementary-base cirquent calculus I: Parallel and choice connectives’ built the sound and complete axiomatization $\textbf{CL16}$ of a propositional fragment of computability logic. The atoms of the language of $\textbf{CL16}$ represent elementary, i.e. moveless, games and the logical vocabulary consists of negation, parallel connectives and choice connectives. The present paper constructs the first-order version $\textbf{CL17}$ of $\textbf{CL16}$, also enjoying soundness and (...)
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  2.  7
    A Propositional Cirquent Calculus for Computability Logic.Giorgi Japaridze - 2024 - Journal of Logic, Language and Information 33 (4):363-389.
    Cirquent calculus is a proof system with inherent ability to account for sharing subcomponents in logical expressions. Within its framework, this article constructs an axiomatization  CL18 \text{ CL18 } CL18 of the basic propositional fragment of computability logic—the game-semantically conceived logic of computational resources and tasks. The nonlogical atoms of this fragment represent arbitrary so called static games, and the connectives of its logical vocabulary are negation and the parallel and choice versions of conjunction and disjunction. The main technical (...)
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  3.  31
    A cirquent calculus system with clustering and ranking.Wenyan Xu - 2016 - Journal of Applied Logic 16:37-49.
  4.  40
    The taming of recurrences in computability logic through cirquent calculus, Part I.Giorgi Japaridze - 2013 - Archive for Mathematical Logic 52 (1-2):173-212.
    This paper constructs a cirquent calculus system and proves its soundness and completeness with respect to the semantics of computability logic. The logical vocabulary of the system consists of negation ${\neg}$ , parallel conjunction ${\wedge}$ , parallel disjunction ${\vee}$ , branching recurrence ⫰, and branching corecurrence ⫯. The article is published in two parts, with (the present) Part I containing preliminaries and a soundness proof, and (the forthcoming) Part II containing a completeness proof.
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  5.  72
    The taming of recurrences in computability logic through cirquent calculus, Part II.Giorgi Japaridze - 2013 - Archive for Mathematical Logic 52 (1-2):213-259.
    This paper constructs a cirquent calculus system and proves its soundness and completeness with respect to the semantics of computability logic. The logical vocabulary of the system consists of negation \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}¬{{\neg}}\end{document}, parallel conjunction \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}{{\wedge}}\end{document}, parallel disjunction \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}{{\vee}}\end{document}, branching recurrence ⫰, and branching corecurrence ⫯. The article is published in two parts, with (...)
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  6.  58
    The Parallel versus Branching Recurrences in Computability Logic.Wenyan Xu & Sanyang Liu - 2013 - Notre Dame Journal of Formal Logic 54 (1):61-78.
    This paper shows that the basic logic induced by the parallel recurrence $\hspace {-2pt}\mbox {\raisebox {-0.01pt}{\@setfontsize \small {7}{8}$\wedge$}\hspace {-3.55pt}\raisebox {4.5pt}{\tiny $\mid$}\hspace {2pt}}$ of computability logic (i.e., the one in the signature $\{\neg,$\wedge$,\vee,\hspace {-2pt}\mbox {\raisebox {-0.01pt}{\@setfontsize \small {7}{8}$\wedge$}\hspace {-3.55pt}\raisebox {4.5pt}{\tiny $\mid$}\hspace {2pt}},\hspace {-2pt}\mbox {\raisebox {0.12cm}{\@setfontsize \small {7}{8}$\vee$}\hspace {-3.6pt}\raisebox {0.02cm}{\tiny $\mid$}\hspace {2pt}}\}$ ) is a proper superset of the basic logic induced by the branching recurrence $\mbox {\raisebox {-0.05cm}{$\circ$}\hspace {-0.11cm}\raisebox {3.1pt}{\tiny $\mid$}\hspace {2pt}}$ (i.e., the one in the signature $\{\neg,$\wedge$,\vee,\mbox {\raisebox {-0.05cm}{$\circ$}\hspace {-0.11cm}\raisebox (...)
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  7. jaskowskps matrix criterion for the iNTurnoNisnc.Proposmonal Calculus - 1973 - In Stanisław J. Surma, Studies in the history of mathematical logic. Wrocław,: Zakład Narodowy im. Ossolinskich. pp. 87.
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  8.  21
    The Mathematical Analysis of Logic: Being an Essay Towards a Calculus of Deductive Reasoning.George Boole - 2017 - Oxford,: Andesite Press.
    This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain (...)
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  9.  45
    On the discussive conjunction in the propositional calculus for inconsistent deductive systems.Stanisław Jaśkowski - 1999 - Logic and Logical Philosophy 7:57.
  10. The first computational theory of mind and brain: A close look at McCulloch and Pitts' Logical Calculus of Ideas Immanent in Nervous Activity.Gualtiero Piccinini - 2004 - Synthese 141 (2):175-215.
    Despite its significance in neuroscience and computation, McCulloch and Pitts's celebrated 1943 paper has received little historical and philosophical attention. In 1943 there already existed a lively community of biophysicists doing mathematical work on neural networks. What was novel in McCulloch and Pitts's paper was their use of logic and computation to understand neural, and thus mental, activity. McCulloch and Pitts's contributions included (i) a formalism whose refinement and generalization led to the notion of finite automata (an important formalism in (...)
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  11.  46
    Almost-disjoint sets the dense set problem and the partition calculus.James E. Baumgartner - 1976 - Annals of Mathematical Logic 9 (4):401-439.
  12. A decision procedure for probability calculus with applications.Branden Fitelson - 2008 - Review of Symbolic Logic 1 (1):111-125.
    (new version: 10/30/07). Click here to download the companion Mathematica 6 notebook that goes along with this paper.
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  13.  82
    Completeness Results for Lambek Syntactic Calculus.Wojciech Buszkowski - 1986 - Mathematical Logic Quarterly 32 (1-5):13-28.
  14.  70
    On the strong semantical completeness of the intuitionistic predicate calculus.Richmond H. Thomason - 1968 - Journal of Symbolic Logic 33 (1):1-7.
  15.  18
    On 2nd order intuitionistic propositional calculus with full comprehension.Dov M. Gabbay - 1974 - Archive for Mathematical Logic 16 (3-4):177-186.
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  16. Logical Questions Concerning the $\mu$-Calculus: Interpolation, Lyndon and Los-Tarski.Giovanna D'agostino & Marco Hollenberg - 2000 - Journal of Symbolic Logic 65 (1):310-332.
  17. The deduction theorem in a functional calculus of first order based on strict implication.Ruth C. Barcan - 1946 - Journal of Symbolic Logic 11 (4):115-118.
  18.  63
    Spatial logic of tangled closure operators and modal mu-calculus.Robert Goldblatt & Ian Hodkinson - 2017 - Annals of Pure and Applied Logic 168 (5):1032-1090.
  19.  98
    A Completeness Theorem for the Lambek Calculus of Syntactic Categories.Kosta Došen - 1985 - Mathematical Logic Quarterly 31 (14-18):235-241.
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  20.  57
    An axiomatization of the finite-valued łukasiewicz calculus.Roman Tuziak - 1988 - Studia Logica 47 (1):49 - 55.
    In this paper the completeness theorems for the finite-valued ukasiewicz logics are proved with the use of the Lindenbaum algebra.
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  21.  12
    The History of the Calculus and Its Conceptual Development: (The Concepts of the Calculus).Carl B. Boyer - 1949 - Courier Corporation.
    Traces the development of the integral and the differential calculus and related theories since ancient times.
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  22.  13
    Extraordinary Responsibility: Politics Beyond the Moral Calculus.Shalini Satkunanandan - 2015 - New York: Cambridge University Press.
    Careful attention to contemporary political debates, including those around global warming, the federal debt, and the use of drone strikes on suspected terrorists, reveals that we often view our responsibility as something that can be quantified and discharged. Shalini Satkunanandan shows how Plato, Kant, Nietzsche, Weber, and Heidegger each suggest that this calculative or bookkeeping mindset both belongs to 'morality', understood as part of our ordinary approach to responsibility, and effaces the incalculable, undischargeable, and more onerous dimensions of our responsibility. (...)
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  23.  49
    Classical logic, storage operators and second-order lambda-calculus.Jean-Louis Krivine - 1994 - Annals of Pure and Applied Logic 68 (1):53-78.
    We describe here a simple method in order to obtain programs from proofs in second-order classical logic. Then we extend to classical logic the results about storage operators proved by Krivine for intuitionistic logic. This work generalizes previous results of Parigot.
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  24.  29
    The Theory of Probability: An Inquiry Into the Logical and Mathematical Foundations of the Calculus of Probability.Donald C. Williams - 1950 - Philosophy and Phenomenological Research 11 (2):252-257.
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  25.  26
    The Calculus of Natural Calculation.René Gazzari - 2021 - Studia Logica 109 (6):1375-1411.
    The calculus of Natural Calculation is introduced as an extension of Natural Deduction by proper term rules. Such term rules provide the capacity of dealing directly with terms in the calculus instead of the usual reasoning based on equations, and therefore the capacity of a natural representation of informal mathematical calculations. Basic proof theoretic results are communicated, in particular completeness and soundness of the calculus; normalisation is briefly investigated. The philosophical impact on a proof theoretic account of (...)
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  26. Differential Calculus Based on the Double Contradiction.Kazuhiko Kotani - 2016 - Open Journal of Philosophy 6 (4):420-427.
    The derivative is a basic concept of differential calculus. However, if we calculate the derivative as change in distance over change in time, the result at any instant is 0/0, which seems meaningless. Hence, Newton and Leibniz used the limit to determine the derivative. Their method is valid in practice, but it is not easy to intuitively accept. Thus, this article describes the novel method of differential calculus based on the double contradiction, which is easier to accept intuitively. (...)
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  27. A calculus of individuals based on "connection".Bowman L. Clarke - 1981 - Notre Dame Journal of Formal Logic 22 (3):204-218.
    Although Aristotle (Metaphysics, Book IV, Chapter 2) was perhaps the first person to consider the part-whole relationship to be a proper subject matter for philosophic inquiry, the Polish logician Stanislow Lesniewski [15] is generally given credit for the first formal treatment of the subject matter in his Mereology.1 Woodger [30] and Tarski [24] made use of a specific adaptation of Lesniewski's work as a basis for a formal theory of physical things and their parts. The term 'calculus of individuals' (...)
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  28.  32
    Robot location estimation in the situation calculus.Vaishak Belle & Hector J. Levesque - 2015 - Journal of Applied Logic 13 (4):397-413.
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  29. The Epsilon Calculus.Jeremy Avigad & Richard Zach - 2012 - In Ed Zalta, Stanford Encyclopedia of Philosophy. Stanford, CA: Stanford Encyclopedia of Philosophy.
    The epsilon calculus is a logical formalism developed by David Hilbert in the service of his program in the foundations of mathematics. The epsilon operator is a term-forming operator which replaces quantifiers in ordinary predicate logic. Specifically, in the calculus, a term εx A denotes some x satisfying A(x), if there is one. In Hilbert's Program, the epsilon terms play the role of ideal elements; the aim of Hilbert's finitistic consistency proofs is to give a procedure which removes (...)
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  30.  73
    The Calculus of Higher-Level Rules, Propositional Quantification, and the Foundational Approach to Proof-Theoretic Harmony.Peter Schroeder-Heister - 2014 - Studia Logica 102 (6):1185-1216.
    We present our calculus of higher-level rules, extended with propositional quantification within rules. This makes it possible to present general schemas for introduction and elimination rules for arbitrary propositional operators and to define what it means that introductions and eliminations are in harmony with each other. This definition does not presuppose any logical system, but is formulated in terms of rules themselves. We therefore speak of a foundational account of proof-theoretic harmony. With every set of introduction rules a canonical (...)
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  31.  39
    An axiomatization of Prior's modal calculus $Q$.R. A. Bull - 1964 - Notre Dame Journal of Formal Logic 5 (3):211-214.
  32.  20
    Spatial reasoning in a fuzzy region connection calculus.Steven Schockaert, Martine De Cock & Etienne E. Kerre - 2009 - Artificial Intelligence 173 (2):258-298.
  33. Bernard Nieuwentijt and the Leibnizian calculus.R. H. Vermij - 1989 - Studia Leibnitiana 21 (1):69-86.
    Bernard Nieuwentijt ist in der Mathematikgeschichte bekannt als Kritiker der Leibnizschen Differentialrechnung. Im Gegensatz zu dem, was häufig angenommen wird, war die Kritik an Leibniz' Methode kein Hauptanliegen Nieuwentijts. Das Ziel seines bedeutendsten mathematischen Werks, Analysis infinitorum , war die Systematisierung und logische Deduzierung der ihm bekannten Infinitesimalmethoden, besonders derer von den Engländern wie Barrow, Wallis u. a. Das Werk Leibnizens war ihm anfangs völlig unbekannt. In dem System, das Nieuwentijt selbständig entwarf, rechnete er nicht mit Infinitesimalen höheren Grades: ihre (...)
     
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  34.  48
    Cut Elimination in a Gentzen-Style ε-Calculus Without Identity.Linda Wessels - 1976 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 23 (36):527-538.
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  35.  43
    A certain conception of the calculus of rough sets.Zbigniew Bonikowski - 1992 - Notre Dame Journal of Formal Logic 33 (3):412-421.
  36.  16
    Lambda-calculus, combinators, and functional programming.György E. Révész - 1988 - New York: Cambridge University Press.
    Provides computer science students and researchers with a firm background in lambda-calculus and combinators.
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  37.  37
    Lambek Calculus with Conjugates.Igor Sedlár & Andrew Tedder - 2020 - Studia Logica 109 (3):447-470.
    We study an expansion of the Distributive Non-associative Lambek Calculus with conjugates of the Lambek product operator and residuals of those conjugates. The resulting logic is well-motivated, under-investigated and difficult to tackle. We prove completeness for some of its fragments and establish that it is decidable. Completeness of the logic is an open problem; some difficulties with applying the usual proof method are discussed.
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  38.  46
    Finite Axiomatizability of Theories in the Predicate Calculus Using Additional Predicate Symbols.S. C. Kleene, W. Craig & R. L. Vaught - 1971 - Journal of Symbolic Logic 36 (2):334-335.
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  39.  33
    Traditional Inference and Its Versions in the Combined Calculus.Lei Ma - 2015 - Philosophical Forum 46 (2):155-174.
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  40.  66
    Scientific theory as partially interpreted calculus.Brent Mundy - 1987 - Erkenntnis 27 (2):173 - 196.
  41.  61
    To H.B. Curry: essays on combinatory logic, lambda calculus, and formalism.Haskell B. Curry, J. Roger Hindley & J. P. Seldin (eds.) - 1980 - New York: Academic Press.
  42.  19
    Transforming Ethics Education Through a Faculty Learning Community: “I’m Coming Around to Seeing Ethics as Being Maybe as Important as Calculus”.Justin L. Hess, Elizabeth Sanders, Grant A. Fore, Martin Coleman, Mary Price, Sammy Nyarko & Brandon Sorge - 2024 - Science and Engineering Ethics 30 (5):1-29.
    Ethics is central to scientific and engineering research and practice, but a key challenge for promoting students’ ethical formation involves enhancing faculty members’ ability and confidence in embedding positive ethical learning experiences into their curriculums. To this end, this paper explores changes in faculty members’ approaches to and perceptions of ethics education following their participation in a multi-year interdisciplinary faculty learning community (FLC). We conducted and thematically analyzed semi-structured interviews with 11 participants following the second year of the FLC. Qualitative (...)
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  43. Sequent calculus in natural deduction style.Sara Negri & Jan von Plato - 2001 - Journal of Symbolic Logic 66 (4):1803-1816.
    A sequent calculus is given in which the management of weakening and contraction is organized as in natural deduction. The latter has no explicit weakening or contraction, but vacuous and multiple discharges in rules that discharge assumptions. A comparison to natural deduction is given through translation of derivations between the two systems. It is proved that if a cut formula is never principal in a derivation leading to the right premiss of cut, it is a subformula of the conclusion. (...)
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  44.  60
    A completeness-proof method for extensions of the implicational fragment of the propositional calculus.Diderik Batens - 1980 - Notre Dame Journal of Formal Logic 21 (3):509-517.
  45.  25
    (2 other versions)Note on Arithmetic Models for Consistent Formulae of the Predicate Calculus II.G. Kreisel - 1953 - Proceedings of the XIth International Congress of Philosophy 14:39-49.
  46.  45
    Lambda calculus with types.H. P. Barendregt - 2013 - New York: Cambridge University Press. Edited by Wil Dekkers & Richard Statman.
    This handbook with exercises reveals the mathematical beauty of formalisms hitherto mostly used for software and hardware design and verification.
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  47. The Quantified Argument Calculus and Natural Logic.Hanoch Ben-Yami - 2020 - Dialectica 74 (2):179-214.
    The formalisation of Natural Language arguments in a formal language close to it in syntax has been a central aim of Moss’s Natural Logic. I examine how the Quantified Argument Calculus (Quarc) can handle the inferences Moss has considered. I show that they can be incorporated in existing versions of Quarc or in straightforward extensions of it, all within sound and complete systems. Moreover, Quarc is closer in some respects to Natural Language than are Moss’s systems – for instance, (...)
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  48.  29
    Note about Ł ukasiewicz's theorem concerning the system of axioms of the implicational propositional calculus.Bolesław Sobociński - 1978 - Notre Dame Journal of Formal Logic 19 (3):457-460.
  49. The Mathematical Analysis of Logic. Being an Essay towards a Calculus of Deductive Reasoning by George Boole - Die mathematische Analyse der Logik. Der Versuch eines Kalküls des deduktiven Schlieβens von George Boole.George Boole - 2004 - Bulletin of Symbolic Logic 10 (1):108-109.
  50.  49
    Models for inconsistent and incomplete differential calculus.Chris Mortensen - 1990 - Notre Dame Journal of Formal Logic 31 (2):274-285.
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