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

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  1. Mark Jago (2013). Recent Work in Relevant Logic. Analysis 73 (3):526-541.score: 180.0
    This paper surveys important work done in relevant logic in the past 10 years.
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  2. Edwin D. Mares (2009). General Information in Relevant Logic. Synthese 167 (2):343 - 362.score: 156.0
    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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  3. Diderik Batens (forthcoming). Propositional Logic Extended with a Pedagogically Useful Relevant Implication. Logic and Logical Philosophy.score: 156.0
    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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  4. Lou Goble (2000). An Incomplete Relevant Modal Logic. Journal of Philosophical Logic 29 (1):103-119.score: 154.0
    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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  5. Wesley H. Holliday (forthcoming). Epistemic Closure and Epistemic Logic I: Relevant Alternatives and Subjunctivism. Journal of Philosophical Logic:1-62.score: 150.0
    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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  6. Edwin David Mares (2004). Relevant Logic: A Philosophical Interpretation. Cambridge Univeristy Press.score: 148.0
    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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  7. Wesley H. Holliday (2012). Epistemic Logic, Relevant Alternatives, and the Dynamics of Context. Lecture Notes in Computer Science 7415:109-129.score: 144.0
    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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  8. Ryszard Mirek (2011). The Systems of Relevance Logic. ARGUMENT 1 (1):87-102.score: 128.0
    The system R, or more precisely the pure implicational fragment R›, is considered by the relevance logicians as the most important. The another central system of relevance logic has been the logic E of entailment that was supposed to capture strict relevant implication. The next system of relevance logic is RM or R-mingle. The question is whether adding mingle axiom to R› yields the pure implicational fragment RM› of the system? As concerns the weak systems there (...)
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  9. Edwin D. Mares (2004). “Four-Valued” Semantics for the Relevant Logic R. Journal of Philosophical Logic 33 (3):327-341.score: 126.0
    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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  10. Kosta Došen (1992). The First Axiomatization of Relevant Logic. Journal of Philosophical Logic 21 (4):339 - 356.score: 126.0
    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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  11. Edwin D. Mares & Robert Goldblatt (2006). An Alternative Semantics for Quantified Relevant Logic. Journal of Symbolic Logic 71 (1):163-187.score: 126.0
    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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  12. Kazimierz Swirydowicz (1999). There Exist Exactly Two Maximal Strictly Relevant Extensions of the Relevant Logic R. Journal of Symbolic Logic 64 (3):1125-1154.score: 126.0
    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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  13. Robert Goldblatt & Michael Kane (2010). An Admissible Semantics for Propositionally Quantified Relevant Logics. Journal of Philosophical Logic 39 (1):73 - 100.score: 122.0
    The Routley-Meyer relational semantics for relevant logics is extended to give a sound and complete model theory for many propositionally quantified relevant logics (and some non-relevant ones). This involves a restriction on which sets of worlds are admissible as propositions, and an interpretation of propositional quantification that makes ∀ pA true when there is some true admissible proposition that entails all p -instantiations of A . It is also shown that without the admissibility qualification many of the (...)
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  14. 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.score: 122.0
    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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  15. Gerson Zaverucha (1992). Relevant Logic as a Basis for Paraconsistent Epistemic Logics. Journal of Applied Non-Classical Logics 2 (2):225-241.score: 122.0
    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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  16. Vladimir L. Vasyukov (2011). Paraconsistency in Categories: Case of Relevance Logic. Studia Logica 98 (3):429-443.score: 120.0
    Categorical-theoretic semantics for the relevance logic is proposed which is based on the construction of the topos of functors from a relevant algebra (considered as a preorder category endowed with the special endofunctors) in the category of sets Set. The completeness of the relevant system R of entailment is proved in respect to the semantic considered.
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  17. 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.score: 120.0
    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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  18. José M. Méndez, A Note on "Recent Work in Relevant Logic&Quot;.score: 120.0
    In his paper “Recent work in relevant logic”, Jago includes a section on Disjunctive Syllogism (DS). 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. Ryo Kashima & Norihiro Kamide (1999). Substructural Implicational Logics Including the Relevant Logic E. Studia Logica 63 (2):181-212.score: 120.0
    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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  20. Harry Deutsch (1985). A Note on the Decidability of a Strong Relevant Logic. Studia Logica 44 (2):159 - 164.score: 120.0
    A modified filtrations argument is used to prove that the relevant logic S of [2] is decidable.
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  21. Edwin D. Mares (1996). Relevant Logic and the Theory of Information. Synthese 109 (3):345 - 360.score: 120.0
    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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  22. Stephen Read (1988). Relevant Logic: A Philosophical Examination of Inference. B. Blackwell.score: 118.0
  23. Richard Routley (1979). Alternative Semantics for Quantified First Degree Relevant Logic. Studia Logica 38 (2):211 - 231.score: 116.0
    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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  24. Diderik Batens (2001). A Dynamic Characterization of the Pure Logic of Relevant Implication. Journal of Philosophical Logic 30 (3):267-280.score: 114.0
    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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  25. Takahiro Seki (2003). General Frames for Relevant Modal Logics. Notre Dame Journal of Formal Logic 44 (2):93-109.score: 114.0
    General frames are often used in classical modal logic. Since they are duals of modal algebras, completeness follows automatically as with algebras but the intuitiveness of Kripke frames is also retained. This paper develops basics of general frames for relevant modal logics by showing that they share many important properties with general frames for classical modal logic.
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  26. Takahiro Seki (2011). The Γ-Admissibility of Relevant Modal Logics I — The Method of Normal Models. Studia Logica 97 (2):199 - 231.score: 114.0
    The admissibility of Ackermann's rule γ is one of the most important problems in relevant logic. While the γ-admissibility of normal modal logics based on the relevant logic R has been previously discussed, the case for weaker relevant modal logics has not yet been considered. The method of normal models has often been used to prove the γ-admissibility. This paper discusses which relevant modal logics admit γ from the viewpoint of the method of normal (...)
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  27. Jan Dejnožka (2010). The Concept of Relevance and the Logic Diagram Tradition. Logica Universalis 4 (1):67-135.score: 110.0
    What is logical relevance? Anderson and Belnap say that the “modern classical tradition [,] stemming from Frege and Whitehead-Russell, gave no consideration whatsoever to the classical notion of relevance.” But just what is this classical notion? I argue that the relevance tradition is implicitly most deeply concerned with the containment of truth-grounds, less deeply with the containment of classes, and least of all with variable sharing in the Anderson–Belnap manner. Thus modern classical logicians such as Peirce, Frege, Russell, Wittgenstein, and (...)
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  28. Ross T. Brady (1994). Rules in Relevant Logic - I: Semantic Classification. [REVIEW] Journal of Philosophical Logic 23 (2):111 - 137.score: 110.0
    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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  29. James Garson (1989). Modularity and Relevant Logic. Notre Dame Journal of Formal Logic 30 (2):207-223.score: 110.0
    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 L (...)
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  30. Takahiro Seki (2013). Some Metacomplete Relevant Modal Logics. Studia Logica 101 (5):1115-1141.score: 110.0
    A logic is called metacomplete if formulas that are true in a certain preferred interpretation of that logic are theorems in its metalogic. In the area of relevant logics, metacompleteness is used to prove primeness, consistency, the admissibility of γ and so on. This paper discusses metacompleteness and its applications to a wider class of modal logics based on contractionless relevant logics and their neighbours using Slaney’s metavaluational technique.
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  31. Edwin Mares (2010). The Nature of Information: A Relevant Approach. Synthese 175 (1):111 - 132.score: 108.0
    In "General Information in Relevant Logic" (Synthese 167, 2009), the semantics for relevant logic is interpreted in terms of objective information. Objective information is potential data that is available in an environment. This paper explores the notion of objective information further. The concept of availability in an environment is developed and used as a foundation for the semantics, in particular, as a basis for the understanding of the information that is expressed by relevant implication. It (...)
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  32. Ryo Kashima (2003). On Semilattice Relevant Logics. Mathematical Logic Quarterly 49 (4):401.score: 108.0
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  33. Gert-Jan C. Lokhorst (2008). Anderson's Relevant Deontic and Eubouliatic Systems. Notre Dame Journal of Formal Logic 49 (1):65-73.score: 108.0
    We present axiomatizations of the deontic fragment of Anderson's relevant deontic logic (the logic of obligation and related concepts) and the eubouliatic fragment of Anderson's eubouliatic logic (the logic of prudence, safety, risk, and related concepts).
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  34. Dmitry Zaitsev & Oleg Grigoriev (2010). Relevant Generalization Starts Here (and Here = 2). Logic and Logical Philosophy 19 (4):329-340.score: 108.0
    There is a productive and suggestive approach in philosophical logic based on the idea of generalized truth values. This idea, which stems essentially from the pioneering works by J.M. Dunn, N. Belnap, and which has recently been developed further by Y. Shramko and H. Wansing, is closely connected to the power-setting formation on the base of some initial truth values. Having a set of generalized truth values, one can introduce fundamental logical notions, more specifically, the ones of logical operations (...)
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  35. Ross T. Brady (1993). Rules in Relevant Logic — II: Formula Representation. Studia Logica 52 (4):565 - 585.score: 104.0
    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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  36. Ross T. Brady (1996). Relevant Implication and the Case for a Weaker Logic. Journal of Philosophical Logic 25 (2):151 - 183.score: 102.0
    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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  37. Gemma Robles & José M. Méndez (2010). A Routley-Meyer Type Semantics for Relevant Logics Including B R Plus the Disjunctive Syllogism. Journal of Philosophical Logic 39 (2):139 - 158.score: 102.0
    Routley-Meyer type ternary relational semantics are defined for relevant logics including Routley and Meyer’s basic logic B plus the reductio rule and the disjunctive syllogism. Standard relevant logics such as E and R (plus γ ) and Ackermann’s logics of ‘strenge Implikation’ Π and Π ′ are among the logics considered.
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  38. Norihiro Kamide (2002). Kripke Semantics for Modal Substructural Logics. Journal of Logic, Language and Information 11 (4):453-470.score: 98.0
    We introduce Kripke semantics for modal substructural logics, and provethe completeness theorems with respect to the semantics. Thecompleteness theorems are proved using an extended Ishihara's method ofcanonical model construction (Ishihara, 2000). The framework presentedcan deal with a broad range of modal substructural logics, including afragment of modal intuitionistic linear logic, and modal versions ofCorsi's logics, Visser's logic, Méndez's logics and relevant logics.
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  39. Takahiro Seki (2012). An Algebraic Proof of the Admissibility of Γ in Relevant Modal Logics. Studia Logica 100 (6):1149-1174.score: 98.0
    The admissibility of Ackermann's rule γ is one of the most important problems in relevant logics. The admissibility of γ was first proved by an algebraic method. However, the development of Routley-Meyer semantics and metavaluational techniques makes it possible to prove the admissibility of γ using the method of normal models or the method using metavaluations, and the use of such methods is preferred. This paper discusses an algebraic proof of the admissibility of γ in relevant modal logics (...)
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  40. Takahiro Seki (2011). The Γ-Admissibility of Relevant Modal Logics II — The Method Using Metavaluations. Studia Logica 97 (3):351 - 383.score: 98.0
    The γ-admissibility is one of the most important problems in the realm of relevant logics. To prove the 7-admissibility, either the method of normal models or the method using metavaluations may be employed. The γ-admissibility of a wide class of relevant modal logics has been discussed in Part I based on a former method, but the γ-admissibility based on metavaluations has not hitherto been fully considered. Sahlqvist axioms are well known as a means of expressing generalized forms of (...)
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  41. Ross Thomas Brady (2010). Free Semantics. Journal of Philosophical Logic 39 (5):511 - 529.score: 96.0
    Free Semantics is based on normalized natural deduction for the weak relevant logic DW and its near neighbours. This is motivated by the fact that in the determination of validity in truth-functional semantics, natural deduction is normally used. Due to normalization, the logic is decidable and hence the semantics can also be used to construct counter-models for invalid formulae. The logic DW is motivated as an entailment logic just weaker than the logic MC of (...)
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  42. 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.score: 96.0
  43. Greg Restall & Tony Roy (2009). On Permutation in Simplified Semantics. Journal of Philosophical Logic 38 (3):333 - 341.score: 96.0
    This note explains an error in Restall’s ‘Simplified Semantics for Relevant Logics (and some of their rivals)’ (Restall, J Philos Logic 22(5):481–511, 1993 ) concerning the modelling conditions for the axioms of assertion A → (( A → B ) → B ) (there called c 6) and permutation ( A → ( B → C )) → ( B → ( A → C )) (there called c 7). We show that the modelling conditions for assertion and (...)
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  44. Neil Tennant (1987). Natural Deduction and Sequent Calculus for Intuitionistic Relevant Logic. Journal of Symbolic Logic 52 (3):665-680.score: 96.0
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  45. J. -F. Pabion (1979). Beth's Tableaux for Relevant Logic. Notre Dame Journal of Formal Logic 20 (4):891-899.score: 96.0
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  46. 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.score: 96.0
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  47. John K. Slaney & Robert K. Meyer (1992). A Structurally Complete Fragment of Relevant Logic. Notre Dame Journal of Formal Logic 33 (4):561-566.score: 96.0
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  48. Nissim Francez (2014). Bilateral Relevant Logic. The Review of Symbolic Logic 7 (2):250-272.score: 96.0
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  49. Yoko Motohama, Robert K. Meyer & Mariangiola Dezani-Ciancaglini (2002). The Semantics of Entailment Omega. Notre Dame Journal of Formal Logic 43 (3):129-145.score: 96.0
    This paper discusses the relation between the minimal positive relevant logic B and intersection and union type theories. There is a marvelous coincidence between these very differently motivated research areas. First, we show a perfect fit between the Intersection Type Discipline ITD and the tweaking BT of B, which saves implication and conjunction but drops disjunction . The filter models of the -calculus (and its intimate partner Combinatory Logic CL) of the first author and her coauthors then (...)
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  50. N. C. A. da Costa (1993). Review: Jean Norman, Richard Sylvan, Directions in Relevant Logic. [REVIEW] Journal of Symbolic Logic 58 (4):1466-1468.score: 96.0
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