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Summary

Relevant logics are a group of logics which attempt to block irrelevant conclusions being drawn from a set of premises. The following inferences are all valid in classical logic, where A and B are any sentences whatsoever: from A to B → A, B → B and B ∨ ¬B; from ¬A to A→B; and from A ∧ ¬A to B. But if A and B are utterly irrelevant to one another, many feel reluctant to call these inferences acceptable. Similarly for the validity of the corresponding material implications, often called ‘paradoxes’ of material implication. Relevant logic can be seen as the attempt to avoid these ‘paradoxes’.

Key works Many trace the beginnings of relevant logic to Anderson & Belnap 1962Anderson & Belnap 1975 is a key early book-length exposition of relevant logics. Routley & Meyer 1972 and Routley & Meyer 1972 develop the relational ‘Routley-Meyer’ semantics for relevant implication, which has proved vital to the success of relevant logics. Read 1988 and Mares 2004 set out the philosophy of relevant logics. Brady 2006 contains much of Brady's work on relevant logics (which has been important throughout their development).  Restall 1995 explores using 4-valued semantics for relevant logics. 
Introductions Mares 2012 is a recent introduction to the area. Jago 2013 surveys some of the most important recent work (2003–13) in relevant logic. The chapter on relevant logic in Priest 2001 introduces the logical details in a concise way.
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  1. added 2019-10-15
    A Note on the Relevance of Semilattice Relevance Logic.Yale Weiss - 2019 - Australasian Journal of Logic 16 (6):177-185.
    A propositional logic has the variable sharing property if φ → ψ is a theorem only if φ and ψ share some propositional variable. In this note, I prove that positive semilattice relevance logic and its extension with an involution negation have the variable sharing property. Typical proofs of the variable sharing property rely on ad hoc, if clever, matrices. However, in this note, I exploit the properties of rather more intuitive arithmetical structures to establish the variable sharing property for (...)
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  2. added 2019-09-28
    A Cognitive View of Relevant Implication.Daniele Porello & Claudio Masolo - 2015 - In Antonio Lieto, Cristina Battaglino, Daniele P. Radicioni & Manuela Sanguinietti (eds.), Proceedings of the 3rd International Workshop on Artificial Intelligence and Cognition, Turin, Italy, September 28-29, 2015. pp. 40--53.
    Relevant logics provide an alternative to classical implication that is capable of accounting for the relationship between the antecedent and the consequence of a valid implication. Relevant implication is usually explained in terms of information required to assess a proposition. By doing so, relevant implication introduces a number of cognitively relevant aspects in the de nition of logical operators. In this paper, we aim to take a closer look at the cognitive feature of relevant implication. For this purpose, we develop (...)
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  3. added 2019-09-28
    Logical Operators for Ontological Modeling.Stefano Borgo, Daniele Porello & Nicolas Troquard - 2014 - In Pawel Garbacz & Oliver Kutz (eds.), Formal Ontology in Information Systems - Proceedings of the Eighth International Conference, {FOIS} 2014, September, 22-25, 2014, Rio de Janeiro, Brazil}. pp. 23--36.
    We show that logic has more to offer to ontologists than standard first order and modal operators. We first describe some operators of linear logic which we believe are particularly suitable for ontological modeling, and suggest how to interpret them within an ontological framework. After showing how they can coexist with those of classical logic, we analyze three notions of artifact from the literature to conclude that these linear operators allow for reducing the ontological commitment needed for their formalization, and (...)
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  4. added 2019-09-28
    Modelling Combinatorial Auctions in Linear Logic.Daniele Porello & Ulle Endriss - 2010 - In Principles of Knowledge Representation and Reasoning: Proceedings of the Twelfth International Conference, {KR} 2010, Toronto, Ontario, Canada, May 9-13, 2010.
    We show that linear logic can serve as an expressive framework in which to model a rich variety of combinatorial auction mechanisms. Due to its resource-sensitive nature, linear logic can easily represent bids in combinatorial auctions in which goods may be sold in multiple units, and we show how it naturally generalises several bidding languages familiar from the literature. Moreover, the winner determination problem, i.e., the problem of computing an allocation of goods to bidders producing a certain amount of revenue (...)
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  5. added 2019-09-28
    Modelling Multilateral Negotiation in Linear Logic.Daniele Porello & Ulle Endriss - 2010 - In {ECAI} 2010 - 19th European Conference on Artificial Intelligence, Lisbon, Portugal, August 16-20, 2010, Proceedings. pp. 381--386.
    We show how to embed a framework for multilateral negotiation, in which a group of agents implement a sequence of deals concerning the exchange of a number of resources, into linear logic. In this model, multisets of goods, allocations of resources, preferences of agents, and deals are all modelled as formulas of linear logic. Whether or not a proposed deal is rational, given the preferences of the agents concerned, reduces to a question of provability, as does the question of whether (...)
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  6. added 2019-09-19
    Substitution in Relevant Logics.Tore Fjetland Øgaard - 2019 - Review of Symbolic Logic:1-26.
    This essay discusses rules and semantic clauses relating to Substitution—Leibniz’s law in the conjunctive-implicational form s=t ∧ A(s) → A(t)—as these are put forward in Priest’s books "In Contradiction" and "An Introduction to Non-Classical Logic: From If to Is." The stated rules and clauses are shown to be too weak in some cases and too strong in others. New ones are presented and shown to be correct. Justification for the various rules are probed and it is argued that Substitution ought (...)
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  7. added 2019-09-12
    Sylvan's Jungle Volume 1: Exploring Meinong's Jungle and Beyond.Maureen Eckert - 2018 - International: Synthese Library.
    In this first volume of The Sylvan Jungle, the editors present a scholarly edition of the first chapter, "Exploring Meinong's Jungle," of Richard Routley's 1000-plus page book, Exploring Meinong's Jungle and Beyond. Going against the Quinean orthodoxy, Routley’s aim was to support Meinong’s idea that we can truthfully refer to non-existent and even impossible objects, like Superman, unicorns and the (infamous) round-square cupola on Berkeley College. The tools of non-classical logic at Routley’s disposal enabled him to update Meinong’s project for (...)
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  8. added 2019-08-06
    Truthmaker Semantics for Relevant Logic.Mark Jago - forthcoming - Journal of Philosophical Logic.
    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 then (...)
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  9. added 2019-06-08
    Notes on Stratified Semantics.Shay Allen Logan - 2019 - Journal of Philosophical Logic 48 (4):749-786.
    In 1988, Kit Fine published a semantic theory for quantified relevant logics. He referred to this theory as stratified semantics. While it has received some attention in the literature, 1–20, 1992; Mares & Goldblatt, Journal of Symbolic Logic 71, 163–187, 2006), stratified semantics has overall received much less attention than it deserves. There are two plausible reasons for this. First, the only two dedicated treatments of stratified semantics available are, 27–59, 1988; Mares, Studia Logica 51, 1–20, 1992), both of which (...)
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  10. added 2019-06-07
    Classical relevant logics. I.R. K. Meyer - 1973 - Studia Logica 32:51.
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  11. added 2019-06-06
    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.
  12. added 2019-06-06
    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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  13. added 2019-06-06
    Der Ackermann aus Böhmen des Johannes von Tepl. Gerhard Hahn.Antonin Hrubý - 1987 - Speculum 62 (1):136-137.
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  14. added 2019-06-06
    Systems with the Converse Ackermann Property.José M. Méndez - 1985 - Theoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 1 (1):253-258.
    A system S has the “converse Ackermann property” if -> C is unprovable in S whenever C is a propositional variable. In this paper we define the fragments with the C.A.P. of some well-know propositional systems in the spectrum between the minimal and classical logic. In the first part we succesively study the implicative and positive fragments and the full calculi. In the second, we prove by a matrix method that each one of the systems has the C.A.P. Thus, we (...)
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  15. added 2019-06-06
    ¿Deducibility Implies Revelance? A Negative Answer (I) (on the Philosophical Status of Relevant Logic).Raúl Orayen - 1983 - Critica 15 (43):3-29.
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  16. added 2019-06-06
    Deducibility Implies Relevance? A Cautious Answer.Raymundo Morado - 1983 - Critica 15 (45):105-108.
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  17. added 2019-06-06
    Deducibility Implies Relevance? A Negative Answer.Raúl Orayen - 1983 - Critica 15 (44):3-25.
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  18. added 2019-06-06
    R-Mingle and Beneath. Extensions of the Routley-Meyer Semantics for R.J. Michael Dunn - 1979 - Notre Dame Journal of Formal Logic 20:369.
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  19. added 2019-06-06
    The Logic of “Relevance” and “Educational Relevance”.Joseph A. Diorio - 1977 - Educational Philosophy and Theory 9 (1):49-61.
  20. added 2019-06-06
    The Paradoxes of Necessitation and Ionic-Entailment.John Woods - 1970 - Critica 4 (10):47-60.
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  21. added 2019-06-06
    Mysticism and Semantics.Y. Bar-Hillel & Paul Henle - 1966 - Journal of Symbolic Logic 31 (3):497.
  22. added 2019-06-06
    Necessary Statements and Entailment.A. R. Lacey - 1962 - Erkenntnis 22 (5):101.
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  23. added 2019-06-06
    Rescher Nicholas. Conditional Permission in Deontic Logic. Philosophical Studies , Vol. 13 , Pp. 1–6.Anderson Alan Ross. Reply to Mr. Rescher. Philosophical Studies , Vol. 13 , Pp. 6–8. [REVIEW]E. J. Lemmon - 1962 - Journal of Symbolic Logic 27 (1):113-114.
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  24. added 2019-06-06
    XI—Entailment and Modality.R. W. Ashby - 1962 - Proceedings of the Aristotelian Society 63 (1):203-216.
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  25. added 2019-06-06
    Anderson Alan Ross. Improved Decision Procedures for Lewis's Calculus S4 and von Wright's Calculus M. [REVIEW]Naoto Yonemitsu - 1955 - Journal of Symbolic Logic 20 (3):302-303.
  26. added 2019-06-06
    Morris Charles. Comments on Mr. Storer's Paper. Philosophy of Science, Vol. 15 , Pp. 330–332.George D. W. Berry - 1950 - Journal of Symbolic Logic 15 (2):149-149.
  27. added 2019-06-05
    The Relevant Fragment of First Order Logic.Guillermo Badia - 2016 - Review of Symbolic Logic 9 (1):143-166.
    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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  28. added 2019-05-30
    Alan Rose. Extensions of Some Theorems of Anderson and Belnap. The Journal of Symbolic Logic, Vol. 27 No. 4 , Pp. 423–425. [REVIEW]David Makinson - 1975 - Journal of Symbolic Logic 40 (3):466-466.
    Review of the paper by Rose mentioned in the title.
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  29. added 2019-05-21
    Robert K. Meyer. A Farewell to Entailment. Foundations of Logic and Linguistics, Problems and Their Solutions, Edited by Georg Dorn and P. Weingartner, Plenum Press, New York and London1985, Pp. 577– 636. [REVIEW]Daniel H. Cohen - 1990 - Journal of Symbolic Logic 55 (1):352-353.
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  30. added 2019-05-21
    Rob R. Brady. The Logicworks. Student Manual. Philosophy Documentation Center, Bowling Green1987, I + 21 Pp. + 2 Disks. - Rob R. Brady. The Logicworks. Guide for Instructors. Philosophy Documentation Center, Bowling Green1987, I + 23 Pp. + Disk. [REVIEW]John N. Martin - 1990 - Journal of Symbolic Logic 55 (1):368-370.
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  31. added 2019-05-06
    Relevant Logics and Their Rivals, Volume II, A Continuation of the Work of Richard Sylvan, Robert Meyer, Val Plumwood and Ross Brady, Edited by Ross Brady, with Contributions by Martin Bunder, André Fuhrmann, Andréa Loparić, Edwin Mares, Chris Mortensen and Alasdair Urquhart. Western Philosophy Series, Vol. 59. Aldershot, Ashgate, 2003, Xiv + 425 Pp. [REVIEW]Nicholas Griffin - 2005 - Bulletin of Symbolic Logic 11 (1):70-72.
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  32. added 2019-03-30
    Stoic Sequent Logic and Proof Theory.Susanne Bobzien - 2019 - History and Philosophy of Logic 40 (3):234-265.
    This paper contends that Stoic logic (i.e. Stoic analysis) deserves more attention from contemporary logicians. It sets out how, compared with contemporary propositional calculi, Stoic analysis is closest to methods of backward proof search for Gentzen-inspired substructural sequent logics, as they have been developed in logic programming and structural proof theory, and produces its proof search calculus in tree form. It shows how multiple similarities to Gentzen sequent systems combine with intriguing dissimilarities that may enrich contemporary discussion. Much of Stoic (...)
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  33. added 2019-03-11
    Skolem Functions in Non-Classical Logics.Tore Fjetland Øgaard - 2017 - Australasian Journal of Logic 14 (1):181-225.
    This paper shows how to conservatively extend theories formulated in non-classical logics such as the Logic of Paradox, the Strong Kleene Logic and relevant logics with Skolem functions. Translations to and from the language extended by Skolem functions into the original one are presented and shown to preserve derivability. It is also shown that one may not always substitute s=f(t) and A(t, s) even though A determines the extension of a function and f is a Skolem function for A.
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  34. added 2019-03-08
    Relevance Via Decomposition.David Makinson - 2017 - Australasian Journal of Logic 14 (3).
    We report on progress and an unsolved problem in our attempt to obtain a clear rationale for relevance logic via semantic decomposition trees. Suitable decomposition rules, constrained by a natural parity condition, generate a set of directly acceptable formulae that contains all axioms of the well-known system R, is closed under substitution and conjunction, satisfies the letter-sharing condition, but is not closed under detachment. To extend it, a natural recursion is built into the procedure for constructing decomposition trees. The resulting (...)
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  35. added 2019-03-08
    Arthur Pap. Logic and the Concept of Entailment. The Journal of Philosophy, Vol. 47 , Pp. 378–387.David Makinson - 1975 - Journal of Symbolic Logic 40 (3):466.
    Review of the paper mentioned in the title.
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  36. added 2019-02-07
    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 sequent calculi (...)
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  37. added 2019-02-01
    Eco-Logical Lives: The Philosophical Lives of Richard Routley/Sylvan and Val Routley/Plumwood, by Dominic Hyde: Cambridge: The White Horse Press, 2014, Viii + 265, £60.00. [REVIEW]Jc Beall - 2015 - Australasian Journal of Philosophy 93 (3):619-621.
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  38. added 2019-01-25
    Relevance for the Classical Logician.Ethan Brauer - forthcoming - Review of Symbolic Logic:1-22.
    Although much technical and philosophical attention has been given to relevance logics, the notion of relevance itself is generally left at an intuitive level. It is difficult to find in the literature an explicit account of relevance in formal reasoning. In this article I offer a formal explication of the notion of relevance in deductive logic and argue that this notion has an interesting place in the study of classical logic. The main idea is that a premise is relevant to (...)
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  39. added 2018-12-24
    Model Definability in Relevant Logic.Guillermo Badia - 2017 - IfCoLog Journal of Logics and Their Applications 3 (4):623-646.
    It is shown that the classes of Routley-Meyer models which are axiomatizable by a theory in a propositional relevant language with fusion and the Ackermann constant can be characterized by their closure under certain model-theoretic operations involving prime filter extensions, relevant directed bisimulations and disjoint unions.
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  40. added 2018-10-23
    E and S4.Robert K. Meyer - 1970 - Notre Dame Journal of Formal Logic 11 (2):181-199.
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  41. added 2018-09-18
    Negation on the Australian Plan.Franz Berto & Greg Restall - 2019 - Journal of Philosophical Logic 1:1-26.
    We present and defend the Australian Plan semantics for negation. This is a comprehensive account, suitable for a variety of different logics. It is based on two ideas. The first is that negation is an exclusion-expressing device: we utter negations to express incompatibilities. The second is that, because incompatibility is modal, negation is a modal operator as well. It can, then, be modelled as a quantifier over points in frames, restricted by accessibility relations representing compatibilities and incompatibilities between such points. (...)
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  42. added 2018-09-13
    Logics for Modelling Collective Attitudes.Daniele Porello - 2018 - Fundamenta Infromaticae 158 (1-3):239-27.
    We introduce a number of logics to reason about collective propositional attitudes that are defined by means of the majority rule. It is well known that majoritarian aggregation is subject to irrationality, as the results in social choice theory and judgment aggregation show. The proposed logics for modelling collective attitudes are based on a substructural propositional logic that allows for circumventing inconsistent outcomes. Individual and collective propositional attitudes, such as beliefs, desires, obligations, are then modelled by means of minimal modalities (...)
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  43. added 2018-08-17
    Reflections on Routley's Ultralogic Program.Daniel Nolan - 2018 - Australasian Journal of Logic 15 (2):407-430.
    In this paper, I take up three tasks in turn. The first is to set out what Routley thought we should demand of an all-purpose universal logic, and some of his reasons for those demands. The second is to sketch Routley's own response to those demands. The third is to explore how else we could satisfy some of the theoretical demands Routley identified, if we are not to follow him in endorsing Routleyan Ultralogic as a foundational logic. As part of (...)
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  44. added 2018-07-24
    Non-Normal Modalities in Variants of Linear Logic.D. Porello & N. Troquard - 2015 - Journal of Applied Non-Classical Logics 25 (3):229-255.
    This article presents modal versions of resource-conscious logics. We concentrate on extensions of variants of linear logic with one minimal non-normal modality. In earlier work, where we investigated agency in multi-agent systems, we have shown that the results scale up to logics with multiple non-minimal modalities. Here, we start with the language of propositional intuitionistic linear logic without the additive disjunction, to which we add a modality. We provide an interpretation of this language on a class of Kripke resource models (...)
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  45. added 2018-04-23
    The Interpretation of Partitioned Frame Semantics.Colin R. Caret - 2009 - Dissertation, University of Connecticut
    The advocate of modal logic or relevant logic has traditionally argued that her preferred system offers the best regimentation of the theory of entailment. Essential to the projects of modal and relevant logic is the importation of non-truth-functional expressive resources into the object language on which the logic is defined. The most elegant technique for giving the semantics of such languages is that of frame semantics, a variation on which features the device of partitioned frames that divide 'points of evaluation' (...)
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  46. added 2018-04-06
    Negation And Contradiction.Richard Routley Val Routley, Richard Sylvan & Richard Routley - 1985 - Revista Columbiana de Mathematicas:201 - 231.
    The problems of the meaning and function of negation are disentangled from ontological issues with which they have been long entangled. The question of the function of negation is the crucial issue separating relevant and paraconsistent logics from classical theories. The function is illuminated by considering the inferential role of contradictions, contradiction being parasitic on negation. Three basic modelings emerge: a cancellation model, which leads towards connexivism, an explosion model, appropriate to classical and intuitionistic theories, and a constraint model, which (...)
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  47. added 2018-03-05
    Trees for E.Shawn Standefer - 2018 - Logic Journal of the IGPL 26 (3):300-315.
  48. added 2018-02-01
    Logically Impossible Worlds.Koji Tanaka - 2018 - Australasian Journal of Logic 15 (2):489.
    What does it mean for the laws of logic to fail? My task in this paper is to answer this question. I use the resources that Routley/Sylvan developed with his collaborators for the semantics of relevant logics to explain a world where the laws of logic fail. I claim that the non-normal worlds that Routley/Sylvan introduced are exactly such worlds. To disambiguate different kinds of impossible worlds, I call such worlds logically impossible worlds. At a logically impossible world, the laws (...)
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  49. added 2018-01-13
    A Decidable Paraconsistent Relevant Logic: Gentzen System and Routley-Meyer Semantics.Norihiro Kamide - 2016 - Mathematical Logic Quarterly 62 (3):177-189.
    In this paper, the positive fragment of the logic math formula of contraction-less relevant implication is extended with the addition of a paraconsistent negation connective similar to the strong negation connective in Nelson's paraconsistent four-valued logic math formula. This extended relevant logic is called math formula, and it has the property of constructible falsity which is known to be a characteristic property of math formula. A Gentzen-type sequent calculus math formula for math formula is introduced, and the cut-elimination and decidability (...)
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  50. added 2018-01-01
    The Weak Theory of Implication.Alonzo Church - 1951 - In A. Menne, A. Wilhelmy & H. Angsil (eds.), KontrolIiertes Denken: Untersuchungen zum Logikkalk\"{u}l und der Logik der Einzelwissenschaften. Munich: Kommissions-verlag Karl Alber. pp. 22-37.
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