Results for 'relevance logic'

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  1.  10
    Advances in Contemporary Logic and Computer Science Proceedings of the Eleventh Brazilian Conference on Mathematical Logic, May 6-10, 1996, Salvador, Bahia, Brazil. [REVIEW]Walter A. Carnielli, Itala M. L. D'ottaviano & Brazilian Conference on Mathematical Logic - 1999 -
    This volume presents the proceedings from the Eleventh Brazilian Logic Conference on Mathematical Logic held by the Brazilian Logic Society (co-sponsored by the Centre for Logic, Epistemology and the History of Science, State University of Campinas, Sao Paulo) in Salvador, Bahia, Brazil. The conference and the volume are dedicated to the memory of professor Mario Tourasse Teixeira, an educator and researcher who contributed to the formation of several generations of Brazilian logicians. Contributions were made from leading (...)
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  2.  58
    Aristotle’s Assertoric Syllogistic and Modern Relevance Logic.Philipp Steinkrüger - 2015 - Synthese 192 (5):1413-1444.
    This paper sets out to evaluate the claim that Aristotle’s Assertoric Syllogistic is a relevance logic or shows significant similarities with it. I prepare the grounds for a meaningful comparison by extracting the notion of relevance employed in the most influential work on modern relevance logic, Anderson and Belnap’s Entailment. This notion is characterized by two conditions imposed on the concept of validity: first, that some meaning content is shared between the premises and the conclusion, (...)
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  3.  32
    Paraconsistency in Categories: Case of Relevance Logic.Vladimir L. Vasyukov - 2011 - Studia Logica 98 (3):429-443.
    Categorical-theoretic semantics for the relevance logic is proposed which is based on the construction of the topos of functors from a relevant algebra (considered as a preorder category endowed with the special endofunctors) in the category of sets Set. The completeness of the relevant system R of entailment is proved in respect to the semantic considered.
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  4.  16
    Substructural Fuzzy-Relevance Logic.Eunsuk Yang - 2015 - Notre Dame Journal of Formal Logic 56 (3):471-491.
    This paper proposes a new topic in substructural logic for use in research joining the fields of relevance and fuzzy logics. For this, we consider old and new relevance principles. We first introduce fuzzy systems satisfying an old relevance principle, that is, Dunn’s weak relevance principle. We present ways to obtain relevant companions of the weakening-free uninorm systems introduced by Metcalfe and Montagna and fuzzy companions of the system R of relevant implication and its neighbors. (...)
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  5.  5
    A Pretabular Classical Relevance Logic.Lisa Galminas & John G. Mersch - 2012 - Studia Logica 100 (6):1211-1221.
    In this paper we construct an extension, ℒ, of Anderson and Belnap's relevance logic R that is classical in the sense that it contains p&p → q as a theorem, and we prove that ℒ is pretabular in the sense that while it does not have a finite characteristic matrix, every proper normal extension of it does. We end the paper by commenting on the possibility of finding other classical relevance logics that are also pretabular.
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  6.  52
    The Concept of Relevance and the Logic Diagram Tradition.Jan Dejnožka - 2010 - Logica Universalis 4 (1):67-135.
    What is logical relevance? Anderson and Belnap say that the “modern classical tradition [,] stemming from Frege and Whitehead-Russell, gave no consideration whatsoever to the classical notion of relevance.” But just what is this classical notion? I argue that the relevance tradition is implicitly most deeply concerned with the containment of truth-grounds, less deeply with the containment of classes, and least of all with variable sharing in the Anderson–Belnap manner. Thus modern classical logicians such as Peirce, Frege, (...)
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  7.  78
    The Systems of Relevance Logic.Ryszard Mirek - 2011 - Argument: Biannual Philosophical Journal 1 (1):87-102.
    The system R, or more precisely the pure implicational fragment R›, is considered by the relevance logicians as the most important. The another central system of relevance logic has been the logic E of entailment that was supposed to capture strict relevant implication. The next system of relevance logic is RM or R-mingle. The question is whether adding mingle axiom to R› yields the pure implicational fragment RM› of the system? As concerns the weak (...)
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  8.  11
    An o-Space Decision Procedure for the Relevance Logic B+.Luca Viganò - 2000 - Studia Logica 66 (3):385-407.
    In previous work we gave a new proof-theoretical method for establishing upper-bounds on the space complexity of the provability problem of modal and other propositional non-classical logics. Here we extend and refine these results to give an O -space decision procedure for the basic positive relevance logic B+. We compute this upper-bound by first giving a sound and complete, cut-free, labelled sequent system for B+, and then establishing bounds on the application of the rules of this system.
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  9.  27
    What is Relevance Logic?Arnon Avron - 2014 - Annals of Pure and Applied Logic 165 (1):26-48.
    We suggest two precise abstract definitions of the notion of ‘relevance logic’ which are both independent of any proof system or semantics. We show that according to the simpler one, R → source is the minimal relevance logic, but R itself is not. In contrast, R and many other logics are relevance logics according to the second definition, while all fragments of linear logic are not.
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  10.  11
    Algebraic Study of Two Deductive Systems of Relevance Logic.Josep Maria Font & Gonzalo Rodríguez - 1994 - Notre Dame Journal of Formal Logic 35 (3):369-397.
    In this paper two deductive systems associated with relevance logic are studied from an algebraic point of view. One is defined by the familiar, Hilbert-style, formalization of R; the other one is a weak version of it, called WR, which appears as the semantic entailment of the Meyer-Routley-Fine semantics, and which has already been suggested by Wójcicki for other reasons. This weaker consequence is first defined indirectly, using R, but we prove that the first one turns out to (...)
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  11.  4
    Relevance Logic: Problems Open and Closed.Alasdair Urquhart - 2016 - Australasian Journal of Logic 13 (1).
    I discuss a collection of problems in relevance logic. The main problems discussed are: the decidability of the positive semilattice system, decidability of the fragments of R in a restricted number of variables, and the complexity of the decision problem for the implicational fragment of R. Some related problems are discussed along the way.
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  12.  15
    Positive Fragments of Relevance Logic and Algebras of Binary Relations.Robin Hirsch & Szabolcs Mikulás - 2010 - Review of Symbolic Logic 4 (1):81-105.
    We prove that algebras of binary relations whose similarity type includes intersection, union, and one of the residuals of relation composition form a nonfinitely axiomatizable quasivariety and that the equational theory is not finitely based. We apply this result to the problem of the completeness of the positive fragment of relevance logic with respect to binary relations.
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  13.  70
    A Three-Valued Interpretation for a Relevance Logic.Fred Johnson - 1976 - The Relevance Logic Newsletter 1 (3):123-128.
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  14.  22
    Semantics for Relevance Logic with Identity.Edwin D. Mares - 1992 - Studia Logica 51 (1):1 - 20.
    Models are constructed for a variety of systems of quantified relevance logic with identity. Models are given for systems with different principles governing the transitivity of identity and substitution, and the relative merits of these principles are discussed. The models in this paper are all extensions of the semantics of Fine's Semantics for Quantified Relevance Logic (Journal of Philosophical Logic 17 (1988)).
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  15.  19
    Restall’s Proof-Theoretic Pluralism and Relevance Logic.Teresa Kouri - 2016 - Erkenntnis 81 (6):1243-1252.
    Restall :279–291, 2014) proposes a new, proof-theoretic, logical pluralism. This is in contrast to the model-theoretic pluralism he and Beall proposed in Beall and Restall :475–493, 2000) and in Beall and Restall. What I will show is that Restall has not described the conditions on being admissible to the proof-theoretic logical pluralism in such a way that relevance logic is one of the admissible logics. Though relevance logic is not hard to add formally, one critical component (...)
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  16.  22
    A Second-Order Relevance Logic with Modality.James B. Freeman & Charles B. Daniels - 1979 - Studia Logica 38 (2):113 - 135.
    In this paper a system, RPF, of second-order relevance logic with S5 necessity is presented which contains a defined, notion of identity for propositions. A complete semantics is provided. It is shown that RPF allows for more than one necessary proposition. RPF contains primitive syntactic counterparts of the following semantic notions: (1) the reflexive, symmetrical, transitive binary alternativeness relation for S5 necessity, (2) the ternary Routley-Meyer alternativeness relation for implication, and (3) the Routley-Meyer notion of a prime intensional (...)
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  17.  18
    Relevance Logic Brings Hope to Hypothetico-Deductivism.C. Kenneth Waters - 1987 - Philosophy of Science 54 (3):453-464.
    Clark Glymour has argued that hypothetico-deductivism, which many take to be an important method of scientific confirmation, is hopeless because it cannot be reconstructed in classical logic. Such reconstructions, as Glymour points out, fail to uphold the condition of relevance between theory and evidence. I argue that the source of the irrelevant confirmations licensed by these reconstructions lies not with hypothetico-deductivism itself, but with the classical logic in which it is typically reconstructed. I present a new reconstruction (...)
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  18.  8
    Relevance Logic as a Conservative Extension of Classical Logic.David C. Makinson - unknown -
    Relevance logic is ordinarily seen as a subsystem of classical logic under the translation that replaces arrows by horseshoes. If, however, we consider the arrow as an additional connective alongside the horseshoe, then another perspective emerges: the theses of relevance logic, specifically the system R, may also be seen as the output of a conservative extension of the relation of classical consequence. We describe two ways in which this may be done. One is by defining (...)
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  19.  25
    Relevance Logic and the Calculus of Relations.Roger D. Maddux - 2010 - Review of Symbolic Logic 3 (1):41-70.
    Sound and complete semantics for classical propositional logic can be obtained by interpreting sentences as sets. Replacing sets with commuting dense binary relations produces an interpretation that turns out to be sound but not complete for R. Adding transitivity yields sound and complete semantics for RM, because all normal Sugihara matrices are representable as algebras of binary relations.
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  20. Relevance Logic.Michael Dunn & Greg Restall - 2002 - In D. Gabbay & F. Guenthner (eds.), Handbook of Philosophical Logic. Kluwer Academic Publishers.
     
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  21. A Natural Deduction Relevance Logic.Fred Johnson - 1977 - The Bulletin of the Section of Logic 6 (4):164-168.
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  22. Compositionality, Relevance, and Peirce's Logic of Existential Graphs.Ahti-Veikko Pietarinen - 2005 - Axiomathes 15 (4):513-540.
    Charles S. Peirce’s pragmatist theory of logic teaches us to take the context of utterances as an indispensable logical notion without which there is no meaning. This is not a spat against compositionality per se , since it is possible to posit extra arguments to the meaning function that composes complex meaning. However, that method would be inappropriate for a realistic notion of the meaning of assertions. To accomplish a realistic notion of meaning (as opposed e.g. to algebraic meaning), (...)
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  23.  46
    On When a Semantics is Not a Semantics: Some Reasons for Disliking the Routley-Meyer Semantics for Relevance Logic[REVIEW]B. J. Copeland - 1979 - Journal of Philosophical Logic 8 (1):399 - 413.
  24.  55
    Semantics for Quantified Relevance Logic.Kit Fine - 1988 - Journal of Philosophical Logic 17 (1):27 - 59.
  25.  6
    Note on Algebraic Models for Relevance Logic.Josep M. Font & Gonzalo Rodríguez - 1990 - Mathematical Logic Quarterly 36 (6):535-540.
  26.  20
    Quantifying Over Propositions in Relevance Logic: Nonaxiomatisability of Primary Interpretations of ∀P and ∃P.Philip Kremer - 1993 - Journal of Symbolic Logic 58 (1):334-349.
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  27. Review: B. J. Copeland, On When a Semantics is Not a Semantics: Some Reasons for Disliking the Routley-Meyer Semantics for Relevance Logic[REVIEW]Johan van Benthem - 1984 - Journal of Symbolic Logic 49 (3):994-995.
  28.  43
    Whither Relevance Logic?Arnon Avron - 1992 - Journal of Philosophical Logic 21 (3):243 - 281.
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  29.  15
    The Complexity of Decision Procedures in Relevance Logic II.Alasdair Urquhart - 1999 - Journal of Symbolic Logic 64 (4):1774-1802.
  30.  13
    An Axiomatic Version of Positive Semilattice Relevance Logic.G. Charlwood - 1981 - Journal of Symbolic Logic 46 (2):233-239.
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  31.  2
    Implicational Relevance Logic is 2-Exptime-Complete.Sylvain Schmitz - 2016 - Journal of Symbolic Logic 81 (2):641-661.
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  32. Review of “Hypothetico-Deductivism is Hopeless” by Clark Glymour,“Relevance Logic Brings Hope for Hypothetico-Deductivism” by C. Kenneth Waters, and “Truth, Content and Hypothetico-Deductive Method” by Thomas Grimes. [REVIEW]Brian Skyrms - 1992 - Journal of Symbolic Logic 57:756-758.
     
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  33.  2
    A Constructive Proof of a Theorem in Relevance Logic.Aleksandar Kron - 1985 - Mathematical Logic Quarterly 31 (25‐28):423-430.
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  34.  26
    A New Classical Relevance Logic.Garrel Pottinger - 1979 - Journal of Philosophical Logic 8 (1):135 - 147.
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  35.  11
    A More Relevant Relevance Logic.M. W. Bunder - 1979 - Notre Dame Journal of Formal Logic 20 (3):701-704.
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  36.  4
    Review: Clark Glymour, Discussion: Hypothetico-Deductivism is Hopeless; C. Kenneth Waters, Relevance Logic Brings Hope to Hypothetico-Deductivism; Thomas R. Grimes, Discussion: Truth, Content, and the Hypothetico-Deductive Method. [REVIEW]Brian Skyrms - 1992 - Journal of Symbolic Logic 57 (2):756-758.
  37.  3
    Glymour Clark. Discussion: Hypothetico-Deductivism is Hopeless. Philosophy of Science, Vol. 47 (1980), Pp. 322–325. Waters C. Kenneth. Relevance Logic Brings Hope to Hypothetico-Deductivism. Philosophy of Science, Vol. 54 (1987), Pp. 453–464. Grimes Thomas R.. Discussion: Truth, Content, and the Hypothetico-Deductive Method. Philosophy of Science, Vol. 57 (1990), Pp. 514–522. [REVIEW]Brian Skyrms - 1992 - Journal of Symbolic Logic 57 (2):756-758.
  38.  2
    Review: J. Michael Dunn, Relevance Logic and Entailment. [REVIEW]Harry Deutsch - 1992 - Journal of Symbolic Logic 57 (2):752-753.
  39. On When a Semantics is Not a Semantics: Some Reasons for Disliking the Routley-Meyer Semantics for Relevance Logic.B. J. Copeland - 1984 - Journal of Symbolic Logic 49 (3):994-995.
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  40. Dunn J. Michael. Relevance Logic and Entailment. Handbook of Philosophical Logic, Volume III, Alternatives to Classical Logic, Edited by Gabbay D. And Guenthner F., Synthese Library, Vol. 166, D. Reidel Publishing Company, Dordrecht Etc. 1986, Pp. 117–224. [REVIEW]Harry Deutsch - 1992 - Journal of Symbolic Logic 57 (2):752-753.
  41. Quantifying Over Propositions in Relevance Logic: Nonaxiomatisability of Primary Interpretations of $\Forall P$ and $\Exists P$.Philip Kremer - 1993 - Journal of Symbolic Logic 58 (1):334-349.
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  42. The Complexity of Decision Procedures in Relevance Logic II.Alasdair Urquhart - 1999 - Journal of Symbolic Logic 64 (4):1774-1802.
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  43. Copeland B. J.. On When a Semantics is Not a Semantics: Some Reasons for Disliking the Routley–Semantics for Relevance Logic. Journal of Philosophical Logic, Vol. 8 , Pp. 399–413. [REVIEW]Johan van Benthem - 1984 - Journal of Symbolic Logic 49 (3):994-995.
  44.  5
    Relevance Logic.Edwin Mares - 2008 - Stanford Encyclopedia of Philosophy.
  45.  14
    Note on Algebraic Models for Relevance Logic.Josep M. Font & Gonzalo Rodríguez - 1990 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 36 (6):535-540.
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  46.  14
    A Constructive Proof of a Theorem in Relevance Logic.Aleksandar Kron - 1985 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 31 (25-28):423-430.
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  47.  47
    Relevance Logic, Classical Logic, and Disjunctive Syllogism.John A. Barker - 1975 - Philosophical Studies 27 (6):361 - 376.
  48.  38
    The Justification for Relevance Logic.Maria Baghramian - 1988 - Philosophical Studies 32:32-43.
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  49. The Justification for Relevance Logic.Maria Baghramian - 1988 - Philosophical Studies 32:32-43.
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  50. Quantified relevance logic and generalised restricted generality.M. W. Bunder - 1980 - Logique Et Analyse 23 (90):319.
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