Search results for 'Propositional calculus' (try it on Scholar)

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  1. Kentaro Kikuchi & Katsumi Sasaki (2003). A Cut-Free Gentzen Formulation of Basic Propositional Calculus. Journal of Logic, Language and Information 12 (2):213-225.score: 240.0
    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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  2. Michael J. Carroll (1976). On Interpreting the S5 Propositional Calculus: An Essay in Philosophical Logic. Dissertation, University of Iowascore: 216.0
    Discusses alternative interpretations of the modal operators, for the modal propositional logic S5.
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  3. Emil Jerábek & Phuong Nguyen (2011). Simulating Non-Prenex Cuts in Quantified Propositional Calculus. Mathematical Logic Quarterly 57 (5):524-532.score: 210.0
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  4. Jordi Rebagliato & Ventura Verdú (1994). A Finite Hilbert‐Style Axiomatization of the Implication‐Less Fragment of the Intuitionistic Propositional Calculus. Mathematical Logic Quarterly 40 (1):61-68.score: 210.0
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  5. René[from old catalog] Calvache (1966). Tables for the Propositional Calculus (Logico-Mathematical Brain). Miami, Fla..score: 210.0
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  6. P. H. Nidditch (1962/1965). Propositional Calculus. New York, Dover Publications.score: 210.0
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  7. Michael Kaminski & Nissim Francez (2014). Relational Semantics of the Lambek Calculus Extended with Classical Propositional Logic. Studia Logica 102 (3):479-497.score: 192.0
    We show that the relational semantics of the Lambek calculus, both nonassociative and associative, is also sound and complete for its extension with classical propositional logic. Then, using filtrations, we obtain the finite model property for the nonassociative Lambek calculus extended with classical propositional logic.
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  8. Andréa Lopari? (2011). Valuation Semantics for Intuitionic Propositional Calculus and Some of its Subcalculi. Principia 14 (1):125-33.score: 186.0
    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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  9. Jaroslav Peregrin, Is Propositional Calculus Categorical?score: 180.0
    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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  10. Stanisław Jaśkowski (1975). Three Contributions to the Two-Valued Propositional Calculus. Studia Logica 34 (1):121 - 132.score: 180.0
    Three chapters contain the results independent of each other. In the first chapter I present a set of axioms for the propositional calculus which are shorter than the ones known so far, in the second one I give a method of defining all ternary connectives, in the third one, I prove that the probability of propositional functions is preserved under reversible substitutions.
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  11. Paul Weingartner (2010). An Alternative Propositional Calculus for Application to Empirical Sciences. Studia Logica 95 (1/2):233 - 257.score: 180.0
    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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  12. T. Thacher Robinson (1968). Independence of Two Nice Sets of Axioms for the Propositional Calculus. Journal of Symbolic Logic 33 (2):265-270.score: 180.0
    Kanger [4] gives a set of twelve axioms for the classical propositional Calculus which, together with modus ponens and substitution, have the following nice properties: (0.1) Each axiom contains $\supset$ , and no axiom contains more than two different connectives. (0.2) Deletions of certain of the axioms yield the intuitionistic, minimal, and classical refutability1 subsystems of propositional calculus. (0.3) Each of these four systems of axioms has the separation property: that if a theorem is provable in (...)
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  13. Othman Qasim Malhas (1987). Quantum Logic and the Classical Propositional Calculus. Journal of Symbolic Logic 52 (3):834-841.score: 180.0
    In much the same way that it is possible to construct a model of hyperbolic geometry in the Euclidean plane, it is possible to model quantum logic within the classical propositional calculus.
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  14. Wim Ruitenburg (1984). On the Period of Sequences (an(P)) in Intuitionistic Propositional Calculus. Journal of Symbolic Logic 49 (3):892 - 899.score: 180.0
    In classical propositional calculus for each proposition A(p) the following holds: $\vdash A(p) \leftrightarrow A^3(p)$ . In this paper we consider what remains of this in the intuitionistic case. It turns out that for each proposition A(p) the following holds: there is an n ∈ N such that $\vdash A^n(p) \leftrightarrow A^{n + 2}(p)$ . As a byproduct of the proof we give some theorems which may be useful elsewhere in propositional calculus.
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  15. Igor Walukiewicz (1996). A Note on the Completeness of Kozen's Axiomatisation of the Propositional Μ-Calculus. Bulletin of Symbolic Logic 2 (3):349-366.score: 180.0
    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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  16. Dexter Kozen (1988). A Finite Model Theorem for the Propositional Μ-Calculus. Studia Logica 47 (3):233 - 241.score: 180.0
    We prove a finite model theorem and infinitary completeness result for the propositional -calculus. The construction establishes a link between finite model theorems for propositional program logics and the theory of well-quasi-orders.
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  17. Mohammad Ardeshir & Wim Ruitenburg (2001). Basic Propositional Calculus II. Interpolation. Archive for Mathematical Logic 40 (5):349-364.score: 180.0
    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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  18. K. Hałkowska (1967). A Note on the System of Propositional Calculus with Primitive Rule of Extensionality. Studia Logica 20 (1):150-150.score: 180.0
    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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  19. T. Prucnal (1967). A Proof of Axiomatizability of Łukasiewicz's Three-Valued Implicational Propositional Calculus. Studia Logica 20 (1):144-144.score: 180.0
    LetL 3 c be the smallest set of propositional formulas, which containsCpCqpCCCpqCrqCCqpCrpCCCpqCCqrqCCCpqppand is closed with respect to substitution and detachment. Let $\mathfrak{M}_3^c $ be Łukasiewicz’s three-valued implicational matrix defined as follows:cxy=min (1,1−x+y), where $x,y \in \{ 0,\tfrac{1}{2},1\}$ . In this paper the following theorem is proved: $$L_3^c = E( \mathfrak{M}_3^c )$$ The idea used in the proof is derived from Asser’s proof of completeness of the two-valued propositional calculus. The proof given here is based on the Pogorzelski’s (...)
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  20. Dimitri Pataraia (2006). Description of All Functions Definable by Formulæ of the 2nd Order Intuitionistic Propositional Calculus on Some Linear Heyting Algebras. Journal of Applied Non-Classical Logics 16 (3-4):457-483.score: 180.0
    Explicit description of maps definable by formulæ of the second order intuitionistic propositional calculus is given on two classes of linear Heyting algebras?the dense ones and the ones which possess successors. As a consequence, it is shown that over these classes every formula is equivalent to a quantifier free formula in the dense case, and to a formula with quantifiers confined to the applications of the successor in the second case.
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  21. Czesław Lejewski (1989). Formalization of Functionally Complete Propositional Calculus with the Functor of Implication as the Only Primitive Term. Studia Logica 48 (4):479 - 494.score: 174.0
    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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  22. Mohammad Ardeshir & Wim Ruitenburg (1998). Basic Propositional Calculus I. Mathematical Logic Quarterly 44 (3):317-343.score: 162.0
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  23. Brian Hill & Francesca Poggiolesi (2010). A Contraction-Free and Cut-Free Sequent Calculus for Propositional Dynamic Logic. Studia Logica 94 (1):47 - 72.score: 156.0
    In this paper we present a sequent calculus for propositional dynamic logic built using an enriched version of the tree-hypersequent method and including an infinitary rule for the iteration operator. We prove that this sequent calculus is theoremwise equivalent to the corresponding Hilbert-style system, and that it is contraction-free and cut-free. All results are proved in a purely syntactic way.
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  24. Alex Citkin (2010). Metalogic of Intuitionistic Propositional Calculus. Notre Dame Journal of Formal Logic 51 (4):485-502.score: 156.0
    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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  25. Peter Schroeder-Heister (forthcoming). The Calculus of Higher-Level Rules, Propositional Quantification, and the Foundational Approach to Proof-Theoretic Harmony. Studia Logica:1-32.score: 156.0
    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 (rather than reductive) account of proof-theoretic harmony. With every set (...)
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  26. Steven Perron (2008). Examining Fragments of the Quantified Propositional Calculus. Journal of Symbolic Logic 73 (3):1051-1080.score: 156.0
    When restricted to proving $\Sigma _{i}^{q}$ formulas, the quantified propositional proof system $G_{i}^{\ast}$ is closely related to the $\Sigma _{i}^{b}$ theorems of Buss's theory $S_{2}^{i}$ . Namely, $G_{i}^{\ast}$ has polynomial-size proofs of the translations of theorems of $S_{2}^{i}$ , and $S_{2}^{i}$ proves that $G_{i}^{\ast}$ is sound. However, little is known about $G_{i}^{\ast}$ when proving more complex formulas. In this paper, we prove a witnessing theorem for $G_{i}^{\ast}$ similar in style to the KPT witnessing theorem for $T_{2}^{i}$ . This witnessing (...)
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  27. Jerome Frazee (1988). A New Symbolic Representation of the Basic Truth-Functions of the Propositional Calculus. History and Philosophy of Logic 9 (1):87-91.score: 152.0
    As with mathematics, logic is easier to do if its symbols and their rules are better. In a graphic way, the logic symbols introduced in thís paper show their truth-table values, their composite truth-functions, and how to say them as either ?or? or ?if ? then? propositions. Simple rules make the converse, add or remove negations, and resolve propositions.
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  28. Alexander Abian (1970). Completeness of the Generalized Propositional Calculus. Notre Dame Journal of Formal Logic 11 (4):449-452.score: 150.0
  29. W. V. Quine (1934). Ontological Remarks on the Propositional Calculus. Mind 43 (172):472-476.score: 150.0
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  30. Michael Dummett (1959). A Propositional Calculus with Denumerable Matrix. Journal of Symbolic Logic 24 (2):97-106.score: 150.0
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  31. Stanisław Jaśkowski (1969). Propositional Calculus for Contradictory Deductive Systems. Studia Logica 24 (1):143 - 160.score: 150.0
  32. W. V. Quine (1938). Completeness of the Propositional Calculus. Journal of Symbolic Logic 3 (1):37-40.score: 150.0
  33. G. E. Hughes (1957). The Independence of Axioms in the Propositional Calculus. Australasian Journal of Philosophy 35 (1):21 – 29.score: 150.0
  34. Hugues Leblanc (1962). Boolean Algebra and the Propositional Calculus. Mind 71 (283):383-386.score: 150.0
  35. Leon Henkin (1949). Fragments of the Propositional Calculus. Journal of Symbolic Logic 14 (1):42-48.score: 150.0
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  36. Alfred Horn (1962). The Separation Theorem of Intuitionist Propositional Calculus. Journal of Symbolic Logic 27 (4):391-399.score: 150.0
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  37. Czesław Lejewski (1968). A Propositional Calculus in Which Three Mutually Undefinable Functors Are Used as Primitive Terms. Studia Logica 22 (1):17 - 50.score: 150.0
  38. Iwao Nishimura (1960). On Formulas of One Variable in Intuitionistic Propositional Calculus. Journal of Symbolic Logic 25 (4):327-331.score: 150.0
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  39. Cecylia Rauszer (1974). A Formalization of the Propositional Calculus of H-B Logic. Studia Logica 33 (1):23 - 34.score: 150.0
  40. Xavier Caicedo Ferrer (1978). A Formal System for the Non-Theorems of the Propositional Calculus. Notre Dame Journal of Formal Logic 19 (1):147-151.score: 150.0
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  41. Diderik Batens (1980). A Completeness-Proof Method for Extensions of the Implicational Fragment of the Propositional Calculus. Notre Dame Journal of Formal Logic 21 (3):509-517.score: 150.0
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  42. Tomasz Furmanowski (1975). Remarks on Discussive Propositional Calculus. Studia Logica 34 (1):39 - 43.score: 150.0
  43. John P. Burgess (1981). The Completeness of Intuitionistic Propositional Calculus for its Intended Interpretation. Notre Dame Journal of Formal Logic 22 (1):17-28.score: 150.0
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  44. A. N. Prior (1958). Peirce's Axioms for Propositional Calculus. Journal of Symbolic Logic 23 (2):135-136.score: 150.0
  45. W. Sadowski (1961). A Proof of Completeness of the Two-Valued Propositional Calculus. Studia Logica 11 (1):55-55.score: 150.0
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  46. A. N. Prior (1969). Propositional Calculus in Implication and Non-Equivalence. Notre Dame Journal of Formal Logic 10 (3):271-272.score: 150.0
  47. C. A. Meredith & A. N. Prior (1963). Notes on the Axiomatics of the Propositional Calculus. Notre Dame Journal of Formal Logic 4 (3):171-187.score: 150.0
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  48. Hector-Neri Casta Neda (1976). Leibniz's Syllogistico-Propositional Calculus. Notre Dame Journal of Formal Logic 17 (4):481-500.score: 150.0
  49. Charles Parsons (1966). A Propositional Calculus Intermediate Between the Minimal Calculus and the Classical. Notre Dame Journal of Formal Logic 7 (4):353-358.score: 150.0
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  50. Hugues Leblanc (1963). Proof Routines for the Propositional Calculus. Notre Dame Journal of Formal Logic 4 (2):81-104.score: 150.0
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