Search results for 'relevant logic' (try it on Scholar)

  1.  6
    Walter A. Carnielli, Itala M. L. D'ottaviano & Brazilian Conference on Mathematical Logic (1999). Advances in Contemporary Logic and Computer Science Proceedings of the Eleventh Brazilian Conference on Mathematical Logic, May 6-10, 1996, Salvador, Bahia, Brazil. [REVIEW] Monograph Collection (Matt - Pseudo).
    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 (...)
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  2. Mark Jago (2013). Recent Work in Relevant Logic. Analysis 73 (3):526-541.
    This paper surveys important work done in relevant logic in the past 10 years.
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  3.  46
    Edwin D. Mares (2009). General Information in Relevant Logic. Synthese 167 (2):343 - 362.
    This paper sets out a philosophical interpretation of the model theory of Mares and Goldblatt (The Journal of Symbolic Logic 71, 2006). This interpretation distinguishes between truth conditions and information conditions. Whereas the usual Tarskian truth condition holds for universally quantified statements, their information condition is quite different. The information condition utilizes general propositions . The present paper gives a philosophical explanation of general propositions and argues that these are needed to give an adequate theory of general information.
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  4.  99
    Wesley H. Holliday (2015). Epistemic Closure and Epistemic Logic I: Relevant Alternatives and Subjunctivism. 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 (...)
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  5.  36
    Edwin David Mares (2004). Relevant Logic: A Philosophical Interpretation. Cambridge Univeristy Press.
    This book introduces the reader to relevant logic and provides it with a philosophical interpretation. The defining feature of relevant logic is that it forces the premises of an argument to be really used ('relevant') in deriving its conclusion. The logic is placed in the context of possible world semantics and situation semantics, which are then applied to provide an understanding of the various logical particles (especially implication and negation) and natural language conditionals. The (...)
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  6.  5
    Diderik Batens (2013). Propositional Logic Extended with a Pedagogically Useful Relevant Implication. Logic and Logical Philosophy.
    First and foremost, this paper concerns the combination of classical propositional logic with a relevant implication. The proposed combination is simple and transparent from a proof theoretic point of view and at the same time extremely useful for relating formal logic to natural language sentences. A specific system will be presented and studied, also from a semantic point of view. The last sections of the paper contain more general considerations on combining classical propositional logic with a (...)
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  7.  18
    Lou Goble (2000). An Incomplete Relevant Modal Logic. Journal of Philosophical Logic 29 (1):103-119.
    The relevant modal logic G is a simple extension of the logic RT, the relevant counterpart of the familiar classically based system T. Using the Routley-Meyer semantics for relevant modal logics, this paper proves three main results regarding G: (i) G is semantically complete, but only with a non-standard interpretation of necessity. From this, however, other nice properties follow. (ii) With a standard interpretation of necessity, G is semantically incomplete; there is no class of frames (...)
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  8.  96
    Wesley H. Holliday (2012). Epistemic Logic, Relevant Alternatives, and the Dynamics of Context. Lecture Notes in Computer Science 7415:109-129.
    According to the Relevant Alternatives (RA) Theory of knowledge, knowing that something is the case involves ruling out (only) the relevant alternatives. The conception of knowledge in epistemic logic also involves the elimination of possibilities, but without an explicit distinction, among the possibilities consistent with an agent’s information, between those relevant possibilities that an agent must rule out in order to know and those remote, far-fetched or otherwise irrelevant possibilities. In this article, I propose formalizations of (...)
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  9.  19
    Ryo Kashima & Norihiro Kamide (1999). Substructural Implicational Logics Including the Relevant Logic E. Studia Logica 63 (2):181-212.
    We introduce several restricted versions of the structural rules in the implicational fragment of Gentzen's sequent calculus LJ. For example, we permit the applications of a structural rule only if its principal formula is an implication. We investigate cut-eliminability and theorem-equivalence among various combinations of them. The results include new cut-elimination theorems for the implicational fragments of the following logics: relevant logic E, strict implication S4, and their neighbors (e.g., E-W and S4-W); BCI-logic, BCK-logic, relevant (...)
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  10.  22
    Edwin D. Mares & Robert Goldblatt (2006). An Alternative Semantics for Quantified Relevant Logic. 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 (...)
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  11.  26
    Kosta Došen (1992). The First Axiomatization of Relevant Logic. Journal of Philosophical Logic 21 (4):339 - 356.
    This is a review, with historical and critical comments, of a paper by I. E. Orlov from 1928, which gives the oldest known axiomatization of the implication-negation fragment of the relevant logic R. Orlov's paper also foreshadows the modal translation of systems with an intuitionistic negation into S4-type extensions of systems with a classical, involutive, negation. Orlov introduces the modal postulates of S4 before Becker, Lewis and Gödel. Orlov's work, which seems to be nearly completely ignored, is related (...)
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  12.  45
    Edwin D. Mares (2004). “Four-Valued” Semantics for the Relevant Logic R. Journal of Philosophical Logic 33 (3):327-341.
    This paper sets out two semantics for the relevant logic R based on Dunn's four-valued semantics for first-degree entailments. Unlike Routley's semantics for weak relevant logics, they do not use two ternary accessibility relations. Unlike Restall's semantics, they capture all of R. But there is a catch. Both of the present semantics are neighbourhood semantics, that is, they include sets of propositions in the specification of their frames.
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  13.  10
    Kazimierz Swirydowicz (1999). There Exist Exactly Two Maximal Strictly Relevant Extensions of the Relevant Logic R. Journal of Symbolic Logic 64 (3):1125-1154.
    In [60] N. Belnap presented an 8-element matrix for the relevant logic R with the following property: if in an implication A → B the formulas A and B do not have a common variable then there exists a valuation v such that v(A → B) does not belong to the set of designated elements of this matrix. A 6-element matrix of this kind can be found in: R. Routley, R.K. Meyer, V. Plumwood and R.T. Brady [82]. Below (...)
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  14.  30
    Edwin D. Mares (1996). Relevant Logic and the Theory of Information. Synthese 109 (3):345 - 360.
    This paper provides an interpretation of the Routley-Meyer semantics for a weak negation-free relevant logic using Israel and Perry's theory of information. In particular, Routley and Meyer's ternary accessibility relation is given an interpretation in information-theoretic terms.
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  15. Edwin D. Mares (2011). Relevant Logic: A Philosophical Interpretation. Cambridge University Press.
    This book introduces the reader to relevant logic and provides the subject with a philosophical interpretation. The defining feature of relevant logic is that it forces the premises of an argument to be really used in deriving its conclusion. The logic is placed in the context of possible world semantics and situation semantics, which are then applied to provide an understanding of the various logical particles and natural language conditionals. The book ends by examining various (...)
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  16.  26
    J. Michael Dunn (1979). A Theorem in 3-Valued Model Theory with Connections to Number Theory, Type Theory, and Relevant Logic. Studia Logica 38 (2):149 - 169.
    Given classical (2 valued) structures and and a homomorphism h of onto , it is shown how to construct a (non-degenerate) 3-valued counterpart of . Classical sentences that are true in are non-false in . Applications to number theory and type theory (with axiom of infinity) produce finite 3-valued models in which all classically true sentences of these theories are non-false. Connections to relevant logic give absolute consistency proofs for versions of these theories formulated in relevant (...) (the proof for number theory was obtained earlier by R. K. Meyer and suggested the present abstract development). (shrink)
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  17.  33
    Edwin Mares (2012). Relevant Logic and the Philosophy of Mathematics. Philosophy Compass 7 (7):481-494.
    This paper sets out three programmes that attempt to use relevant logic as the basis for a philosophy of mathematics. Although these three programmes do not exhaust the possible approaches to mathematics through relevant logic, they are fairly representative of the current state of the field. The three programmes are compared and their relative strengths and weaknesses set out. At the end of the paper I examine the consequences of adopting each programme for the realist debate (...)
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  18.  25
    José M. Méndez, A Note on "Recent Work in Relevant Logic".
    In his paper “Recent work in relevant logic”, Jago includes a section on Disjunctive Syllogism . The content of the section essentially consists of (a) a valuation of some work by Robles and Méndez on the topic as “not particularly interesting in itself”; (b) a statement establishing that “What would be interesting is to discover just how weak a relevant logic needs to be before disjunctive syllogism becomes inadmissible”. The main problem with this section of Jago’s (...)
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  19.  13
    Harry Deutsch (1985). A Note on the Decidability of a Strong Relevant Logic. 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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  20.  3
    Gerson Zaverucha (1992). Relevant Logic as a Basis for Paraconsistent Epistemic Logics. Journal of Applied Non-Classical Logics 2 (2):225-241.
    ABSTRACT In this work we argue for relevant logics as a basis for paraconsistent epistemic logics. In order to do so, a paraconsistent nonmonotonic multi-agent epistemic logic, MDR (for Modal Defeasible Relevant), is briefly introduced. In MDR each agent has two kinds of belief: an absolute belief that P, represented by AiP, and a defeasible belief that P, represented by DiP. Therefore, an agent can reason with his own absolute and defeasible beliefs about the world and also (...)
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  21.  4
    Kazimierz Swirydowicz (2008). There Exists an Uncountable Set of Pretabular Extensions of the Relevant Logic R and Each Logic of This Set is Generated by a Variety of Finite Height. Journal of Symbolic Logic 73 (4):1249-1270.
    In "Handbook of Philosophical Logic" M. Dunn formulated a problem of describing pretabular extensions of relevant logics (cf. M. Dunn [1984], p. 211: M. Dunn, G. Restall [2002], p. 79). The main result of this paper described in the title.
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  22. Edwin D. Mares (2009). Relevant Logic: A Philosophical Interpretation. Cambridge University Press.
    This book introduces the reader to relevant logic and provides the subject with a philosophical interpretation. The defining feature of relevant logic is that it forces the premises of an argument to be really used in deriving its conclusion. The logic is placed in the context of possible world semantics and situation semantics, which are then applied to provide an understanding of the various logical particles and natural language conditionals. The book ends by examining various (...)
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  23. Edwin D. Mares (2007). Relevant Logic: A Philosophical Interpretation. Cambridge University Press.
    This book introduces the reader to relevant logic and provides the subject with a philosophical interpretation. The defining feature of relevant logic is that it forces the premises of an argument to be really used in deriving its conclusion. The logic is placed in the context of possible world semantics and situation semantics, which are then applied to provide an understanding of the various logical particles and natural language conditionals. The book ends by examining various (...)
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  24.  17
    Richard Routley (1979). Alternative Semantics for Quantified First Degree Relevant Logic. Studia Logica 38 (2):211 - 231.
    A system FDQ of first degree entailment with quantification, extending classical quantification logic Q by an entailment connective, is axiomatised, and the choice of axioms defended and also, from another viewpoint, criticised. The system proves to be the equivalent to the first degree part of the quantified entailmental system EQ studied by Anderson and Belnap; accordingly the semantics furnished are alternative to those provided for the first degree of EQ by Belnap. A worlds semantics for FDQ is presented, and (...)
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  25.  31
    Stephen Read (1988). Relevant Logic: A Philosophical Examination of Inference. B. Blackwell.
  26.  28
    Ross T. Brady (1994). Rules in Relevant Logic - I: Semantic Classification. [REVIEW] Journal of Philosophical Logic 23 (2):111 - 137.
    We provide five semantic preservation properties which apply to the various rules -- primitive, derived and admissible -- of Hilbert-style axiomatizations of relevant logics. These preservation properties are with respect to the Routley-Meyer semantics, and consist of various truth- preservations and validity-preservations from the premises to the conclusions of these rules. We establish some deduction theorems, some persistence theorems and some soundness and completeness theorems, for these preservation properties. We then apply the above ideas, as best we can, to (...)
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  27.  12
    Reinhard Kahle (2007). Edwin D. Mares, Relevant Logic—a Philosophical Interpretation. Studia Logica 85 (3):419-424.
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  28.  19
    Diderik Batens (2001). A Dynamic Characterization of the Pure Logic of Relevant Implication. Journal of Philosophical Logic 30 (3):267-280.
    This paper spells out a dynamic proof format for the pure logic of relevant implication. (A proof is dynamic if a formula derived at some stage need not be derived at a later stage.) The paper illustrates three interesting points. (i) A set of properties that characterizes an inference relation on the (very natural) dynamic proof interpretation, need not characterize the same inference relation (or even any inference relation) on the usual settheoretical interpretation. (ii) A proof format may (...)
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  29.  4
    James Garson (1989). Modularity and Relevant Logic. Notre Dame Journal of Formal Logic 30 (2):207-223.
    A practical system of reasoning must be both correct and efficient. An efficient system which contains a large body of information can not search for the proof of a conclusion from all information available. Efficiency requires that deduction of the conclusion be carried out in a modular way using only a relatively small and quickly identified subset of the total information. One might assume that data modularity is incompatible with correctness, where a system is correct for a logic (...)
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  30. Edwin Mares (2009). General Information in Relevant Logic. Synthese 167 (2):343-362.
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  31.  11
    Guillermo Badia (forthcoming). The Relevant Fragment of First Order Logic. Review of Symbolic Logic:1-24.
    Under a proper translation, the languages of propositional (and quantified relevant logic) with an absurdity constant are characterized as the fragments of first order logic preserved under (world-object) relevant directed bisimulations. Furthermore, the properties of pointed models axiomatizable by sets of propositional relevant formulas have a purely algebraic characterization. Finally, a form of the interpolation property holds for the relevant fragment of first order logic.
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  32. Neil Tennant (1987). Natural Deduction and Sequent Calculus for Intuitionistic Relevant Logic. Journal of Symbolic Logic 52 (3):665-680.
  33.  4
    John K. Slaney & Robert K. Meyer (1992). A Structurally Complete Fragment of Relevant Logic. Notre Dame Journal of Formal Logic 33 (4):561-566.
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  34.  5
    Robert K. Meyer (1976). Ackermann, Takeuti, and Schnitt: For Higher-Order Relevant Logic. Bulletin of the Section of Logic 5 (4):138-142.
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  35.  26
    Kosta Došen (1981). A Reduction of Classical Propositional Logic to the Conjunction-Negation Fragment of an Intuitionistic Relevant Logic. Journal of Philosophical Logic 10 (4):399 - 408.
  36.  28
    Ross T. Brady (1993). Rules in Relevant Logic — II: Formula Representation. Studia Logica 52 (4):565 - 585.
    This paper surveys the various forms of Deduction Theorem for a broad range of relevant logics. The logics range from the basic system B of Routley-Meyer through to the system R of relevant implication, and the forms of Deduction Theorem are characterized by the various formula representations of rules that are either unrestricted or restricted in certain ways. The formula representations cover the iterated form,A 1 .A 2 . ... .A n B, the conjunctive form,A 1&A 2 & (...)
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  37.  3
    N. C. A. da Costa (1993). Review: Jean Norman, Richard Sylvan, Directions in Relevant Logic. [REVIEW] Journal of Symbolic Logic 58 (4):1466-1468.
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  38.  2
    Mirosław Szatkowski (1986). Some Model‐Theoretic Results for the Relevant Logic with Quantification. Mathematical Logic Quarterly 32 (19‐24):355-363.
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  39.  1
    N. C. A. da Costa (1993). Directions in Relevant Logic, Edited by Norman Jean and Sylvan Richard, Reason and Argument, Vol. 1, Kluwer Academic Publishers, Dordrecht, Boston, and London, 1989, Xii+ 453 Pp. [REVIEW] Journal of Symbolic Logic 58 (4):1466-1468.
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  40.  2
    Nissim Francez (2014). Bilateral Relevant Logic. Review of Symbolic Logic 7 (2):250-272.
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  41.  5
    J. -F. Pabion (1979). Beth's Tableaux for Relevant Logic. Notre Dame Journal of Formal Logic 20 (4):891-899.
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  42.  4
    John K. Slaney (1988). On the Structure of De Morgan Monoids with Corollaries on Relevant Logic and Theories. Notre Dame Journal of Formal Logic 30 (1):117-129.
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  43. Robert K. Meyer & Richard Routley (1973). An Undecidable Relevant Logic. Mathematical Logic Quarterly 19 (26‐29):389-397.
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  44. S. Read (1991). J. NORMAN and R. SYLVAN "Directions in Relevant Logic". [REVIEW] History and Philosophy of Logic 12 (2):254.
     
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  45.  64
    Peter Milne (1994). Intuitionistic Relevant Logic and Perfect Validity. Analysis 54 (3):140 - 142.
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  46. Jean Norman & Richard Sylvan (1989). Directions in Relevant Logic.
     
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  47.  35
    Ross T. Brady (1996). Relevant Implication and the Case for a Weaker Logic. Journal of Philosophical Logic 25 (2):151 - 183.
    We collect together some misgivings about the logic R of relevant inplication, and then give support to a weak entailment logic $DJ^{d}$ . The misgivings centre on some recent negative results concerning R, the conceptual vacuousness of relevant implication, and the treatment of classical logic. We then rectify this situation by introducing an entailment logic based on meaning containment, rather than meaning connection, which has a better relationship with classical logic. Soundness and completeness (...)
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  48.  5
    Mirosław Szatkowski (1986). Some Model-Theoretic Results for the Relevant Logic with Quantification. Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 32 (19-24):355-363.
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  49. Edwin Mares (2006). Relevant Logic, Probabilistic Information, and Conditionals. Logique Et Analyse 49:399-411.
     
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  50. Edwin Mares (2003). Halldén-Completeness and Modal Relevant Logic. Logique Et Analyse 46.
     
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