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  1. The Γ-Admissibility of Relevant Modal Logics II — The Method Using Metavaluations.Takahiro Seki - 2011 - Studia Logica 97 (3):351-383.
    The?-admissibility is one of the most important problems in the realm of relevant logics. To prove the 7-admissibility, either the method of normal models or the method using metavaluations may be employed. The?-admissibility of a wide class of relevant modal logics has been discussed in Part I based on a former method, but the?-admissibility based on metavaluations has not hitherto been fully considered. Sahlqvist axioms are well known as a means of expressing generalized forms of formulas with modal operators. This (...)
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  • The Γ-Admissibility of Relevant Modal Logics I — The Method of Normal Models.Takahiro Seki - 2011 - Studia Logica 97 (2):199-231.
    The admissibility of Ackermann's rule? is one of the most important problems in relevant logic. While the?-admissibility of normal modal logics based on the relevant logic R has been previously discussed, the case for weaker relevant modal logics has not yet been considered. The method of normal models has often been used to prove the?-admissibility. This paper discusses which relevant modal logics admit? from the viewpoint of the method of normal models.
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  • The Semantics of Entailment II.Richard Routley & Robert K. Meyer - 1972 - Journal of Philosophical Logic 1 (1):53 - 73.
  • Semantics for Relevant Logics.Alasdair Urquhart - 1972 - Journal of Symbolic Logic 37 (1):159-169.
  • Star and Perp: Two Treatments of Negation.J. Michael Dunn - 1993 - Philosophical Perspectives 7:331-357.
  • Models for Entailment.Kit Fine - 1974 - Journal of Philosophical Logic 3 (4):347 - 372.
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  • The Connectives.Ian Humberstone - unknown
     
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  • Epistemic Closure and Epistemic Logic I: Relevant Alternatives and Subjunctivism.Wesley H. Holliday - 2015 - Journal of Philosophical Logic 44 (1):1-62.
    Epistemic closure has been a central issue in epistemology over the last forty years. According to versions of the relevant alternatives and subjunctivist theories of knowledge, epistemic closure can fail: an agent who knows some propositions can fail to know a logical consequence of those propositions, even if the agent explicitly believes the consequence (having “competently deduced” it from the known propositions). In this sense, the claim that epistemic closure can fail must be distinguished from the fact that agents do (...)
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  • The Ontology of Justifications in the Logical Setting.Sergei N. Artemov - 2012 - Studia Logica 100 (1-2):17-30.
    Justification Logic provides an axiomatic description of justifications and delegates the question of their nature to semantics. In this note, we address the conceptual issue of the logical type of justifications: we argue that justifications in the logical setting are naturally interpreted as sets of formulas which leads to a class of epistemic models that we call modular models . We show that Fitting models for Justification Logic naturally encode modular models and can be regarded as convenient pre-models of the (...)
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  • Relevant Agents.Marta Bílková, Ondrej Majer, Michal Peliš & Greg Restall - 2010 - In Lev Beklemishev, Valentin Goranko & Valentin Shehtman (eds.), Advances in Modal Logic, Volume 8. CSLI Publications. pp. 22-38.
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  • Indicative Versus Subjunctive Conditionals, Congruential Versus Non-Hyperintensional Contexts.Timothy Williamson - 2006 - Philosophical Issues 16 (1):310–333.
    §0. A familiar if obscure idea: an indicative conditional presents its consequent as holding in the actual world on the supposition that its antecedent so holds, whereas a subjunctive conditional merely presents its consequent as holding in a world, typically counterfactual, in which its antecedent holds. Consider this pair.
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  • Ecidence Logic: A New Look at Neighborhood Structures.Johan van Benthem, David Fernández-Duque & Eric Pacuit - 2012 - In Thomas Bolander, Torben Braüner, Silvio Ghilardi & Justin Moss (eds.), Advances in Modal Logic, Volume 9. CSLI Publications. pp. 97-118.
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  • The Logic of Justification.Sergei Artemov - 2008 - Review of Symbolic Logic 1 (4):477-513.
    We describe a general logical framework, Justification Logic, for reasoning about epistemic justification. Justification Logic is based on classical propositional logic augmented by justification assertions t: F that read t is a justification for F. Justification Logic absorbs basic principles originating from both mainstream epistemology and the mathematical theory of proofs. It contributes to the studies of the well-known Justified True Belief vs. Knowledge problem. We state a general Correspondence Theorem showing that behind each epistemic modal logic, there is a (...)
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  • A Modality Called ‘Negation’.Francesco Berto - 2015 - Mind 124 (495):761-793.
    I propose a comprehensive account of negation as a modal operator, vindicating a moderate logical pluralism. Negation is taken as a quantifier on worlds, restricted by an accessibility relation encoding the basic concept of compatibility. This latter captures the core meaning of the operator. While some candidate negations are then ruled out as violating plausible constraints on compatibility, different specifications of the notion of world support different logical conducts for negations. The approach unifies in a philosophically motivated picture the following (...)
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  • Substructural Epistemic Logics.Igor Sedlár - 2015 - Journal of Applied Non-Classical Logics 25 (3):256-285.
    The article introduces substructural epistemic logics of belief supported by evidence. The logics combine normal modal epistemic logics with distributive substructural logics. Pieces of evidence are represented by points in substructural models and availability of evidence is modelled by a function on the point set. The main technical result is a general completeness theorem. Axiomatisations are provided by means of two-sorted Hilbert-style calculi. It is also shown that the framework presents a natural solution to the problem of logical omniscience.
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  • Justifications for Common Knowledge.Samuel Bucheli, Roman Kuznets & Thomas Studer - 2011 - Journal of Applied Non-Classical Logics 21 (1):35-60.
    Justification logics are epistemic logics that explicitly include justifications for the agents' knowledge. We develop a multi-agent justification logic with evidence terms for individual agents as well as for common knowledge. We define a Kripke-style semantics that is similar to Fitting's semantics for the Logic of Proofs LP. We show the soundness, completeness, and finite model property of our multi-agent justification logic with respect to this Kripke-style semantics. We demonstrate that our logic is a conservative extension of Yavorskaya's minimal bimodal (...)
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  • Relevant Logic: A Philosophical Interpretation.Reinhard Kahle - 2007 - Studia Logica 85 (3):419-424.
  • Entailment: The Logic of Relevance and Necessity.[author unknown] - 1975 - Studia Logica 54 (2):261-266.
  • The Γ-Admissibility of Relevant Modal Logics I — The Method of Normal Models.Takahiro Seki - 2011 - Studia Logica 97 (2):199-231.
    The admissibility of Ackermann’s rule γ is one of the most important problems in relevant logic. While the γ-admissibility of normal modal logics based on the relevant logic R has been previously discussed, the case for weaker relevant modal logics has not yet been considered. The method of normal models has often been used to prove the γ-admissibility. This paper discusses which relevant modal logics admit γ from the viewpoint of the method of normal models.
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  • An Algebraic Proof of the Admissibility of Γ in Relevant Modal Logics.Takahiro Seki - 2012 - Studia Logica 100 (6):1149-1174.
    The admissibility of Ackermann's rule γ is one of the most important problems in relevant logics. The admissibility of γ was first proved by an algebraic method. However, the development of Routley-Meyer semantics and metavaluational techniques makes it possible to prove the admissibility of γ using the method of normal models or the method using metavaluations, and the use of such methods is preferred. This paper discusses an algebraic proof of the admissibility of γ in relevant modal logics based on (...)
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  • Some Metacomplete Relevant Modal Logics.Takahiro Seki - 2013 - Studia Logica 101 (5):1115-1141.
    A logic is called metacomplete if formulas that are true in a certain preferred interpretation of that logic are theorems in its metalogic. In the area of relevant logics, metacompleteness is used to prove primeness, consistency, the admissibility of γ and so on. This paper discusses metacompleteness and its applications to a wider class of modal logics based on contractionless relevant logics and their neighbours using Slaney’s metavaluational technique.
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  • Entailment and Relevant Implication.Robert K. Meyer - 1968 - Logique Et Analyse 11:472-479.
  • Natural deduction systems for some quantified relevant logics.Ross T. Brady - 1984 - Logique Et Analyse 27 (8):355--377.
  • Neighborhoods for Entailment.Lou Goble - 2003 - Journal of Philosophical Logic 32 (5):483-529.
    This paper presents a neighborhood semantics for logics of entailment. It begins with a minimal system Min that expresses the most fundamental assumptions about the entailment relation, and continues by examining various extensions that reflect further assumptions that might be made about entailment. This leads first to the logic B that is the basic relevant logic, and then to more powerful systems. All of these logics are proved to be sound and strongly complete. With B the neighborhood semantics meets the (...)
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  • A Sahlqvist Theorem for Relevant Modal Logics.Takahiro Seki - 2003 - Studia Logica 73 (3):383-411.
    Kripke-completeness of every classical modal logic with Sahlqvist formulas is one of the basic general results on completeness of classical modal logics. This paper shows a Sahlqvist theorem for modal logic over the relevant logic Bin terms of Routley- Meyer semantics. It is shown that usual Sahlqvist theorem for classical modal logics can be obtained as a special case of our theorem.
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  • Why We Need a Relevant Theory of Conditionals.Edwin D. Mares - 1994 - Topoi 13 (1):31-36.
    This paper presents ConR (Conditional R), a logic of conditionals based on Anderson and Belnap''s system R. A Routley-Meyer-style semantics for ConR is given for the system (the completeness of ConR over this semantics is proved in E. Mares and A. Fuhrmann, A Relevant Theory of Conditionals (unpublished MS)). Moreover, it is argued that adopting a relevant theory of conditionals will improve certain theories that utilize conditionals, i.e. Lewis'' theory of causation, Lewis'' dyadic deontic logic, and Chellas'' dyadic deontic logic.
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  • Diamonds Are a Philosopher's Best Friends.Heinrich Wansing - 2002 - Journal of Philosophical Logic 31 (6):591-612.
    The knowability paradox is an instance of a remarkable reasoning pattern (actually, a pair of such patterns), in the course of which an occurrence of the possibility operator, the diamond, disappears. In the present paper, it is pointed out how the unwanted disappearance of the diamond may be escaped. The emphasis is not laid on a discussion of the contentious premise of the knowability paradox, namely that all truths are possibly known, but on how from this assumption the conclusion is (...)
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  • An Admissible Semantics for Propositionally Quantified Relevant Logics.Robert Goldblatt & Michael Kane - 2010 - Journal of Philosophical Logic 39 (1):73-100.
    The Routley-Meyer relational semantics for relevant logics is extended to give a sound and complete model theory for many propositionally quantified relevant logics (and some non-relevant ones). This involves a restriction on which sets of worlds are admissible as propositions, and an interpretation of propositional quantification that makes ∀ pA true when there is some true admissible proposition that entails all p -instantiations of A . It is also shown that without the admissibility qualification many of the systems considered are (...)
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  • Models for Relevant Modal Logics.André Fuhrmann - 1990 - Studia Logica 49 (4):501 - 514.
    Semantics are given for modal extensions of relevant logics based on the kind of frames introduced in [7]. By means of a simple recipe we may obtain from a class FRM (L) of unreduced frames characterising a (non-modal) logic L, frame-classes FRM (L.M) characterising conjunctively regular modal extensions L.M of L. By displaying an incompleteness phenomenon, it is shown how the recipe fails when reduced frames are under consideration.
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  • From the Knowability Paradox to the Existence of Proofs.W. Dean & H. Kurokawa - 2010 - Synthese 176 (2):177 - 225.
    The Knowability Paradox purports to show that the controversial but not patently absurd hypothesis that all truths are knowable entails the implausible conclusion that all truths are known. The notoriety of this argument owes to the negative light it appears to cast on the view that there can be no verification-transcendent truths. We argue that it is overly simplistic to formalize the views of contemporary verificationists like Dummett, Prawitz or Martin-Löf using the sort of propositional modal operators which are employed (...)
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  • Explicit Provability and Constructive Semantics.Sergei N. Artemov - 2001 - Bulletin of Symbolic Logic 7 (1):1-36.
    In 1933 Godel introduced a calculus of provability (also known as modal logic S4) and left open the question of its exact intended semantics. In this paper we give a solution to this problem. We find the logic LP of propositions and proofs and show that Godel's provability calculus is nothing but the forgetful projection of LP. This also achieves Godel's objective of defining intuitionistic propositional logic Int via classical proofs and provides a Brouwer-Heyting-Kolmogorov style provability semantics for Int which (...)
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  • Grafting Modalities Onto Substructural Implication Systems.Marcello D'agostino, Dov M. Gabbay & Alessandra Russo - 1997 - Studia Logica 59 (1):65-102.
    We investigate the semantics of the logical systems obtained by introducing the modalities and into the family of substructural implication logics (including relevant, linear and intuitionistic implication). Then, in the spirit of the LDS (Labelled Deductive Systems) methodology, we "import" this semantics into the classical proof system KE. This leads to the formulation of a uniform labelled refutation system for the new logics which is a natural extension of a system for substructural implication developed by the first two authors in (...)
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  • A Relevant Theory of Conditionals.Edwin D. Mares & André Fuhrmann - 1995 - Journal of Philosophical Logic 24 (6):645 - 665.
    In this paper we set out a semantics for relevant (counterfactual) conditionals. We combine the Routley-Meyer semantics for relevant logic with a semantics for conditionals based on selection functions. The resulting models characterize a family of conditional logics free from fallacies of relevance, in particular counternecessities and conditionals with necessary consequents receive a non-trivial treatment.
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  • The Semantics Ofr.Edwin D. Mares & Robert K. Meyer - 1993 - Journal of Philosophical Logic 22 (1):95 - 110.
    The Logic R4 is obtained by adding the axiom □(A v B) → (◇A v □B) to the modal relevant logic NR. We produce a model theory for this logic and show completeness. We also show that there is a natural embedding of a Kripke model for S4 in each R4 model structure.
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  • Relevant Logics and Their Rivals.Richard Routley, Val Plumwood, Robert K. Meyer & Ross T. Brady - 1982 - Ridgeview.
     
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  • The Semantics of R4.Edwin D. Mares & Robert K. Meyer - 1993 - Journal of Philosophical Logic 22 (1):95-110.
    The Logic R4 is obtained by adding the axiom □ → to the modal relevant logic NR. We produce a model theory for this logic and show completeness. We also show that there is a natural embedding of a Kripke model for S4 in each R4 model structure.
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  • Halldén Completeness for Relevant Modal Logics.Takahiro Seki - 2015 - Notre Dame Journal of Formal Logic 56 (2):333-350.
    Halldén completeness closely resembles the relevance property. To prove Halldén completeness in terms of Kripke-style semantics, the van Benthem–Humberstone theorem is often used. In relevant modal logics, the Halldén completeness of Meyer–Fuhrmann logics has been obtained using the van Benthem–Humberstone theorem. However, there remain a number of Halldén-incomplete relevant modal logics. This paper discusses the Halldén completeness of a wider class of relevant modal logics, namely, those with some Sahlqvist axioms.
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  • The Logic of Proofs, Semantically.Melvin Fitting - 2005 - Annals of Pure and Applied Logic 132 (1):1-25.
    A new semantics is presented for the logic of proofs (LP), [1, 2], based on the intuition that it is a logic of explicit knowledge. This semantics is used to give new proofs of several basic results concerning LP. In particular, the realization of S4 into LP is established in a way that carefully examines and explicates the role of the + operator. Finally connections are made with the conventional approach, via soundness and completeness results.
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  • An Alternative Semantics for Quantified Relevant Logic.Edwin D. Mares & Robert Goldblatt - 2006 - Journal of Symbolic Logic 71 (1):163-187.
    The quantified relevant logic RQ is given a new semantics in which a formula for all xA is true when there is some true proposition that implies all x-instantiations of A. Formulae are modelled as functions from variable-assignments to propositions, where a proposition is a set of worlds in a relevant model structure. A completeness proof is given for a basic quantificational system QR from which RQ is obtained by adding the axiom EC of 'extensional confinement': for all x(A V (...)
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  • The Single-Conclusion Proof Logic and Inference Rules Specification.Vladimir N. Krupski - 2001 - Annals of Pure and Applied Logic 113 (1-3):181-206.
    The logic of single-conclusion proofs () is introduced. It combines the verification property of proofs with the single valuedness of proof predicate and describes the operations on proofs induced by modus ponens rule and proof checking. It is proved that is decidable, sound and complete with respect to arithmetical proof interpretations based on single-valued proof predicates. The application to arithmetical inference rules specification and -admissibility testing is considered. We show that the provability in gives the complete admissibility test for the (...)
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  • Logic of Proofs.Sergei Artëmov - 1994 - Annals of Pure and Applied Logic 67 (1-3):29-59.
    In this paper individual proofs are integrated into provability logic. Systems of axioms for a logic with operators “A is provable” and “p is a proof of A” are introduced, provided with Kripke semantics and decision procedure. Completeness theorems with respect to the arithmetical interpretation are proved.
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  • Classically Complete Modal Relevant Logics.Edwin D. Mares - 1993 - Mathematical Logic Quarterly 39 (1):165-177.
    A variety of modal logics based on the relevant logic R are presented. Models are given for each of these logics and completeness is shown. It is also shown that each of these logics admits Ackermann's rule γ and as a corollary of this it is proved that each logic is a conservative extension of its counterpart based on classical logic, hence we call them “classically complete”. MSC: 03B45, 03B46.
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  • Paraconsistent Logic, Evidence, and Justification.Melvin Fitting - 2017 - Studia Logica 105 (6):1149-1166.
    In a forthcoming paper, Walter Carnielli and Abilio Rodrigues propose a Basic Logic of Evidence whose natural deduction rules are thought of as preserving evidence instead of truth. BLE turns out to be equivalent to Nelson’s paraconsistent logic N4, resulting from adding strong negation to Intuitionistic logic without Intuitionistic negation. The Carnielli/Rodrigues understanding of evidence is informal. Here we provide a formal alternative, using justification logic. First we introduce a modal logic, KX4, in which \ can be read as asserting (...)
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  • Decidability for Some Justification Logics with Negative Introspection.Thomas Studer - 2013 - Journal of Symbolic Logic 78 (2):388-402.
    Justification logics are modal logics that include justifications for the agent's knowledge. So far, there are no decidability results available for justification logics with negative introspection. In this paper, we develop a novel model construction for such logics and show that justification logics with negative introspection are decidable for finite constant specifications.
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  • A Sahlqvist Theorem for Relevant Modal Logics.Takahiro Seki - 2003 - Studia Logica 73 (3):383-411.
    Kripke-completeness of every classical modal logic with Sahlqvist formulas is one of the basic general results on completeness of classical modal logics. This paper shows a Sahlqvist theorem for modal logic over the relevant logic B in terms of Routley-Meyer semantics. It is shown that usual Sahlqvist theorem for classical modal logics can be obtained as a special case of our theorem.
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  • The Connectives.Lloyd Humberstone - 2011 - MIT Press.
    It will be an essential resource for philosophers, mathematicians, computer scientists, linguists, or any scholar who finds connectives, and the conceptual issues surrounding them, to be a source of interest.This landmark work offers both ...
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  • Halldén-Completeness and Modal Relevant Logic.Edwin Mares - 2003 - Logique Et Analyse 46.
  • Reasoning with Justifications.Melvin Fitting - unknown
    This is an expository paper in which the basic ideas of a family of Justification Logics are presented. Justification Logics evolved from a logic called LP, introduced by Sergei Artemov [1, 3], which formed the central part of a project to provide an arithmetic semantics for propositional intuitionistic logic. The project was successful, but there was a considerable bonus: LP came to be understood as a logic of knowledge with explicit justifications and, as such, was capable of addressing in a (...)
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  • Semantics of Entailment 0.Robert K. Meyer & Edwin D. Mares - 1993 - In Peter Schroeder-Heister & Kosta Dosen (eds.), Substructural Logics. Oxford Science Publications. pp. 239-258.
  • The Semantic Completeness Of Rk.Edwin Mares - 1992 - Reports on Mathematical Logic:3-10.
    This paper extends the argument of Mares, ``Classically Complete Modal Relevant Logics'' Zeitschrift fur mathematische Logik und Grundlagen der Mathematik, to show that the system RK is complete over an Extension of the Routley-Meyer semantics.
     
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