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  1. Decidable Variables for Constructive Logics.Satoru Niki - 2020 - Mathematical Logic Quarterly 66 (4):484-493.
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  • The Dynamics of Belief as a Basis for Logic.Peter Gärdenfors - 1984 - British Journal for the Philosophy of Science 35 (1):1-10.
  • Unification and Admissible Rules for Paraconsistent Minimal Johanssonsʼ Logic J and Positive Intuitionistic Logic IPC.Sergei Odintsov & Vladimir Rybakov - 2013 - Annals of Pure and Applied Logic 164 (7-8):771-784.
    We study unification problem and problem of admissibility for inference rules in minimal Johanssonsʼ logic J and positive intuitionistic logic IPC+. This paper proves that the problem of admissibility for inference rules with coefficients is decidable for the paraconsistent minimal Johanssonsʼ logic J and the positive intuitionistic logic IPC+. Using obtained technique we show also that the unification problem for these logics is also decidable: we offer algorithms which compute complete sets of unifiers for any unifiable formula. Checking just unifiability (...)
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  • Subformula and Separation Properties in Natural Deduction Via Small Kripke Models: Subformula and Separation Properties.Peter Milne - 2010 - Review of Symbolic Logic 3 (2):175-227.
    Various natural deduction formulations of classical, minimal, intuitionist, and intermediate propositional and first-order logics are presented and investigated with respect to satisfaction of the separation and subformula properties. The technique employed is, for the most part, semantic, based on general versions of the Lindenbaum and Lindenbaum–Henkin constructions. Careful attention is paid to which properties of theories result in the presence of which rules of inference, and to restrictions on the sets of formulas to which the rules may be employed, restrictions (...)
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  • Logic of Classical Refutability and Class of Extensions of Minimal Logic.Sergei P. Odintsov - 2001 - Logic and Logical Philosophy 9:91.
  • For Want of an 'And': A Puzzle About Non-Conservative Extension.Lloyd Humberstone - 2005 - History and Philosophy of Logic 26 (3):229-266.
    Section 1 recalls a point noted by A. N. Prior forty years ago: that a certain formula in the language of a purely implicational intermediate logic investigated by R. A. Bull is unprovable in that logic but provable in the extension of the logic by the usual axioms for conjunction, once this connective is added to the language. Section 2 reminds us that every formula is interdeducible with (i.e. added to intuitionistic logic, yields the same intermediate logic as) some conjunction-free (...)
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  • On Two Properties of Structurally Complete Logics.Andrzej Biela & Wies law Dziobiak - 1982 - Bulletin of the Section of Logic 11 (3/4):154-158.
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  • Non-Classical Operations Hidden in Classical Logic.Vladimir Sotirov - 2008 - Journal of Applied Non-Classical Logics 18 (2-3):309-324.
    Objects of consideration are various non-classical connectives “hidden” in the classical logic in the form of G˛s with ˛ —a classical connective, and s—a propositional variable. One of them is negation, which is defined as G ⇒ s; another is necessity, which is defined as G ∧ s. The new operations are axiomatized and it is shown that they belong to the 4-valued logic of Lukasiewicz. A 2-point Kripke semantics is built leading directly to the 4-valued logical tables.
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  • Interpolation and Definability Over the Logic Gl.Larisa Maksimova - 2011 - Studia Logica 99 (1-3):249-267.
    In a previous paper [ 21 ] all extensions of Johansson’s minimal logic J with the weak interpolation property WIP were described. It was proved that WIP is decidable over J. It turned out that the weak interpolation problem in extensions of J is reducible to the same problem over a logic Gl, which arises from J by adding tertium non datur. In this paper we consider extensions of the logic Gl. We prove that only finitely many logics over Gl (...)
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  • Quine and Slater on Paraconsistency and Deviance.Francesco Paoli - 2003 - Journal of Philosophical Logic 32 (5):531-548.
    In a famous and controversial paper, B. H. Slater has argued against the possibility of paraconsistent logics. Our reply is centred on the distinction between two aspects of the meaning of a logical constant *c* in a given logic: its operational meaning, given by the operational rules for *c* in a cut-free sequent calculus for the logic at issue, and its global meaning, specified by the sequents containing *c* which can be proved in the same calculus. Subsequently, we use the (...)
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  • Semantical Analyses of Propositional Systems of Fitch and Nelson.Richard Routley - 1974 - Studia Logica 33 (3):283 - 298.
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  • The Pleasures of Anticipation: Enriching Intuitionistic Logic. [REVIEW]Lloyd Humberstone - 2001 - Journal of Philosophical Logic 30 (5):395-438.
    We explore a relation we call 'anticipation' between formulas, where A anticipates B (according to some logic) just in case B is a consequence (according to that logic, presumed to support some distinguished implicational connective →) of the formula A → B. We are especially interested in the case in which the logic is intuitionistic (propositional) logic and are much concerned with an extension of that logic with a new connective, written as "a", governed by rules which guarantee that for (...)
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  • Expressive Power and Semantic Completeness: Boolean Connectives in Modal Logic.I. L. Humberstone - 1990 - Studia Logica 49 (2):197 - 214.
    We illustrate, with three examples, the interaction between boolean and modal connectives by looking at the role of truth-functional reasoning in the provision of completeness proofs for normal modal logics. The first example (§ 1) is of a logic (more accurately: range of logics) which is incomplete in the sense of being determined by no class of Kripke frames, where the incompleteness is entirely due to the lack of boolean negation amongst the underlying non-modal connectives. The second example (§ 2) (...)
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  • On the Extension of Intuitionistic Propositional Logic with Kreisel-Putnam's and Scott's Schemes.Pierluigi Minari - 1986 - Studia Logica 45 (1):55-68.
    LetSKP be the intermediate prepositional logic obtained by adding toI (intuitionistic p.l.) the axiom schemes:S = (( ) ) (Scott), andKP = ()()() (Kreisel-Putnam). Using Kripke's semantics, we prove:1) SKP has the finite model property; 2) SKP has the disjunction property. In the last section of the paper we give some results about Scott's logic S = I+S.
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  • A Note on the Decidability of a Strong Relevant Logic.Harry Deutsch - 1985 - Studia Logica 44 (2):159 - 164.
    A modified filtrations argument is used to prove that the relevant logic S of [2] is decidable.
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  • Relatedness and Implication.Richard L. Epstein - 1979 - Philosophical Studies 36 (2):137 - 173.
  • Variations on da Costa C Systems and Dual-Intuitionistic Logics I. Analyses of Cω and CCω.Richard Sylvan - 1990 - Studia Logica 49 (1):47-65.
    Da Costa's C systems are surveyed and motivated, and significant failings of the systems are indicated. Variations are then made on these systems in an attempt to surmount their defects and limitations. The main system to emerge from this effort, system CC , is investigated in some detail, and dual-intuitionistic semantical analyses are developed for it and surrounding systems. These semantics are then adapted for the original C systems, first in a rather unilluminating relational fashion, subsequently in a more illuminating (...)
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  • Non-Classical Negation in the Works of Helena Rasiowa and Their Impact on the Theory of Negation.Dimiter Vakarelov - 2006 - Studia Logica 84 (1):105-127.
    The paper is devoted to the contributions of Helena Rasiowa to the theory of non-classical negation. The main results of Rasiowa in this area concerns–constructive logic with strong (Nelson) negation.
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  • A Kripke-Style Semantics for R-Mingle Using a Binary Accessibility Relation.J. Michael Dunn - 1976 - Studia Logica 35 (2):163 - 172.
  • The Revival of Rejective Negation.Lloyd Humberstone - 2000 - Journal of Philosophical Logic 29 (4):331-381.
    Whether assent ("acceptance") and dissent ("rejection") are thought of as speech acts or as propositional attitudes, the leading idea of rejectivism is that a grasp of the distinction between them is prior to our understanding of negation as a sentence operator, this operator then being explicable as applying to A to yield something assent to which is tantamount to dissent from A. Widely thought to have been refuted by an argument of Frege's, rejectivism has undergone something of a revival in (...)
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  • Negative Equivalence of Extensions of Minimal Logic.Sergei P. Odintsov - 2004 - Studia Logica 78 (3):417-442.
    Two logics L1 and L2 are negatively equivalent if for any set of formulas X and any negated formula ¬, ¬ can be deduced from the set of hypotheses X in L1 if and only if it can be done in L2. This article is devoted to the investigation of negative equivalence relation in the class of extensions of minimal logic.
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  • On the Degree of Complexity of Sentential Logics. A Couple of Examples.Jacek Hawranek & Jan Zygmunt - 1981 - Studia Logica 40 (2):141 - 153.
    The first part of the paper is a reminder of fundamental results connected with the adequacy problem for sentential logics with respect to matrix semantics. One of the main notions associated with the problem, namely that of the degree of complexity of a sentential logic, is elucidated by a couple of examples in the second part of the paper. E.g., it is shown that the minimal logic of Johansson and some of its extensions have degree of complexity 2. This is (...)
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  • Weak Logics with Strict Implication.Giovanna Corsi - 1987 - Mathematical Logic Quarterly 33 (5):389-406.
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  • Decidability Results in Non-Classical Logics. Part I.Dov M. Gabbay - 1975 - Annals of Mathematical Logic 8 (3):237.
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  • The Decidability of the Kreisel-Putnam System.Dov M. Gabbay - 1970 - Journal of Symbolic Logic 35 (3):431-437.
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  • Prior’s OIC Nonconservativity Example Revisited.Lloyd Humberstone - 2014 - Journal of Applied Non-Classical Logics 24 (3):209-235.
    In his 1964 note, ‘Two Additions to Positive Implication’, A. N. Prior showed that standard axioms governing conjunction yield a nonconservative extension of the pure implicational intermediate logic OIC of R. A. Bull. Here, after reviewing the situation with the aid of an adapted form of the Kripke semantics for intuitionistic and intermediate logics, we proceed to illuminate this example by transposing it to the setting of modal logic, and then relate it to the propositional logic of what have been (...)
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  • A Sequence of Decidable Finitely Axiomatizable Intermediate Logics with the Disjunction Property.D. M. Gabbay & D. H. J. De Jongh - 1974 - Journal of Symbolic Logic 39 (1):67-78.
  • Choice of Primitives: A Note on Axiomatizing Intuitionistic Logic.I. L. Humberstone - 1998 - History and Philosophy of Logic 19 (1):31-40.
    A purported axiomatization, by P. Gärdenfors, of intuitionistic propositional logic is shown to be incomplete, and that the mistaken claim to completeness is seen to result from carelessness in the choice of primitive logical vocabulary. This leads to a consideration of various ways of conceiving the distinction between primitive and defined vocabularies, along with the bearing of these differences on such matters as are discussed in connection with Gärdenfors.
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  • First Steps in Intuitionistic Model Theory.H. de Swart - 1978 - Journal of Symbolic Logic 43 (1):3-12.
  • Finite and Finitely Separable Intermediate Propositional Logics.Fabio Bellissima - 1988 - Journal of Symbolic Logic 53 (2):403-420.
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  • 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 sets of "constructive" (...)
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  • A Theorem of the Degree of Complexity of Some Sentential Logics.Jacek Hawranek & Jan Zygmunt - 1980 - Bulletin of the Section of Logic 9 (2):67-69.
    x1. This paper is a contribution to matrix semantics for sentential logics as presented in Los and Suszko [1] and Wojcicki [3], [4]. A generalization of Lindenbaum completeness lemma says that for each sentential logic there is a class K of matrices of the form such that the class is adequate for the logic, i.e., C = CnK.
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  • Mathematical Modal Logic: A View of its Evolution.Robert Goldblatt - 2003 - Journal of Applied Logic 1 (5-6):309-392.
  • Decidability of Some Extensions of J.R. I. Goldblatt - 1974 - Mathematical Logic Quarterly 20 (13‐18):203-206.
  • A Note on JP'.Peter W. Woodruff - 1970 - Theoria 36 (2):183-184.
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  • On the Structure of Paraconsistent Extensions of Johansson's Logic.Sergei P. Odintsov - 2005 - Journal of Applied Logic 3 (1):43-65.
  • Arithmetical Necessity, Provability and Intuitionistic Logic.Rob Goldblatt - 1978 - Theoria 44 (1):38-46.
  • Decidability of Some Extensions ofJ.R. I. Goldblatt - 1974 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 20 (13-18):203-206.
  • Grothendieck Topology as Geometric Modality.Robert I. Goldblatt - 1981 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 27 (31-35):495-529.
  • Grothendieck Topology as Geometric Modality.Robert I. Goldblatt - 1981 - Mathematical Logic Quarterly 27 (31‐35):495-529.