Results for 'propositional calculus'

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  1.  32
    Basic Propositional Calculus I.Mohammad Ardeshir & Wim Ruitenburg - 1998 - Mathematical Logic Quarterly 44 (3):317-343.
    We present an axiomatization for Basic Propositional Calculus BPC and give a completeness theorem for the class of transitive Kripke structures. We present several refinements, including a completeness theorem for irreflexive trees. The class of intermediate logics includes two maximal nodes, one being Classical Propositional Calculus CPC, the other being E1, a theory axiomatized by T → ⊥. The intersection CPC ∩ E1 is axiomatizable by the Principle of the Excluded Middle A V ∨ ⌝A. If (...)
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  2.  88
    Quantified propositional calculus and a second-order theory for NC1.Stephen Cook & Tsuyoshi Morioka - 2005 - Archive for Mathematical Logic 44 (6):711-749.
    Let H be a proof system for quantified propositional calculus (QPC). We define the Σqj-witnessing problem for H to be: given a prenex Σqj-formula A, an H-proof of A, and a truth assignment to the free variables in A, find a witness for the outermost existential quantifiers in A. We point out that the Σq1-witnessing problems for the systems G*1and G1 are complete for polynomial time and PLS (polynomial local search), respectively. We introduce and study the systems G*0 (...)
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  3.  41
    Basic Propositional Calculus II. Interpolation: II. Interpolation.Mohammad Ardeshir & Wim Ruitenburg - 2001 - Archive for Mathematical Logic 40 (5):349-364.
    Let ℒ and ? be propositional languages over Basic Propositional Calculus, and ℳ = ℒ∩?. Weprove two different but interrelated interpolation theorems. First, suppose that Π is a sequent theory over ℒ, and Σ∪ {C⇒C′} is a set of sequents over ?, such that Π,Σ⊢C⇒C′. Then there is a sequent theory Φ over ℳ such that Π⊢Φ and Φ, Σ⊢C⇒C′. Second, let A be a formula over ℒ, and C 1, C 2 be formulas over ?, such (...)
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  4.  15
    Propositional calculus.Peter Harold Nidditch - 1962 - New York,: Dover Publications.
  5.  64
    A propositional calculus for inconsistent deductive systems.Stanisław Jaśkowski - 1999 - Logic and Logical Philosophy 7:35.
  6. Propositional calculus for contradictory deductive systems.Stanisław Jaśkowski - 1969 - Studia Logica 24 (1):143 - 160.
  7.  61
    Is propositional calculus categorical?Jaroslav Peregrin - manuscript
    According to the standard definition, a first-order theory is categorical if all its models are isomorphic. The idea behind this definition obviously is that of capturing semantic notions in axiomatic terms: to be categorical is to be, in this respect, successful. Thus, for example, we may want to axiomatically delimit the concept of natural number, as it is given by the pre-theoretic semantic intuitions and reconstructed by the standard model. The well-known results state that this cannot be done within first-order (...)
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  8. A propositional calculus with denumerable matrix.Michael Dummett - 1959 - Journal of Symbolic Logic 24 (2):97-106.
  9. How May the Propositional Calculus Represent?Tristan Haze - 2017 - South American Journal of Logic 3 (1):173-184.
    This paper is a conceptual study in the philosophy of logic. The question considered is 'How may formulae of the propositional calculus be brought into a representational relation to the world?'. Four approaches are distinguished: (1) the denotational approach, (2) the abbreviational approach, (3) the truth-conditional approach, and (4) the modelling approach. (2) and (3) are very familiar, so I do not discuss them. (1), which is now largely obsolete, led to some interesting twists and turns in early (...)
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  10.  19
    A propositional calculus without the law of extensionality.R. Wielądek - 1969 - Studia Logica 24 (1):207-207.
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  11.  32
    iH-propositional calculus.A. Figallo Jr, G. Ramón & S. Saad - 2006 - Bulletin of the Section of Logic 35 (4):157-162.
  12.  9
    Sets, classes and the propositional calculus.E. Lopez-Escobar - 2005 - Manuscrito 28 (2):417-448.
    The propositional calculus AoC, “Algebra of Classes”,and the extended propositional calculus EAC, “Extended Algebra ofClasses” are introduced in this paper. They are extensions, by additionalpropositional functions which are not invariant under the biconditional,of the corresponding classical propositional systems. Theirorigin lies in an analysis, motivated by Cantor’s concept of the cardinalnumbers, of A. P. Morse’s impredicative, polysynthetic set theory.
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  13.  12
    A propositional calculus in which expressions are loosing their sense.K. Piróg-Rzepecka - 1966 - Studia Logica 18 (1):163-164.
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  14. Tables for the propositional calculus (logico-mathematical brain).René Calvache - 1966 - Miami, Fla.: Miami, Fla.. Edited by Sanabria, E. F. & [From Old Catalog].
     
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  15.  8
    Propositional Calculus.G. Hasenjaeger - 1965 - Journal of Symbolic Logic 30 (3):357-357.
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  16.  47
    Propositional calculus in implication and non-equivalence.A. N. Prior - 1969 - Notre Dame Journal of Formal Logic 10 (3):271-272.
  17.  39
    A propositional calculus in which three mutually undefinable functors are used as primitive terms.Czesław Lejewski - 1968 - Studia Logica 22 (1):17 - 50.
  18.  56
    An Alternative Propositional Calculus for Application to Empirical Sciences.Paul Weingartner - 2010 - Studia Logica 95 (1-2):233 - 257.
    The purpose of the paper is to show that by cleaning Classical Logic (CL) from redundancies (irrelevances) and uninformative complexities in the consequence class and from too strong assumptions (of CL) one can avoid most of the paradoxes coming up when CL is applied to empirical sciences including physics. This kind of cleaning of CL has been done successfully by distinguishing two types of theorems of CL by two criteria. One criterion (RC) forbids such theorems in which parts of the (...)
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  19.  66
    A formalization of the propositional calculus of H-B logic.Cecylia Rauszer - 1974 - Studia Logica 33 (1):23 - 34.
  20.  28
    A Finite Hilbert‐Style Axiomatization of the Implication‐Less Fragment of the Intuitionistic Propositional Calculus.Jordi Rebagliato & Ventura Verdú - 1994 - Mathematical Logic Quarterly 40 (1):61-68.
    In this paper we obtain a finite Hilbert-style axiomatization of the implicationless fragment of the intuitionistic propositional calculus. As a consequence we obtain finite axiomatizations of all structural closure operators on the algebra of {–}-formulas containing this fragment.
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  21.  27
    A propositional calculus intermediate between the minimal calculus and the classical.Charles Parsons - 1966 - Notre Dame Journal of Formal Logic 7 (4):353-358.
  22.  21
    Axiomatics.Propositional Calculus.R. H. Stoothoff, Robert Blanche, G. B. Keene & P. H. Nidditch - 1963 - Philosophical Quarterly 13 (52):278.
  23. On Interpreting the S5 Propositional Calculus: an essay in philosophical logic.Michael J. Carroll - 1976 - Dissertation, University of Iowa
    Discusses alternative interpretations of the modal operators, for the modal propositional logic S5.
     
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  24.  40
    Formalization of functionally complete propositional calculus with the functor of implication as the only primitive term.Czes?aw Lejewski - 1989 - Studia Logica 48 (4):479 - 494.
    The most difficult problem that Leniewski came across in constructing his system of the foundations of mathematics was the problem of defining definitions, as he used to put it. He solved it to his satisfaction only when he had completed the formalization of his protothetic and ontology. By formalization of a deductive system one ought to understand in this context the statement, as precise and unambiguous as possible, of the conditions an expression has to satisfy if it is added to (...)
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  25.  42
    Remarks on discussive propositional calculus.Tomasz Furmanowski - 1975 - Studia Logica 34 (1):39 - 43.
  26.  14
    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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  27.  39
    A cut-free Gentzen formulation of basic propositional calculus.Kentaro Kikuchi & Katsumi Sasaki - 2003 - Journal of Logic, Language and Information 12 (2):213-225.
    We introduce a Gentzen style formulation of Basic Propositional Calculus(BPC), the logic that is interpreted in Kripke models similarly tointuitionistic logic except that the accessibility relation of eachmodel is not necessarily reflexive. The formulation is presented as adual-context style system, in which the left hand side of a sequent isdivided into two parts. Giving an interpretation of the sequents inKripke models, we show the soundness and completeness of the system withrespect to the class of Kripke models. The cut-elimination (...)
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  28.  19
    The Classical Propositional Calculus of Arguments.Robert Bull - 1984 - Mathematical Logic Quarterly 30 (1-6):45-86.
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  29.  52
    Fragments of the propositional calculus.Leon Henkin - 1949 - Journal of Symbolic Logic 14 (1):42-48.
  30.  31
    Problems of substitution and admissibility in the modal system Grz and in intuitionistic propositional calculus.V. V. Rybakov - 1990 - Annals of Pure and Applied Logic 50 (1):71-106.
    Questions connected with the admissibility of rules of inference and the solvability of the substitution problem for modal and intuitionistic logic are considered in an algebraic framework. The main result is the decidability of the universal theory of the free modal algebra imageω extended in signature by adding constants for free generators. As corollaries we obtain: there exists an algorithm for the recognition of admissibility of rules with parameters in the modal system Grz, the substitution problem for Grz and for (...)
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  31.  48
    Metalogic of Intuitionistic Propositional Calculus.Alex Citkin - 2010 - Notre Dame Journal of Formal Logic 51 (4):485-502.
    With each superintuitionistic propositional logic L with a disjunction property we associate a set of modal logics the assertoric fragment of which is L . Each formula of these modal logics is interdeducible with a formula representing a set of rules admissible in L . The smallest of these logics contains only formulas representing derivable in L rules while the greatest one contains formulas corresponding to all admissible in L rules. The algebraic semantic for these logics is described.
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  32.  49
    Leibniz's syllogistico-propositional calculus.Hector-Neri Casta Neda - 1976 - Notre Dame Journal of Formal Logic 17 (4):481-500.
  33.  27
    Axiomatization of propositional calculus with Sheffer functors.Thomas W. Scharle - 1965 - Notre Dame Journal of Formal Logic 6 (3):209-217.
  34.  34
    Valuation Semantics for Intuitionic Propositional Calculus and some of its Subcalculi.Andréa Loparić - 2010 - Principia: An International Journal of Epistemology 14 (1):125-33.
    In this paper, we present valuation semantics for the Propositional Intuitionistic Calculus (also called Heyting Calculus) and three important subcalculi: the Implicative, the Positive and the Minimal Calculus (also known as Kolmogoroff or Johansson Calculus). Algorithms based in our definitions yields decision methods for these calculi. DOI:10.5007/1808-1711.2010v14n1p125.
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  35.  69
    Relationships between basic propositional calculus and substructural logics.Kentaro Kikuchi - 2001 - Bulletin of the Section of Logic 30 (1):15-20.
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  36.  29
    Note on duality in propositional calculus.Chandler Works & Wolfgang Yourgrau - 1968 - Notre Dame Journal of Formal Logic 9 (3):284-288.
  37. Peirce's axioms for propositional calculus.A. N. Prior - 1958 - Journal of Symbolic Logic 23 (2):135-136.
  38.  19
    x1. Introduction. The classical propositional calculus has an undeserved reputation among logicians as being essentially trivial. I hope to convince the reader that it presents some of the most challenging and intriguing problems in modern logic. Although the problem of the complexity of propositional proofs is very. [REVIEW]Alasdair Urquhart - 1995 - Bulletin of Symbolic Logic 1 (4):425-467.
    §1. Introduction. The classical propositional calculus has an undeserved reputation among logicians as being essentially trivial. I hope to convince the reader that it presents some of the most challenging and intriguing problems in modern logic. Although the problem of the complexity of propositional proofs is very natural, it has been investigated systematically only since the late 1960s. Interest in the problem arose from two fields connected with computers, automated theorem proving and computational complexity theory. The earliest (...)
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  39. Completeness of intuitionistic propositional calculus.Harvey Friedman - manuscript
    An assignment is a function f that assigns subsets of N to some atoms. Then f is extended to f* which sends every formula A of HPC to a subset of S(A).
     
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  40.  39
    Ideographic computation in the propositional calculus.Gerald B. Standley - 1954 - Journal of Symbolic Logic 19 (3):169-171.
  41.  19
    Proof routines for the propositional calculus.Hugues Leblanc - 1963 - Notre Dame Journal of Formal Logic 4 (2):81-104.
  42.  4
    Henkin Leon. Fragments of propositional calculus.Andrzej Mostowski - 1949 - Journal of Symbolic Logic 14 (3):197-198.
  43. A note on the completeness of Kozen's axiomatisation of the propositional μ-calculus.Igor Walukiewicz - 1996 - Bulletin of Symbolic Logic 2 (3):349-366.
    The propositional μ -calculus is an extension of the modal system K with a least fixpoint operator. Kozen posed a question about completeness of the axiomatisation of the logic which is a small extension of the axiomatisation of the modal system K. It is shown that this axiomatisation is complete.
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  44.  43
    A note on the system of propositional calculus with primitive rule of extensionality.K. Hałkowska - 1967 - Studia Logica 20 (1):150-150.
    The present paper deals with a systemS of propositional calculus, conjunction, equivalence and falsum being its primitive terms.The only primitive rule inS is the rule of extensionality defined by the scheme: $\frac{{E\alpha \beta ,\Phi (\alpha )}}{{\Phi (\beta )}}$.
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  45.  8
    A. the propositional calculus.Rudolf Carnap - 1959 - In Introduction to Semantics and Formalization of Logic. Harvard University Press. pp. 279-307.
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  46.  12
    A note on propositional calculus.Shalom Rosenberg - 1972 - Notre Dame Journal of Formal Logic 13 (4):506-510.
  47.  23
    A Formalisation of the Propositional Calculus Corresponding to Wang's Calculus of Partial Predicates.Alan Rose - 1963 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 9 (12-15):177-198.
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  48.  2
    Epistemological Remarks on the Propositional Calculus.Karl Britton - 1936 - Journal of Symbolic Logic 1 (2):69-70.
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  49.  1
    A Formalisation of the Propositional Calculus Corresponding to Wang's Calculus of Partial Predicates.Alan Rose - 1963 - Mathematical Logic Quarterly 9 (12‐15):177-198.
  50.  2
    A generalised propositional calculus.Peter Jablon - 1975 - Notre Dame Journal of Formal Logic 16 (2):295-297.
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