Results for 'Relevance logic'

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  1. Relevant Logic: A Philosophical Interpretation.Edwin Mares - 2004 - New York: 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 (...)
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  2. Incompleteness for Quantified Relevance Logics.Kit Fine - 1989 - In J. Norman & R. Sylvan (eds.), Directions in Relevant Logic. Dordrecht and Boston: Springer. 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 (...)
     
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  3.  14
    (1 other version)Relevance Logic.Edwin D. Mares - 2002 - In Dale Jacquette (ed.), A Companion to Philosophical Logic. Malden, MA, USA: Wiley-Blackwell. pp. 607–627.
    This chapter contains sections titled: Non‐Sequiturs are Bad The Real Use of Premises Implication From Proof Theory to Semantics Adding Conjunction The Problem of Disjunction Routley and Meyer's Ternary Relation Rules for Disjunction The Semantics of Negation Rules for Negation Disjunctive Syllogism Logics Stronger than R Logics Weaker than R Relevant Logics and Natural Language Conditionals Theory of Properties Summary.
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  4.  90
    Relevance Logic.Shay Allen Logan - 2024 - New York, NY, USA: Cambridge University Press.
    Relevance logics are a misunderstood lot. Despite being the subject of intense study for nearly a century, they remain maligned as too complicated, too abstruse, or too silly to be worth learning much about. This Element aims to dispel these misunderstandings. By focusing on the weak relevant logic B, the discussion provides an entry point into a rich and diverse family of logics. Also, it contains the first-ever textbook treatment of quantification in relevance logics, as well as (...)
  5.  68
    The relevance logic of Boolean groups.Yale Weiss - 2023 - Logic Journal of the IGPL 31 (1):96-114.
    In this article, I consider the positive logic of Boolean groups (i.e. Abelian groups where every non-identity element has order 2), where these are taken as frames for an operational semantics à la Urquhart. I call this logic BG. It is shown that the logic over the smallest nontrivial Boolean group, taken as a frame, is identical to the positive fragment of a quasi-relevance logic that was developed by Robles and Méndez (an extension of this (...)
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  6.  69
    Quantified Modal Relevant Logics.Nicholas Ferenz - 2023 - Review of Symbolic Logic 16 (1):210-240.
    Here, I combine the semantics of Mares and Goldblatt [20] and Seki [29, 30] to develop a semantics for quantified modal relevant logics extending ${\bf B}$. The combination requires demonstrating that the Mares–Goldblatt approach is apt for quantified extensions of ${\bf B}$ and other relevant logics, but no significant bridging principles are needed. The result is a single semantic approach for quantified modal relevant logics. Within this framework, I discuss the requirements a quantified modal relevant logic must satisfy to (...)
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  7.  46
    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 (...)
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  8. 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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  9. Relevant logic, probabilistic information, and conditionals.Edwin Mares - 2006 - Logique Et Analyse 49:399-411.
  10.  84
    Relevance Logic.Michael Dunn & Greg Restall - 1983 - In Dov M. Gabbay & Franz Guenthner (eds.), Handbook of Philosophical Logic. Dordrecht, Netherland: Kluwer Academic Publishers.
  11.  35
    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 necessary property (...)
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  12.  82
    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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  13. 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 between (...)
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  14.  10
    Simplified Semantics for Further Relevant Logics I: Unreduced Semantics for E and Π′.Tore Fjetland Øgaard - forthcoming - Logic and Logical Philosophy.
    This paper shows that the relevant logics E and Π′ are strongly sound and complete with regards to a version of the “simplified” Routley-Meyer semantics. Such a semantics for E has been thought impossible. Although it is impossible if an admissible rule of E – the rule of restricted assertion or equivalently Ackermann’s δ-rule – is solely added as a primitiverule, it is very much possible when E is axiomatized in the way Anderson and Belnap did. The simplified semantics for (...)
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  15. 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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  16.  77
    Classical relevant logics II.Robert K. Meyer & Richard Routley - 1974 - Studia Logica 33 (2):183 - 194.
  17. 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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  18. Classical relevant logics. I.R. K. Meyer & Richard Routley - 1973 - Studia Logica 32:51.
  19.  35
    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. 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 (...)
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  20.  13
    Relevant Logics and Their Rivals.Richard Routley, Val Plumwood, Robert K. Meyer & Ross T. Brady - 1982 - Ridgeview. Edited by Richard Sylvan & Ross Brady.
  21.  75
    Relevant logics and their rivals.Richard Sylvan & Ross Brady (eds.) - 1982 - Atascadero, CA: Ridgeview Pub. Co..
    Relevant Logics and their Rivals, Volume II extends the material of the first volume in two ways.
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  22. Relevant logic: a philosophical examination of inference.Stephen Read - 1988 - Oxford: 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 (...)
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  23.  51
    Relevance Logic: Problems Open and Closed.Alasdair Urquhart - 2016 - Australasian Journal of Logic 13 (1):11-20.
    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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  24. Relevant Logic : a Philosophical Examination of Inference.Stephen Read - 1988 - Revue Philosophique de la France Et de l'Etranger 179 (4):656-656.
     
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  25.  36
    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 also reason about (...)
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  26.  20
    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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  27.  3
    Relevance logic without impossibilities.Michael De - forthcoming - Inquiry: An Interdisciplinary Journal of Philosophy.
    The idea that impossibilities have an important semantic role to play is becoming widely accepted on various grounds, including grounds of relevance. I argue that this is a mistake, that it has led to various foundational objections to relevance logic, and that these objections are avoidable given a semantics that clearly distinguishes two types of conditional or inferential fallacies, namely, those concerning truth preservation from those concerning a relation between content or subject matter. I argue that we (...)
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  28.  25
    Relevant Logics.Edwin D. Mares & Robert K. Meyer - 2001 - In Lou Goble (ed.), The Blackwell Guide to Philosophical Logic. Malden, Mass.: Wiley-Blackwell. pp. 280–308.
    Once upon a time, modal logic was castigated because it ‘had no semantics.’ Kripke, Hintikka, Kanger, and others changed all that. In a similar way, when Relevant Logic was introduced by Anderson and Belnap, it too was castigated for ‘having no semantics.’ The present overview marks a culmination of that effort. The semantic approach described here brings together a number of hitherto disparate efforts to set out formal systems for logics of relevant implication and entailment. It also makes (...)
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  29.  56
    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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  30.  93
    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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  31.  47
    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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  32.  96
    Whither relevance logic?Arnon Avron - 1992 - Journal of Philosophical Logic 21 (3):243 - 281.
  33. 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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  34.  59
    On semilattice relevant logics.Ryo Kashima - 2003 - Mathematical Logic Quarterly 49 (4):401.
    The semilattice relevant logics ∪R, ∪T, ∪RW, and ∪TW are defined by semilattice models in which conjunction and disjunction are interpreted in a natural way. For each of them, there is a cut-free labelled sequent calculus with plural succedents . We prove that these systems are equivalent, with respect to provable formulas, to the restricted systems with single succedents . Moreover, using this equivalence, we give a new Hilbert-style axiomatizations for ∪R and ∪T and prove equivalence between two semantics for (...)
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  35. 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 relevant implication. I (...)
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  36.  21
    Directions in Relevant Logic.J. Norman & R. Sylvan (eds.) - 1989 - Dordrecht and Boston: Springer.
    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 - not, (...)
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  37.  7
    Simplified Semantics for Further Relevant Logics I.Tore Fjetland Øgaard - forthcoming - Logic and Logical Philosophy:1-43.
    This paper shows that the relevant logics E and Π′ are strongly sound and complete with regards to a version of the “simplified” Routley-Meyer semantics. Such a semantics for E has been thought impossible. Although it is impossible if an admissible rule of E  the rule of restricted assertion or equivalently Ackermann’s δ-rule  is solely added as a primitive rule, it is very much possible when E is axiomatized in the way Anderson and Belnap did. The simplified semantics (...)
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  38.  25
    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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  39.  64
    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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  40. 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 it provides a (...)
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  41.  44
    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 (and so, the K axioms).
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  42. 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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  43. Relevant Logics and Their Rivals, Volume II.Richard Sylvan & Ross Brady - 2005 - Bulletin of Symbolic Logic 11 (1):70-72.
  44. Action frames for weak relevant logics.Igor Sedlár - 2015 - In Pavel Arazim & Michal Dancak (eds.), The Logica Yearbook 2014. College Publications. pp. 267-279.
    The article introduces extended models for the propositional dynamic logic PDL. In extended models, valuation assigns to every state a set of atomic formulas and a PDL program. The program is informally construed as an action preferred by a contextually fixed agent. PDL is then extended by introducing a conditional connective expressing partial correctness claims. The main contribution of the article is the observation that the partial correctness conditional is in fact a substructural implication. It is shown that a (...)
     
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  45. Halldén-Completeness and Modal Relevant Logic.Edwin Mares - 2003 - Logique Et Analyse 46.
  46.  93
    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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  47.  33
    A Second Pretabular Classical Relevance Logic.Asadollah Fallahi - 2018 - Studia Logica 106 (1):191-214.
    Pretabular logics are those that lack finite characteristic matrices, although all of their normal proper extensions do have some finite characteristic matrix. Although for Anderson and Belnap’s relevance logic R, there exists an uncountable set of pretabular extensions :1249–1270, 2008), for the classical relevance logic \\rightarrow B\}\) there has been known so far a pretabular extension: \. In Section 1 of this paper, we introduce some history of pretabularity and some relevance logics and their algebras. (...)
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  48.  96
    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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  49. Minimal Non-relevant Logics Without The K Axiom.Gemma Robles & Jose Mendez - 2007 - Reports on Mathematical Logic.
    The logic B$_{+}$ is Routley and Meyer's basic positive logic. The logic B$_{K+}$ is B$_{+}$ plus the $K$ rule. We add to B$_{K+}$ four intuitionistic-type negations. We show how to extend the resulting logics within the modal and relevance spectra. We prove that all the logics defined lack the K axiom.
     
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  50. 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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