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  1. Relevance Logic.Michael Dunn & Greg Restall - 1983 - In Dov M. Gabbay & Franz Guenthner (eds.), Handbook of Philosophical Logic. Dordrecht, Netherland: Kluwer Academic Publishers.
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  • New Consecution Calculi for R→t.Katalin Bimbó & J. Michael Dunn - 2012 - Notre Dame Journal of Formal Logic 53 (4):491-509.
    The implicational fragment of the logic of relevant implication, $R_{\to}$ is one of the oldest relevance logics and in 1959 was shown by Kripke to be decidable. The proof is based on $LR_{\to}$ , a Gentzen-style calculus. In this paper, we add the truth constant $\mathbf{t}$ to $LR_{\to}$ , but more importantly we show how to reshape the sequent calculus as a consecution calculus containing a binary structural connective, in which permutation is replaced by two structural rules that involve $\mathbf{t}$ (...)
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  • (1 other version)Entailment: The Logic of Relevance and Neccessity, Vol. I.Alan Ross Anderson & Nuel D. Belnap - 1975 - Princeton, N.J.: Princeton University Press. Edited by Nuel D. Belnap & J. Michael Dunn.
    In spite of a powerful tradition, more than two thousand years old, that in a valid argument the premises must be relevant to the conclusion, twentieth-century logicians neglected the concept of relevance until the publication of Volume I of this monumental work. Since that time relevance logic has achieved an important place in the field of philosophy: Volume II of Entailment brings to a conclusion a powerful and authoritative presentation of the subject by most of the top people working in (...)
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  • An alternative semantics for quantified relevant logic.Edwin D. Mares & Robert Goldblatt - 2006 - Journal of Symbolic Logic 71 (1):163-187.
    The quantified relevant logic RQ is given a new semantics in which a formula for all xA is true when there is some true proposition that implies all x-instantiations of A. Formulae are modelled as functions from variable-assignments to propositions, where a proposition is a set of worlds in a relevant model structure. A completeness proof is given for a basic quantificational system QR from which RQ is obtained by adding the axiom EC of 'extensional confinement': for all x(A V (...)
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  • General Frames for Relevant Modal Logics.Takahiro Seki - 2003 - Notre Dame Journal of Formal Logic 44 (2):93-109.
    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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  • (1 other version)Semantical Analysis of Modal Logic I. Normal Propositional Calculi.Saul A. Kripke - 1963 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 9 (5‐6):67-96.
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  • Conservativity of Heyting implication over relevant quantification.Robert Goldblatt - 2009 - Review of Symbolic Logic 2 (2):310-341.
    It is known that propositional relevant logics can be conservatively extended by the addition of a Heyting (intuitionistic) implication connective. We show that this same conservativity holds for a range of first-order relevant logics with strong identity axioms, using an adaptation of Fine’s stratified model theory. For systems without identity, the question of conservatively adding Heyting implication is thereby reduced to the question of conservatively adding the axioms for identity. Some results in this direction are also obtained. The conservative presence (...)
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  • Relevant Logics and Their Rivals.Richard Routley, Val Plumwood, Robert K. Meyer & Ross T. Brady - 1982 - Ridgeview. Edited by Richard Sylvan & Ross Brady.
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  • The complexity of decision procedures in relevance logic II.Alasdair Urquhart - 1999 - Journal of Symbolic Logic 64 (4):1774-1802.
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  • The semantics of entailment — III.Richard Routley & Robert K. Meyer - 1972 - Journal of Philosophical Logic 1 (2):192 - 208.
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  • (1 other version)A completeness theorem in modal logic.Saul Kripke - 1959 - Journal of Symbolic Logic 24 (1):1-14.
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  • Normal modal substructural logics with strong negation.Norihiro Kamide - 2003 - Journal of Philosophical Logic 32 (6):589-612.
    We introduce modal propositional substructural logics with strong negation, and prove the completeness theorems (with respect to Kripke models) for these logics.
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  • Quantification and RM.J. Michael Dunn - 1976 - Studia Logica 35 (3):315 - 322.
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  • (2 other versions)Kripke models for linear logic.Gerard Allwein & J. Michael Dunn - 1993 - Journal of Symbolic Logic 58 (2):514-545.
    We present a Kripke model for Girard's Linear Logic (without exponentials) in a conservative fashion where the logical functors beyond the basic lattice operations may be added one by one without recourse to such things as negation. You can either have some logical functors or not as you choose. Commutatively and associatively are isolated in such a way that the base Kripke model is a model for noncommutative, nonassociative Linear Logic. We also extend the logic by adding a coimplication operator, (...)
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  • (2 other versions)The Semantics of Entailment.Richard Routley & Robert K. Meyer - 1973 - In Hugues Leblanc (ed.), Truth, Syntax, and Modality: Proceedings Of The Temple University Conference On Alternative Semantlcs. Amsterdam and London: North-Holland Publishing Company. pp. 199-243.
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  • 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 relevant logic and (...)
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  • (2 other versions)Kripke Models for Linear Logic.Allwein Gerard & Dunn J. Michael - 1993 - Journal of Symbolic Logic 58 (2):514-545.
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  • Decision problems for propositional linear logic.Patrick Lincoln, John Mitchell, Andre Scedrov & Natarajan Shankar - 1992 - Annals of Pure and Applied Logic 56 (1-3):239-311.
    Linear logic, introduced by Girard, is a refinement of classical logic with a natural, intrinsic accounting of resources. This accounting is made possible by removing the ‘structural’ rules of contraction and weakening, adding a modal operator and adding finer versions of the propositional connectives. Linear logic has fundamental logical interest and applications to computer science, particularly to Petri nets, concurrency, storage allocation, garbage collection and the control structure of logic programs. In addition, there is a direct correspondence between polynomial-time computation (...)
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  • Investigations into Logical Deduction.Gerhard Gentzen - 1964 - American Philosophical Quarterly 1 (4):288 - 306.
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  • Linear logic displayed.Nuel Belnap - 1989 - Notre Dame Journal of Formal Logic 31 (1):14-25.
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  • (1 other version)Semantical Analysis of Modal Logic II. Non-Normal Modal Propositional Calculi.Saul A. Kripke - 1965 - In J. W. Addison (ed.), The theory of models. Amsterdam,: North-Holland Pub. Co.. pp. 206-20.
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  • (2 other versions)The semantics of entailment II.Richard Routley & Robert K. Meyer - 1972 - Journal of Philosophical Logic 1 (1):53 - 73.
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  • (1 other version)The completeness of the first-order functional calculus.Leon Henkin - 1949 - Journal of Symbolic Logic 14 (3):159-166.
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  • Topological Representations of Distributive Lattices and Brouwerian Logics.M. H. Stone - 1938 - Journal of Symbolic Logic 3 (2):90-91.
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  • The theory of Representations for Boolean Algebras.M. H. Stone - 1936 - Journal of Symbolic Logic 1 (3):118-119.
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  • Substructural Logics.Peter Joseph Schroeder-Heister & Kosta Došen - 1993 - Oxford, England: Oxford University Press on Demand.
    The new area of logic and computation is now undergoing rapid development. This has affected the social pattern of research in the area. A new topic may rise very quickly with a significant body of research around it. The community, however, cannot wait the traditional two years for a book to appear. This has given greater importance to thematic collections of papers, centred around a topic and addressing it from several points of view, usually as a result of a workshop, (...)
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  • On the decidability of implicational ticket entailment.Katalin Bimbó & J. Michael Dunn - 2013 - Journal of Symbolic Logic 78 (1):214-236.
    The implicational fragment of the logic of relevant implication, $R_\to$ is known to be decidable. We show that the implicational fragment of the logic of ticket entailment, $T_\to$ is decidable. Our proof is based on the consecution calculus that we introduced specifically to solve this 50-year old open problem. We reduce the decidability problem of $T_\to$ to the decidability problem of $R_\to$. The decidability of $T_\to$ is equivalent to the decidability of the inhabitation problem of implicational types by combinators over (...)
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  • 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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  • CE is not a conservative extension of E.Edwin D. Mares - 2000 - Journal of Philosophical Logic 29 (3):263-275.
    The logic CE (for "Classical E") results from adding Boolean negation to Anderson and Belnap's logic E. This paper shows that CE is not a conservative extension of E.
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  • (2 other versions)The Semantics of Entailment.Richard Routley & Robert K. Meyer - 1977 - Journal of Symbolic Logic 42 (2):315-316.
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  • (1 other version)A truth value semantics for modal logic.J. Michael Dunn - 1973 - Journal of Symbolic Logic 42 (2):87--100.
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  • Combinatory Logic: Pure, Applied and Typed.Katalin Bimbó - 2011 - Taylor & Francis.
    Reader-friendly without compromising the precision of exposition, the book includes many new research results not found in the available literature.
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  • (2 other versions)Entailment: The Logic of Relevance and Necessity, Vol. II.Alan Ross Anderson, Nuel D. Belnap & J. Michael Dunn - 1992 - Princeton University Press.
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  • (1 other version)Semantical Analysis of Intuitionistic Logic I.Saul A. Kripke - 1963 - In Michael Dummett & J. N. Crossley (eds.), Formal Systems and Recursive Functions. Amsterdam,: North Holland. pp. 92-130.
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  • Foundations of mathematical logic.Haskell Brooks Curry - 1963 - New York: Dover Publications.
    Comprehensive account of constructive theory of first-order predicate calculus. Covers formal methods including algorithms and epi-theory, brief treatment of Markov’s approach to algorithms, elementary facts about lattices and similar algebraic systems, more. Philosophical and reflective as well as mathematical. Graduate-level course. 1963 ed. Exercises.
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  • Display logic.Nuel D. Belnap - 1982 - Journal of Philosophical Logic 11 (4):375-417.
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  • (1 other version)Semantical Analysis of Intuitionistic Logic I.Saul A. Kripke, J. N. Crossley & M. A. E. Dummett - 1970 - Journal of Symbolic Logic 35 (2):330-332.
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  • Display Logic And Gaggle Theory.Greg Restall - 1995 - Reports on Mathematical Logic:133-146.
    This paper is a revised version of a talk given at the Logic and Logical Philosophy conference in Poland in September 1995. In it, I sketch the connections between Nuel Belnap's Display Logic and J. Michael Dunn's Gaggle Theory.
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  • Four Variables Suffice.Alasdair Urquhart - 2007 - Australasian Journal of Logic 5:66-73.
    What I wish to propose in the present paper is a new form of “career induction” for ambitious young logicians. The basic problem is this: if we look at the n-variable fragments of relevant propositional logics, at what point does undecidability begin? Focus, to be definite, on the logic R. John Slaney showed that the 0-variable fragment of R (where we allow the sentential con- stants t and f) contains exactly 3088 non-equivalent propositions, and so is clearly decidable. In the (...)
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  • The Collected Papers of Gerhard Gentzen. [REVIEW]G. Kreisel - 1971 - Journal of Philosophy 68 (8):238-265.
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  • BLASS. A., A game semantics for linear logic CENZER, D. and REMMEL, J., Polynomial-time Abehan groups CLOTE, P. and TAKEUTI, G., Bounded arithmetic for NC, ALogTIME, L and NL. [REVIEW]P. Lincoln, J. Mitchell & A. Scedrov - 1992 - Annals of Pure and Applied Logic 56:365.
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  • Converse Ackermann property and constructive negation defined with a negation connective.Gemma Robles & José M. Méndez - 2006 - Logic and Logical Philosophy 15 (2):113-130.
    The Converse Ackermann Property is the unprovability of formulas of the form (A -> B) -> C when C does contain neither -> nor ¬. Intuitively, the CAP amounts to rule out the derivability of pure non-necessitive propositions from non-necessitive ones. A constructive negation of the sort historically defined by, e.g., Johansson is added to positive logics with the CAP in the spectrum delimited by Ticket Entailment and Dummett’s logic LC.
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  • Kripke semantics for modal substructural logics.Norihiro Kamide - 2002 - Journal of Logic, Language and Information 11 (4):453-470.
    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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  • Proof theory: sequent calculi and related formalisms.Katalin Bimbó - 2015 - Boca Raton: CRC Press, Taylor & Francis Group.
    Sequent calculi constitute an interesting and important category of proof systems. They are much less known than axiomatic systems or natural deduction systems are, and they are much less known than they should be. Sequent calculi were designed as a theoretical framework for investigations of logical consequence, and they live up to the expectations completely as an abundant source of meta-logical results. The goal of this book is to provide a fairly comprehensive view of sequent calculi -- including a wide (...)
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  • Four-valued Logic.Katalin Bimbó & J. Michael Dunn - 2001 - Notre Dame Journal of Formal Logic 42 (3):171-192.
    Four-valued semantics proved useful in many contexts from relevance logics to reasoning about computers. We extend this approach further. A sequent calculus is defined with logical connectives conjunction and disjunction that do not distribute over each other. We give a sound and complete semantics for this system and formulate the same logic as a tableaux system. Intensional conjunction and its residuals can be added to the sequent calculus straightforwardly. We extend a simplified version of the earlier semantics for this system (...)
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  • A Kripke-style semantics for R-Mingle using a binary accessibility relation.J. Michael Dunn - 1976 - Studia Logica 35 (2):163 - 172.
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  • Linear Logic.Jean-Yves Girard - 1987 - Theoretical Computer Science 50:1–102.
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  • The Semantics and Proof Theory of Linear Logic.Arnon Avron - 1988 - Theoretical Computer Science 57 (2):161-184.
    Linear logic is a new logic which was recently developed by Girard in order to provide a logical basis for the study of parallelism. It is described and investigated in Gi]. Girard's presentation of his logic is not so standard. In this paper we shall provide more standard proof systems and semantics. We shall also extend part of Girard's results by investigating the consequence relations associated with Linear Logic and by proving corresponding str ong completeness theorems. Finally, we shall investigate (...)
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  • Classical relevant logics. I.R. K. Meyer & Richard Routley - 1973 - Studia Logica 32:51.
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  • An Introduction to Substructural Logics.Greg Restall - 1999 - New York: Routledge.
    This book introduces an important group of logics that have come to be known under the umbrella term 'susbstructural'. Substructural logics have independently led to significant developments in philosophy, computing and linguistics. _An Introduction to Substrucural Logics_ is the first book to systematically survey the new results and the significant impact that this class of logics has had on a wide range of fields.The following topics are covered: * Proof Theory * Propositional Structures * Frames * Decidability * Coda Both (...)
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