Results for 'Relevant logics'

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  1.  66
    Relevant Logic: A Philosophical Interpretation.Edwin D. Mares - 2004 - 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 applications of (...) logic and presenting some interesting open problems. It will be of interest to a range of readers including advanced students of logic, philosophical and mathematical logicians, and computer scientists. (shrink)
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  2. Relevant Logics and Their Rivals.Richard Routley, Val Plumwood, Robert K. Meyer & Ross T. Brady - 1982 - Ridgeview.
     
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  3.  89
    Relevant Logic: A Philosophical Examination of Inference.Stephen Read - 1988 - Oxford: Wiley-Blackwell.
    The logician's central concern is with the validity of argument. A logical theory ought, therefore, to provide a general criterion of validity. This book sets out to find such a criterion, and to describe the philosophical basis and the formal theory of a logic in which the premises of a valid argument are relevant to its conclusion. The notion of relevance required for this theory is obtained by an analysis of the grounds for asserting a formula in a proof.
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  4. Relevant Logics Obeying Component Homogeneity.Roberto Ciuni, Damian Szmuc & Thomas Macaulay Ferguson - 2018 - Australasian Journal of Logic 15 (2):301-361.
    This paper discusses three relevant logics that obey Component Homogeneity - a principle that Goddard and Routley introduce in their project of a logic of significance. The paper establishes two main results. First, it establishes a general characterization result for two families of logic that obey Component Homogeneity - that is, we provide a set of necessary and sufficient conditions for their consequence relations. From this, we derive characterization results for S*fde, dS*fde, crossS*fde. Second, the paper establishes complete (...)
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  5. The Relevant Logic E and Some Close Neighbours: A Reinterpretation.Edwin Mares & Shawn Standefer - 2017 - IfCoLog Journal of Logics and Their Applications 4 (3):695--730.
    This paper has two aims. First, it sets out an interpretation of the relevant logic E of relevant entailment based on the theory of situated inference. Second, it uses this interpretation, together with Anderson and Belnap’s natural deduc- tion system for E, to generalise E to a range of other systems of strict relevant implication. Routley–Meyer ternary relation semantics for these systems are produced and completeness theorems are proven. -/- .
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  6. Recent Work in Relevant Logic.Mark Jago - 2013 - Analysis 73 (3):526-541.
    This paper surveys important work done in relevant logic in the past 10 years.
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  7.  21
    Relevance Logic.Michael Dunn & Greg Restall - 2002 - In D. Gabbay & F. Guenthner (eds.), Handbook of Philosophical Logic. Kluwer Academic Publishers.
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  8.  37
    Relevant Logics and Their Rivals: The Basic Philosophical and Semintical Theory.Richard Sylvan & Ross Brady (eds.) - 1982 - Ridgeview Pub. Co..
    Relevant Logics and their Rivals, Volume II extends the material of the first volume in two ways.
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  9.  84
    Relevant Logic and the Theory of Information.Edwin Mares - 1996 - 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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  10. Truthmaker Semantics for Relevant Logic.Mark Jago - 2020 - Journal of Philosophical Logic 49 (4):681-702.
    I develop and defend a truthmaker semantics for the relevant logic R. The approach begins with a simple philosophical idea and develops it in various directions, so as to build a technically adequate relevant semantics. The central philosophical idea is that truths are true in virtue of specific states. Developing the idea formally results in a semantics on which truthmakers are relevant to what they make true. A very natural notion of conditionality is added, giving us (...) implication. I then investigate ways to add conjunction, disjunction, and negation; and I discuss how to justify contraposition and excluded middle within a truthmaker semantics. (shrink)
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  11.  17
    Relevance Logic.Edwin Mares - 2008 - Stanford Encyclopedia of Philosophy.
  12.  76
    Classical relevant logics. I.R. K. Meyer - 1973 - Studia Logica 32:51.
  13.  10
    Relevant Logic: A Philosophical Interpretation.Reinhard Kahle - 2007 - Studia Logica 85 (3):419-424.
  14.  78
    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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  15.  33
    Classical Relevant Logics II.Robert K. Meyer & Richard Routley - 1974 - Studia Logica 33 (2):183 - 194.
  16.  13
    Non-Boolean Classical Relevant Logics I.Tore Fjetland Øgaard - 2019 - Synthese (8):1-32.
    Relevant logics have traditionally been viewed as paraconsistent. This paper shows that this view of relevant logics is wrong. It does so by showing forth a logic which extends classical logic, yet satisfies the Entailment Theorem as well as the variable sharing property. In addition it has the same S4-type modal feature as the original relevant logic E as well as the same enthymematical deduction theorem. The variable sharing property was only ever regarded as a (...)
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  17. Relevant Logics.Edwin D. Mares & Robert K. Meyer - 2001 - In Lou Goble (ed.), The Blackwell Guide to Philosophical Logic. Blackwell. pp. 280--308.
     
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  18.  43
    Actual Issues for Relevant Logics.Shawn Standefer - 2020 - Ergo: An Open Access Journal of Philosophy 7.
    In this paper, I motivate the addition of an actuality operator to relevant logics. Straightforward ways of doing this are in tension with standard motivations for relevant logics, but I show how to add the operator in a way that permits one to maintain the intuitions behind relevant logics. I close by exploring some of the philosophical consequences of the addition.
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  19.  33
    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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  20.  14
    A Relevant Logic of Questions.Vít Punčochář - 2020 - Journal of Philosophical Logic 49 (5):905-939.
    This paper introduces the inquisitive extension of R, denoted as InqR, which is a relevant logic of questions based on the logic R as the background logic of declaratives. A semantics for InqR is developed, and it is shown that this semantics is, in a precisely defined sense, dual to Routley-Meyer semantics for R. Moreover, InqR is axiomatized and completeness of the axiomatic system is established. The philosophical interpretation of the duality between Routley-Meyer semantics and the semantics for InqR (...)
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  21. Relevant Logic : a Philosophical Examination of Inference.Stephen Read - 1989 - Revue Philosophique de la France Et de l'Etranger 179 (4):656-656.
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  22. Relevance Logics and Relation Algebras.Katalin Bimbó, J. Michael Dunn & Roger D. Maddux - 2009 - Review of Symbolic Logic 2 (1):102-131.
    Relevance logics are known to be sound and complete for relational semantics with a ternary accessibility relation. This paper investigates the problem of adequacy with respect to special kinds of dynamic semantics (i.e., proper relation algebras and relevant families of relations). We prove several soundness results here. We also prove the completeness of a certain positive fragment of R as well as of the first-degree fragment of relevance logics. These results show that some core ideas are shared (...)
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  23. Relevant Logic: A Philosophical Examination of Inference.Stephen Read - 1990 - Mind 99 (393):140-142.
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  24.  80
    Relevant Logic and the Philosophy of Mathematics.Edwin Mares - 2012 - 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 about mathematical (...)
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  25.  31
    Relevance Logics, Paradoxes of Consistency and the K Rule II. A Non-Constructive Negation.José M. Méndez & Gemma Robles - 2007 - Logic and Logical Philosophy 15 (3):175-191.
    The logic B+ is Routley and Meyer’s basic positive logic. We define the logics BK+ and BK'+ by adding to B+ the K rule and to BK+ the characteristic S4 axiom, respectively. These logics are endowed with a relatively strong non-constructive negation. We prove that all the logics defined lack the K axiom and the standard paradoxes of consistency.
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  26.  37
    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 of hypothetico-deductivism in (...)
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  27.  66
    Whither Relevance Logic?Arnon Avron - 1992 - Journal of Philosophical Logic 21 (3):243 - 281.
  28.  16
    Relevance Logic as a Conservative Extension of Classical Logic.David C. Makinson - 2014 - In Sven Ove Hansson (ed.), David Makinson on Classical Methods for Non-Classical Problems. Series: Outstanding Contributions to Logic. New York: Springer.
    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 a suitable closure relation out (...)
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  29. Information Flow and Relevant Logics.Greg Restall - 1996 - In Jerry Seligman & Dag Westerståhl (eds.), Logic, Language and Computation. CSLI Publications, Stanford. pp. 463–477.
  30. Relevant Logics and Their Rivals, Volume II.Richard Sylvan & Ross Brady - 2005 - Bulletin of Symbolic Logic 11 (1):70-72.
  31. Incompleteness for Quantified Relevance Logics.Kit Fine - 1989 - In J. Norman & Richard Sylvan (eds.), Directions in Relevant Logic. Springer, Dordrecht. pp. 205-225.
    In the early seventies, several logicians developed a semantics for propositional systems of relevance logic. The essential ingredients of this semantics were a privileged point o, an ‘accessibility’ relation R and a special operator * for evaluating negation. Under the truth- conditions of the semantics, each formula A(Pl,…,Pn) could be seen as expressing a first order condition A+(pl,…,pn, o, R,*) on sets p1,…,pn and o, R, *, while each formula-scheme could be regarded as expressing the second-order condition ∀p1,…,∀pn A+(p1,…,pn, o, (...)
     
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  32.  1
    Directions in Relevant Logic: Papers From the International Conference on Relevant Logic.Jean Norman & Richard Sylvan (eds.) - 1989 - Dordrecht and Boston: Kluwer Academic Publishers.
    Relevance logics came of age with the one and only International Conference on relevant logics in 1974. They did not however become accepted, or easy to promulgate. In March 1981 we received most of the typescript of IN MEMORIAM: ALAN ROSS ANDERSON Proceedings of the International Conference of Relevant Logic from the original editors, Kenneth W. Collier, Ann Gasper and Robert G. Wolf of Southern Illinois University. 1 They had, most unfortunately, failed to find a publisher (...)
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  33.  11
    Non-Boolean Classical Relevant Logics II: Classicality Through Truth-Constants.Tore Fjetland Øgaard - 2021 - Synthese (3-4):1-33.
    This paper gives an account of Anderson and Belnap’s selection criteria for an adequate theory of entailment. The criteria are grouped into three categories: criteria pertaining to modality, those pertaining to relevance, and those related to expressive strength. The leitmotif of both this paper and its prequel is the relevant legitimacy of disjunctive syllogism. Relevant logics are commonly held to be paraconsistent logics. It is shown in this paper, however, that both E and R can be (...)
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  34.  7
    Implicational Relevance Logic is 2-Exptime-Complete.Sylvain Schmitz - 2016 - Journal of Symbolic Logic 81 (2):641-661.
    We show that provability in the implicational fragment of relevance logic is complete for doubly exponential time, using reductions to and from coverability in branching vector addition systems.
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  35.  22
    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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  36.  65
    Simplified Semantics for Relevant Logics (and Some of Their Rivals).Greg Restall - 1993 - Journal of Philosophical Logic 22 (5):481 - 511.
    This paper continues the work of Priest and Sylvan in Simplified Semantics for Basic Relevant Logics, a paper on the simplified semantics of relevant logics, such as B⁺ and B. We show that the simplified semantics can also be used for a large number of extensions of the positive base logic B⁺, and then add the dualising '*' operator to model negation. This semantics is then used to give conservative extension results for Boolean negation.
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  37. Four-Valued Semantics for Relevant Logics (and Some of Their Rivals).Greg Restall - 1995 - Journal of Philosophical Logic 24 (2):139 - 160.
    This paper gives an outline of three different approaches to the four-valued semantics for relevant logics (and other non-classical logics in their vicinity). The first approach borrows from the 'Australian Plan' semantics, which uses a unary operator '⋆' for the evaluation of negation. This approach can model anything that the two-valued account can, but at the cost of relying on insights from the Australian Plan. The second approach is natural, well motivated, independent of the Australian Plan, and (...)
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  38.  62
    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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  39.  59
    The First Axiomatization of Relevant Logic.Kosta Došen - 1992 - 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 to (...)
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  40.  45
    Semantics for Relevant Logics.Alasdair Urquhart - 1972 - Journal of Symbolic Logic 37 (1):159-169.
  41. Relevant Logics and Their Rivals: Part 1. The Basic Philosophical and Semantical Theory.Richard Routley, Robert K. Meyer, Val Plumwood & Ross T. Brady - 1988 - Studia Logica 47 (2):169-172.
  42.  83
    Why Intuitionistic Relevant Logic Cannot Be a Core Logic.Joseph Vidal-Rosset - 2017 - Notre Dame Journal of Formal Logic 58 (2):241-248.
    At the end of the 1980s, Tennant invented a logical system that he called “intuitionistic relevant logic”. Now he calls this same system “Core logic.” In Section 1, by reference to the rules of natural deduction for $\mathbf{IR}$, I explain why $\mathbf{IR}$ is a relevant logic in a subtle way. Sections 2, 3, and 4 give three reasons to assert that $\mathbf{IR}$ cannot be a core logic.
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  43.  93
    General Information in Relevant Logic.Edwin D. Mares - 2009 - 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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  44.  9
    Structural Completeness in Relevance Logics.J. G. Raftery & K. Świrydowicz - 2016 - Studia Logica 104 (3):381-387.
    It is proved that the relevance logic \ has no structurally complete consistent axiomatic extension, except for classical propositional logic. In fact, no other such extension is even passively structurally complete.
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  45.  52
    Negation in Relevant Logics (How I Stopped Worrying and Learned to Love the Routley Star).Greg Restall - 1999 - In Dov Gabbay & Heinrich Wansing (eds.), What is Negation? Kluwer Academic Publishers. pp. 53-76.
  46.  39
    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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  47.  65
    Relevance Logic, Classical Logic, and Disjunctive Syllogism.John A. Barker - 1975 - Philosophical Studies 27 (6):361 - 376.
  48.  25
    Relevance Logics and Intuitionistic Negation.José M. Méndez & Gemma Robles - 2008 - Journal of Applied Non-Classical Logics 18 (1):49-65.
    The logic B+ is Routley and Meyer's basic positive logic. We show how to introduce a minimal intuitionistic negation and an intuitionistic negation in B+. The two types of negation are introduced in a wide spectrum of relevance logics built up from B+. It is proved that although all these logics have the characteristic paradoxes of consistency, they lack the K rule.
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  49.  13
    Relevant Logic as a Basis for Paraconsistent Epistemic Logics.Gerson Zaverucha - 1992 - 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 (...)
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  50.  15
    Are Relevant Logics Deviant?Robert G. Wolf - 1978 - Philosophia 7 (2):327-340.
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