Results for 'Constructive propositional logic'

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  1.  10
    Constructing Natural Extensions of Propositional Logics.Adam Přenosil - 2016 - Studia Logica 104 (6):1179-1190.
    The proofs of some results of abstract algebraic logic, in particular of the transfer principle of Czelakowski, assume the existence of so-called natural extensions of a logic by a set of new variables. Various constructions of natural extensions, claimed to be equivalent, may be found in the literature. In particular, these include a syntactic construction due to Shoesmith and Smiley and a related construction due to Łoś and Suszko. However, it was recently observed by Cintula and Noguera that (...)
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  2.  34
    A Weak Intuitionistic Propositional Logic with Purely Constructive Implication.Mitsuhiro Okada - 1987 - Studia Logica 46 (4):371 - 382.
    We introduce subsystems WLJ and SI of the intuitionistic propositional logic LJ, by weakening the intuitionistic implication. These systems are justifiable by purely constructive semantics. Then the intuitionistic implication with full strength is definable in the second order versions of these systems. We give a relationship between SI and a weak modal system WM. In Appendix the Kripke-type model theory for WM is given.
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  3.  28
    Bounded Arithmetic, Propositional Logic and Complexity Theory.Jan Krajíček - 1995 - Cambridge University Press.
    This book presents an up-to-date, unified treatment of research in bounded arithmetic and complexity of propositional logic, with emphasis on independence proofs and lower bound proofs. The author discusses the deep connections between logic and complexity theory and lists a number of intriguing open problems. An introduction to the basics of logic and complexity theory is followed by discussion of important results in propositional proof systems and systems of bounded arithmetic. More advanced topics are then (...)
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  4.  29
    Propositional Logics of Closed and Open Substitutions Over Heyting's Arithmetic.Albert Visser - 2006 - Notre Dame Journal of Formal Logic 47 (3):299-309.
    In this note we compare propositional logics for closed substitutions and propositional logics for open substitutions in constructive arithmetical theories. We provide a strong example where these logics diverge in an essential way. We prove that for Markov's Arithmetic, that is, Heyting's Arithmetic plus Markov's principle plus Extended Church's Thesis, the logic of closed and the logic of open substitutions are the same.
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  5.  16
    Propositional Logic: Response to Ken López-Escobar.O. Chateaubriand - 2008 - Manuscrito 31 (1):115-120.
    Ken López-Escobar questions the timeless status of various entities—propositions, numbers, etc.—as well as my characterization of pure propositional logic as an ontological theory. In my response I argue that my characterization of propositional logic does not depend on timeless propositions, or on other abstract truth bearers, but is a characterization in terms of truth relations between any truth bearers. I also discuss his views on numbers as cultural constructs, as well as his use of quantification in (...)
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  6.  30
    On the Rosser–Turquette Method of Constructing Axiom Systems for Finitely Many-Valued Propositional Logics of Łukasiewicz.Mateusz M. Radzki - 2017 - Journal of Applied Non-Classical Logics 27 (1-2):27-32.
    A method of constructing Hilbert-type axiom systems for standard many-valued propositional logics was offered by Rosser and Turquette. Although this method is considered to be a solution of the problem of axiomatisability of a wide class of many-valued logics, the article demonstrates that it fails to produce adequate axiom systems. The article concerns finitely many-valued propositional logics of Łukasiewicz. It proves that if standard propositional connectives of the Rosser–Turquette axiom systems are definable in terms of the (...) connectives of Łukasiewicz’s logics, and thus, they are normal ones, then every Rosser–Turquette axiom system for a finite-valued Łukasiewicz’s logic is semantically incomplete. (shrink)
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  7.  89
    A Propositional Logic with Relative Identity Connective and a Partial Solution to the Paradox of Analysis.Xuefeng Wen - 2007 - Studia Logica 85 (2):251-260.
    We construct a a system PLRI which is the classical propositional logic supplied with a ternary construction , interpreted as the intensional identity of statements and in the context . PLRI is a refinement of Roman Suszko’s sentential calculus with identity (SCI) whose identity connective is a binary one. We provide a Hilbert-style axiomatization of this logic and prove its soundness and completeness with respect to some algebraic models. We also show that PLRI can be used to (...)
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  8.  1
    Propositions: Ontology and Logic.Robert Stalnaker - 2022 - New York, NY: Oxford University Press.
    A defense of an ontology of propositions and of some logical resources for representing them. It begins with an austere formulation of a theory of propositions in a first-order extensional logic, but then uses the commitments of this theory to justify an enrichment to modal logic - the logic of necessity and possibility - as an appropriate framework for regimented languages that are constructed to represent any of our scientific and philosophical commitments. Both the proof-theory and the (...)
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  9.  44
    Informational Interpretation of Substructural Propositional Logics.Heinrich Wansing - 1993 - Journal of Logic, Language and Information 2 (4):285-308.
    This paper deals with various substructural propositional logics, in particular with substructural subsystems of Nelson's constructive propositional logics N– and N. Doen's groupoid semantics is extended to these constructive systems and is provided with an informational interpretation in terms of information pieces and operations on information pieces.
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  10.  5
    On the Methods of Constructing Hilbert-Type Axiom Systems for Finite-Valued Propositional Logics of Łukasiewicz.Mateusz M. Radzki - 2021 - History and Philosophy of Logic 43 (1):70-79.
    The article explores the following question: which among the most often examined in the literature method of constructing Hilbert-type axiom systems for finite-valued propositional logics of Łukasi...
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  11.  25
    Constructing a Continuum of Predicate Extensions of Each Intermediate Propositional Logic.Nobu-Yuki Suzuki - 1995 - Studia Logica 54 (2):173 - 198.
    Wajsberg and Jankov provided us with methods of constructing a continuum of logics. However, their methods are not suitable for super-intuitionistic and modal predicate logics. The aim of this paper is to present simple ways of modification of their methods appropriate for such logics. We give some concrete applications as generic examples. Among others, we show that there is a continuum of logics (1) between the intuitionistic predicate logic and the logic of constant domains, (2) between a predicate (...)
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  12.  32
    Intuitionistic Propositional Logic Without 'Contraction' but with 'Reductio'.J. M. Méndez & F. Salto - 2000 - Studia Logica 66 (3):409-418.
    Routley- Meyer type relational complete semantics are constructed for intuitionistic contractionless logic with reductio. Different negation completions of positive intuitionistic logic without contraction are treated in a systematical, unified and semantically complete setting.
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  13.  4
    The Construction of a Bi-Modal Propositional Logic S2-S2 and its Decision Method.Hidesuke Ohsawa - 1978 - Kagaku Tetsugaku 11:119-137.
  14.  6
    Constructing Sequent Rules for Generalized Propositional Logics.Richard L. Call - 1984 - Notre Dame Journal of Formal Logic 25 (2):171-178.
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  15.  72
    Logical Connectives for Constructive Modal Logic.Heinrich Wansing - 2006 - Synthese 150 (3):459-482.
    Model-theoretic proofs of functional completenes along the lines of [McCullough 1971, Journal of Symbolic Logic 36, 15–20] are given for various constructive modal propositional logics with strong negation.
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  16.  18
    Some Applications of Propositional Logic to Cellular Automata.Stefano Cavagnetto - 2009 - Mathematical Logic Quarterly 55 (6):605-616.
    In this paper we give a new proof of Richardson's theorem [31]: a global function G[MATHEMATICAL DOUBLE-STRUCK CAPITAL A] of a cellular automaton [MATHEMATICAL DOUBLE-STRUCK CAPITAL A] is injective if and only if the inverse of G[MATHEMATICAL DOUBLE-STRUCK CAPITAL A] is a global function of a cellular automaton. Moreover, we show a way how to construct the inverse cellular automaton using the method of feasible interpolation from [20]. We also solve two problems regarding complexity of cellular automata formulated by Durand (...)
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  17.  44
    A Pragmatic Interpretation of Intuitionistic Propositional Logic.Carlo Dalla Pozza & Claudio Garola - 1995 - Erkenntnis 43 (1):81-109.
    We construct an extension P of the standard language of classical propositional logic by adjoining to the alphabet of a new category of logical-pragmatic signs. The well formed formulas of are calledradical formulas (rfs) of P;rfs preceded by theassertion sign constituteelementary assertive formulas of P, which can be connected together by means of thepragmatic connectives N, K, A, C, E, so as to obtain the set of all theassertive formulas (afs). Everyrf of P is endowed with atruth value (...)
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  18.  59
    Teaching the Practical Relevance of Propositional Logic.Marvin J. Croy - 2010 - Teaching Philosophy 33 (3):253-270.
    This article advances the view that propositional logic can and should be taught within general education logic courses in ways that emphasizes its practical usefulness, much beyond what commonly occurs in logic textbooks. Discussion and examples of this relevance include database searching, understanding structured documents, and integrating concepts of proof construction with argument analysis. The underlying rationale for this approach is shown to have import for questions concerning the design of logic courses, textbooks, and the (...)
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  19.  91
    A Short Note on Intuitionistic Propositional Logic with Multiple Conclusions.Valéria de Paiva & Luiz Pereira - 2005 - Manuscrito 28 (2):317-329.
    A common misconception among logicians is to think that intuitionism is necessarily tied-up with single conclusion calculi. Single conclusion calculi can be used to model intuitionism and they are convenient, but by no means are they necessary. This has been shown by such influential textbook authors as Kleene, Takeuti and Dummett, to cite only three. If single conclusions are not necessary, how do we guarantee that only intuitionistic derivations are allowed? Traditionally one insists on restrictions on particular rules: implication right, (...)
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  20.  16
    An Infinite Class of Maximal Intermediate Propositional Logics with the Disjunction Property.Pierangelo Miglioli - 1992 - Archive for Mathematical Logic 31 (6):415-432.
    Infinitely many intermediate propositional logics with the disjunction property are defined, each logic being characterized both in terms of a finite axiomatization and in terms of a Kripke semantics with the finite model property. The completeness theorems are used to prove that any two logics are constructively incompatible. As a consequence, one deduces that there are infinitely many maximal intermediate propositional logics with the disjunction property.
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  21.  9
    Review: N. N. Vorob'ev, The Problem of Deducibility in the Constructive Propositional Calculus with Strong Negation. [REVIEW]Andrzej Mostowski - 1953 - Journal of Symbolic Logic 18 (3):258-258.
  22.  5
    Review: N. N. Vorob'ev, A Constructive Propositional Calculus with Strong Negation. [REVIEW]Andrzej Mostowski - 1953 - Journal of Symbolic Logic 18 (3):257-258.
  23.  67
    On an Interpretation of Second Order Quantification in First Order Intuitionistic Propositional Logic.Andrew M. Pitts - 1992 - Journal of Symbolic Logic 57 (1):33-52.
    We prove the following surprising property of Heyting's intuitionistic propositional calculus, IpC. Consider the collection of formulas, φ, built up from propositional variables (p,q,r,...) and falsity $(\perp)$ using conjunction $(\wedge)$ , disjunction (∨) and implication (→). Write $\vdash\phi$ to indicate that such a formula is intuitionistically valid. We show that for each variable p and formula φ there exists a formula Apφ (effectively computable from φ), containing only variables not equal to p which occur in φ, and such (...)
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  24.  10
    A Method to Single Out Maximal Propositional Logics with the Disjunction Property II.Mauro Ferrari & Pierangelo Miglioli - 1995 - Annals of Pure and Applied Logic 76 (2):117-168.
    This is the second part of a paper devoted to the study of the maximal intermediate propositional logics with the disjunction property , whose first part has appeared in this journal with the title “A method to single out maximal propositional logics with the disjunction property I”. In the first part we have explained the general results upon which a method to single out maximal constructive logics is based and have illustrated such a method by exhibiting the (...)
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  25.  23
    Exhibiting Wide Families of Maximal Intermediate Propositional Logics with the Disjunction Property.Guido Bertolotti, Pierangelo Miglioli & Daniela Silvestrini - 1996 - Mathematical Logic Quarterly 42 (1):501-536.
    We provide results allowing to state, by the simple inspection of suitable classes of posets , that the corresponding intermediate propositional logics are maximal among the ones which satisfy the disjunction property. Starting from these results, we directly exhibit, without using the axiom of choice, the Kripke frames semantics of 2No maximal intermediate propositional logics with the disjunction property. This improves previous evaluations, giving rise to the same conclusion but made with an essential use of the axiom of (...)
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  26.  15
    A(Nother) Characterization of Intuitionistic Propositional Logic.Rosalie Iemhoff - 2001 - Annals of Pure and Applied Logic 113 (1-3):161-173.
    In Iemhoff we gave a countable basis for the admissible rules of . Here, we show that there is no proper superintuitionistic logic with the disjunction property for which all rules in are admissible. This shows that, relative to the disjunction property, is maximal with respect to its set of admissible rules. This characterization of is optimal in the sense that no finite subset of suffices. In fact, it is shown that for any finite subset X of , for (...)
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  27.  32
    Matrix Representations for Structural Strengthenings of a Propositional Logic.Piotr Wojtylak - 1979 - Studia Logica 38 (3):263 - 266.
    The aim of this paper is to show that the operations of forming direct products and submatrices suffice to construct exhaustive semantics for all structural strengthenings of the consequence determined by a given class of logical matrices.
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  28. Sentence, Proposition, Judgment, Statement, and Fact: Speaking About the Written English Used in Logic.John Corcoran - 2009 - In W. A. Carnielli (ed.), The Many Sides of Logic. College Publications. pp. 71-103.
    The five English words—sentence, proposition, judgment, statement, and fact—are central to coherent discussion in logic. However, each is ambiguous in that logicians use each with multiple normal meanings. Several of their meanings are vague in the sense of admitting borderline cases. In the course of displaying and describing the phenomena discussed using these words, this paper juxtaposes, distinguishes, and analyzes several senses of these and related words, focusing on a constellation of recommended senses. One of the purposes of this (...)
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  29.  3
    Review: N. N. Vorob'ev, A New Algorithm of Deducibility in the Constructive Propositional Calculus. [REVIEW]E. M. Fels - 1964 - Journal of Symbolic Logic 29 (2):109-109.
  30.  28
    The Basic Constructive Logic for Negation-Consistency Defined with a Propositional Falsity Constant.José M. Méndez, Gemma Robles & Francisco Salto - 2007 - Bulletin of the Section of Logic 36 (1-2):45-58.
  31. Propositional Dynamic Logic as a Logic of Belief Revision Vol. 5110 Lnai.Jan van Eijck & Yanjing Wang - 2008
    This paper shows how propositional dynamic logic can be interpreted as a logic for multi-agent belief revision. For that we revise and extend the logic of communication and change of [9]. Like LCC, our logic uses PDL as a base epistemic language. Unlike LCC, we start out from agent plausibilities, add their converses, and build knowledge and belief operators from these with the PDL constructs. We extend the update mechanism of LCC to an update mechanism (...)
     
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  32.  29
    Constructive Logic and the Medvedev Lattice.Sebastiaan A. Terwijn - 2006 - Notre Dame Journal of Formal Logic 47 (1):73-82.
    We study the connection between factors of the Medvedev lattice and constructive logic. The algebraic properties of these factors determine logics lying in between intuitionistic propositional logic and the logic of the weak law of the excluded middle (also known as De Morgan, or Jankov, logic). We discuss the relation between the weak law of the excluded middle and the algebraic notion of join-reducibility. Finally we discuss autoreducible degrees.
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  33. Non-Constructive Procedural Theory of Propositional Problems and the Equivalence of Solutions.Ivo Pezlar - 2019 - In Igor Sedlár & Martin Blicha (eds.), The Logica Yearbook 2018. London: College Publications. pp. 197-210.
    We approach the topic of solution equivalence of propositional problems from the perspective of non-constructive procedural theory of problems based on Transparent Intensional Logic (TIL). The answer we put forward is that two solutions are equivalent if and only if they have equivalent solution concepts. Solution concepts can be understood as a generalization of the notion of proof objects from the Curry-Howard isomorphism.
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  34.  7
    The Basic Constructive Logic for Absolute Consistency Defined with a Propositional Falsity Constant.Gemma Robles - 2008 - Logic Journal of the IGPL 16 (3):275-291.
    The logic BKc6 is the basic constructive logic in the ternary relational semantics adequate to consistency understood as absolute consistency, i.e., non-triviality. Negation is introduced in BKc6 with a negation connective. The aim of this paper is to define the logic BKc6F. In this logic negation is introduced via a propositional falsity constant. We prove that BKc6 and BKc6F are definitionally equivalent. Then, we show how to extend BKc6F within the spectrum of logics delimited (...)
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  35.  4
    The Basic Constructive Logic for a Weak Sense of Consistency Defined with a Propositional Falsity Constant.G. Robles & J. M. Mendez - 2008 - Logic Journal of the IGPL 16 (1):33-41.
    The logic BKc1 is the basic constructive logic in the ternary relational semantics adequate to consistency understood as the absence of the negation of any theorem. Negation is introduced in BKc1 with a negation connective. The aim of this paper is to define the logic BKc1F. In this logic negation is introduced via a propositional falsity constant. We prove that BKc1 and BKc1F are definitionally equivalent.
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  36. Propositional Epistemic Logics with Quantification Over Agents of Knowledge.Gennady Shtakser - 2018 - Studia Logica 106 (2):311-344.
    The paper presents a family of propositional epistemic logics such that languages of these logics are extended by quantification over modal operators or over agents of knowledge and extended by predicate symbols that take modal operators as arguments. Denote this family by \}\). There exist epistemic logics whose languages have the above mentioned properties :311–350, 1995; Lomuscio and Colombetti in Proceedings of ATAL 1996. Lecture Notes in Computer Science, vol 1193, pp 71–85, 1996). But these logics are obtained from (...)
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  37.  14
    A Constructive Negation Defined with a Negation Connective for Logics Including Bp+.Gemma Robles, Francisco Salto & José M. Méndez - 2005 - Bulletin of the Section of Logic 34 (3):177-190.
    The concept of constructive negation we refer to in this paper is (minimally) intuitionistic in character (see [1]). The idea is to understand the negation of a proposition A as equivalent to A implying a falsity constant of some sort. Then, negation is introduced either by means of this falsity constant or, as in this paper, by means of a propositional connective defined with the constant. But, unlike intuitionisitc logic, the type of negation we develop here is, (...)
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  38. Propositional Dynamic Logic as a Logic of Knowledge Update and Belief Revision.Jan van Eijck - unknown
    This talk shows how propositional dynamic logic (PDL) can be interpreted as a logic for multi-agent knowledge update and belief revision, or as a logic of preference change, if the basic relations are read as preferences instead of plausibilities. Our point of departure is the logic of communication and change (LCC) of [9]. Like LCC, our logic uses PDL as a base epistemic language. Unlike LCC, we start out from agent plausibilities, add their converses, (...)
     
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  39.  21
    Construction of Tableaux for Classical Logic: Tableaux as Combinations of Branches, Branches as Chains of Sets.Tomasz Jarmużek - 2007 - Logic and Logical Philosophy 16 (1):85-101.
    The paper is devoted to an approach to analytic tableaux for propositional logic, but can be successfully extended to other logics. The distinguishing features of the presented approach are:(i) a precise set-theoretical description of tableau method; (ii) a notion of tableau consequence relation is defined without help of a notion of tableau, in our universe of discourse the basic notion is a branch;(iii) we define a tableau as a finite set of some chosen branches which is enough to (...)
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  40.  43
    Structured Propositions and the Logical Form of Predication.Gary Ostertag - 2019 - Synthese 196 (4):1475-1499.
    Jeffrey King, Scott Soames, and others have recently challenged the familiar identification of a Russellian proposition, such as the proposition that Brutus stabbed Caesar, with an ordered sequence constructed out of objects, properties, and relations. There is, as they point out, a surplus of candidate sequences available that are each equally serviceable. If so, any choice among these candidates will be arbitrary. In this paper, I show that, unless a controversial assumption is made regarding the nature of nonsymmetrical relations, none (...)
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  41.  19
    Classical and Nonclassical Logics: An Introduction to the Mathematics of Propositions.Eric Schechter - 2005 - Princeton University Press.
    Classical logic is traditionally introduced by itself, but that makes it seem arbitrary and unnatural. This text introduces classical alongside several nonclassical logics (relevant, constructive, quantative, paraconsistent).
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  42.  45
    Constructive Interpolation in Hybrid Logic.Patrick Blackburn & Maarten Marx - 2003 - Journal of Symbolic Logic 68 (2):463-480.
    Craig's interpolation lemma (if φ → ψ is valid, then φ → θ and θ → ψ are valid, for θ a formula constructed using only primitive symbols which occur both in φ and ψ) fails for many propositional and first order modal logics. The interpolation property is often regarded as a sign of well-matched syntax and semantics. Hybrid logicians claim that modal logic is missing important syntactic machinery, namely tools for referring to worlds, and that adding such (...)
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  43.  17
    Propositional Epistemic Logics with Quantification Over Agents of Knowledge (An Alternative Approach).Gennady Shtakser - 2019 - Studia Logica 107 (4):753-780.
    In the previous paper with a similar title :311–344, 2018), we presented a family of propositional epistemic logics whose languages are extended by two ingredients: by quantification over modal operators or over agents of knowledge and by predicate symbols that take modal operators as arguments. We denoted this family by \}\). The family \}\) is defined on the basis of a decidable higher-order generalization of the loosely guarded fragment of first-order logic. And since HO-LGF is decidable, we obtain (...)
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  44.  16
    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 B is (...)
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  45.  32
    Propositional Identity and Logical Necessity.David B. Martens - 2004 - Australasian Journal of Logic 2:1-11.
    In two early papers, Max Cresswell constructed two formal logics of propositional identity, pcr and fcr, which he observed to be respectively deductively equivalent to modal logics s4 and s5. Cresswell argued informally that these equivalences respectively “give . . . evidence” for the correctness of s4 and s5 as logics of broadly logical necessity. In this paper, I describe weaker propositional identity logics than pcr that accommodate core intuitions about identity and I argue that Cresswell’s informal arguments (...)
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  46.  36
    Quantum Logic and the Classical Propositional Calculus.Othman Qasim Malhas - 1987 - Journal of Symbolic Logic 52 (3):834-841.
    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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  47. A Canonical Model Construction For Substructural Logics With Strong Negation.N. Kamide - 2002 - Reports on Mathematical Logic:95-116.
    We introduce Kripke models for propositional substructural logics with strong negation, and show the completeness theorems for these logics using an extended Ishihara's canonical model construction method. The framework presented can deal with a broad range of substructural logics with strong negation, including a modified version of Nelson's logic N$^-$, Wansing's logic COSPL, and extended versions of Visser's basic propositional logic, positive relevant logics, Corsi's logics and M\'endez's logics.
     
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  48.  7
    Towards Logical Operations Research—Propositional Case.Gennady Davydov & Inna Davydova - 2001 - Annals of Pure and Applied Logic 113 (1-3):95-119.
    Tautology is interpreted as a necessary condition for the workability of an operations system. This condition suggests the following possibilities: the stable solvability of balance equations between available resources and requests for them; the calculation of potential and kinetic of the system together with the estimation of the contribution of every operation to the kinetic of the system; the construction of a deadlockless infinite cyclic process for performance of some works.
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  49. Counting the Maximal Intermediate Constructive Logics.Mauro Ferrari & Pierangelo Miglioli - 1993 - Journal of Symbolic Logic 58 (4):1365-1401.
    A proof is given that the set of maximal intermediate propositional logics with the disjunction property and the set of maximal intermediate predicate logics with the disjunction property and the explicit definability property have the power of continuum. To prove our results, we introduce various notions which might be interesting by themselves. In particular, we illustrate a method to generate wide sets of pairwise "constructively incompatible constructive logics". We use a notion of "semiconstructive" logic and define wide (...)
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  50.  44
    On a Second Order Propositional Operator in Intuitionistic Logic.A. S. Troelstra - 1981 - Studia Logica 40 (2):113 - 139.
    This paper studies, by way of an example, the intuitionistic propositional connective * defined in the language of second order propositional logic by. In full topological models * is not generally definable, but over Cantor-space and the reals it can be classically shown that; on the other hand, this is false constructively, i.e. a contradiction with Church's thesis is obtained. This is comparable with some well-known results on the completeness of intuitionistic first-order predicate logic.Over [0, 1], (...)
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