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Edwin D. Mares [38]Edwin Mares [33]Edwin David Mares [1]
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Edwin Mares
Victoria University of Wellington
  1. Logical Consequence and the Paradoxes.Edwin Mares & Francesco Paoli - 2014 - Journal of Philosophical Logic 43 (2-3):439-469.
    We group the existing variants of the familiar set-theoretical and truth-theoretical paradoxes into two classes: connective paradoxes, which can in principle be ascribed to the presence of a contracting connective of some sort, and structural paradoxes, where at most the faulty use of a structural inference rule can possibly be blamed. We impute the former to an equivocation over the meaning of logical constants, and the latter to an equivocation over the notion of consequence. Both equivocation sources are tightly related, (...)
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  2.  49
    Relevant Logic: A Philosophical Interpretation.Edwin D. Mares - 2007 - 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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  3. On the Ternary Relation and Conditionality.Jc Beall, Ross Brady, J. Michael Dunn, A. P. Hazen, Edwin Mares, Robert K. Meyer, Graham Priest, Greg Restall, David Ripley, John Slaney & Richard Sylvan - 2012 - Journal of Philosophical Logic 41 (3):595 - 612.
    One of the most dominant approaches to semantics for relevant (and many paraconsistent) logics is the Routley-Meyer semantics involving a ternary relation on points. To some (many?), this ternary relation has seemed like a technical trick devoid of an intuitively appealing philosophical story that connects it up with conditionality in general. In this paper, we respond to this worry by providing three different philosophical accounts of the ternary relation that correspond to three conceptions of conditionality. We close by briefly discussing (...)
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  4.  29
    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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  5. Informational Semantics as a Third Alternative?Patrick Allo & Edwin Mares - 2012 - Erkenntnis 77 (2):167-185.
    Informational semantics were first developed as an interpretation of the model-theory of substructural (and especially relevant) logics. In this paper we argue that such a semantics is of independent value and that it should be considered as a genuine alternative explication of the notion of logical consequence alongside the traditional model-theoretical and the proof-theoretical accounts. Our starting point is the content-nonexpansion platitude which stipulates that an argument is valid iff the content of the conclusion does not exceed the combined content (...)
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  6.  69
    Who's Afraid of Impossible Worlds?Edwin D. Mares - 1997 - Notre Dame Journal of Formal Logic 38 (4):516-526.
    A theory of ersatz impossible worlds is developed to deal with the problem of counterpossible conditionals. Using only tools standardly in the toolbox of possible worlds theorists, it is shown that we can construct a model for counterpossibles. This model is a natural extension of Lewis's semantics for counterfactuals, but instead of using classical logic as its base, it uses the logic LP.
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  7.  76
    General Information in Relevant Logic.Edwin 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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  8.  90
    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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  9. A Star-Free Semantics for R.Edwin D. Mares - 1995 - Journal of Symbolic Logic 60 (2):579 - 590.
    The purpose of this paper is to show that semantics for relevance logic, based on the Routley-Meyer semantics, can be given without using the Routley star operator to treat negation. In the resulting semantics, negation is treated implicationally. It is shown that, by the use of restrictions on the ternary accessibility relation, simplified by the use of some definitions, a semantics can be stipulated over which R is complete.
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  10. Realism and Anti-Realism.Stuart Brock & Edwin Mares - 2006 - Routledge.
    There are a bewildering variety of ways the terms "realism" and "anti-realism" have been used in philosophy and furthermore the different uses of these terms are only loosely connected with one another. Rather than give a piecemeal map of this very diverse landscape, the authors focus on what they see as the core concept: realism about a particular domain is the view that there are facts or entities distinctive of that domain, and their existence and nature is in some important (...)
     
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  11.  44
    A Paraconsistent Theory of Belief Revision.Edwin D. Mares - 2002 - Erkenntnis 56 (2):229 - 246.
    This paper presents a theory of belief revision that allows people to come tobelieve in contradictions. The AGM theory of belief revision takes revision,in part, to be consistency maintenance. The present theory replacesconsistency with a weaker property called coherence. In addition to herbelief set, we take a set of statements that she rejects. These two sets arecoherent if they do not overlap. On this theory, belief revision maintains coherence.
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  12.  13
    Belief Revision, Probabilism, and Logic Choice.Edwin Mares - 2014 - Review of Symbolic Logic 7 (4):647-670.
  13. Relevant Logic: A Philosophical Interpretation.Edwin D. Mares - 2007 - Studia Logica 85 (3):419-424.
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  14.  56
    The Nature of Information: A Relevant Approach.Edwin Mares - 2010 - Synthese 175 (1):111 - 132.
    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 is also used to understand (...)
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  15.  60
    Relevant Logic and the Theory of Information.Edwin D. 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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  16.  6
    Relevance Logic.Edwin Mares - 2008 - Stanford Encyclopedia of Philosophy.
  17. Relevant Logics.Edwin D. Mares & Robert K. Meyer - 2001 - In Lou Goble (ed.), The Blackwell Guide to Philosophical Logic. Blackwell. pp. 280--308.
     
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  18. Paraconsistency: Logic and Applications.Francesco Berto, Edwin Mares, Koji Tanaka & Francesco Paoli (eds.) - 2013 - Springer.
    A logic is called 'paraconsistent' if it rejects the rule called 'ex contradictione quodlibet', according to which any conclusion follows from inconsistent premises. While logicians have proposed many technically developed paraconsistent logical systems and contemporary philosophers like Graham Priest have advanced the view that some contradictions can be true, and advocated a paraconsistent logic to deal with them, until recent times these systems have been little understood by philosophers. This book presents a comprehensive overview on paraconsistent logical systems to change (...)
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  19.  25
    Propositional Function.Edwin Mares - forthcoming - Stanford Encyclopedia of Philosophy.
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  20.  3
    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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  21. Molinist Conditionals.Edwin Mares & Ken Perszyk - 2011 - In Ken Perszyk (ed.), Molinism: The Contemporary Debate. Oxford University Press. pp. 96--117.
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  22.  26
    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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  23.  20
    The Admissibility of $\Gamma$ in ${\Rm R}4$.Edwin D. Mares & Robert K. Meyer - 1992 - Notre Dame Journal of Formal Logic 33 (2):197-206.
  24. Introduction: Post-Analytic and Meta-Continental Philosophy.Jack Reynolds, James Chase, James Williams & Edwin Mares - 2010 - In James Williams, Jack Reynolds, James Chase & Edwin Mares (eds.), Postanalytic and Metacontinental: Crossing Philosophical Divides. Continuum.
    This chapter sketches some of the difficulties involved in defining analytic and continental philosophy, but begins to elaborate an argument for the centrality of methodology to the 'divide'.
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  25.  65
    Supererogation in Deontic Logic: Metatheory for DWE and Some Close Neighbours.Edwin D. Mares & Paul McNamara - 1997 - Studia Logica 59 (3):397-415.
    In "Doing Well Enough: Toward a Logic for Common Sense Morality", Paul McNamara sets out a semantics for a deontic logic which contains the operator It is supererogatory that. As well as having a binary accessibility relation on worlds, that semantics contains a relative ordering relation, . For worlds u, v and w, we say that u w v when v is at least as good as u according to the standards of w. In this paper we axiomatize logics complete (...)
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  26.  7
    Information, Negation, and Paraconsistency.Edwin D. Mares - 2013 - In Francesco Berto, Edwin Mares, Koji Tanaka & Francesco Paoli (eds.), Paraconsistency: Logic and Applications. Springer. pp. 43--55.
  27. Semantic Dialetheism.Edwin D. Mares - 2004 - In Graham Priest, J. C. Beall & Bradley Armour-Garb (eds.), The Law of Non-Contradiction. Clarendon Press.
     
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  28.  62
    Conditionals, Probability, and Non-Triviality.Charles G. Morgan & Edwin D. Mares - 1995 - Journal of Philosophical Logic 24 (5):455-467.
    We show that the implicational fragment of intuitionism is the weakest logic with a non-trivial probabilistic semantics which satisfies the thesis that the probabilities of conditionals are conditional probabilities. We also show that several logics between intuitionism and classical logic also admit non-trivial probability functions which satisfy that thesis. On the other hand, we also prove that very weak assumptions concerning negation added to the core probability conditions with the restriction that probabilities of conditionals are conditional probabilities are sufficient to (...)
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  29.  18
    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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  30.  91
    A Relevant Theory of Conditionals.Edwin D. Mares & André Fuhrmann - 1995 - Journal of Philosophical Logic 24 (6):645 - 665.
    In this paper we set out a semantics for relevant (counterfactual) conditionals. We combine the Routley-Meyer semantics for relevant logic with a semantics for conditionals based on selection functions. The resulting models characterize a family of conditional logics free from fallacies of relevance, in particular counternecessities and conditionals with necessary consequents receive a non-trivial treatment.
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  31. Paraconsistent Probability Theory and Paraconsistent Bayesianism.Edwin Mares - 1997 - Logique Et Analyse 160:375-84.
     
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  32.  14
    The Semantics Ofr.Edwin D. Mares & Robert K. Meyer - 1993 - Journal of Philosophical Logic 22 (1):95 - 110.
    The Logic R4 is obtained by adding the axiom □(A v B) → (◇A v □B) to the modal relevant logic NR. We produce a model theory for this logic and show completeness. We also show that there is a natural embedding of a Kripke model for S4 in each R4 model structure.
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  33. Relevant Logic, Probabilistic Information, and Conditionals.Edwin Mares - 2006 - Logique Et Analyse 49:399-411.
     
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  34.  57
    “Four-Valued” Semantics for the Relevant Logic R.Edwin D. Mares - 2004 - Journal of Philosophical Logic 33 (3):327-341.
    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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  35.  17
    Even Dialetheists Should Hate Contradictions.Edwin D. Mares - 2000 - Australasian Journal of Philosophy 78 (4):503 – 516.
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  36.  76
    Why We Need a Relevant Theory of Conditionals.Edwin D. Mares - 1994 - Topoi 13 (1):31-36.
    This paper presents ConR (Conditional R), a logic of conditionals based on Anderson and Belnap''s system R. A Routley-Meyer-style semantics for ConR is given for the system (the completeness of ConR over this semantics is proved in E. Mares and A. Fuhrmann, A Relevant Theory of Conditionals (unpublished MS)). Moreover, it is argued that adopting a relevant theory of conditionals will improve certain theories that utilize conditionals, i.e. Lewis'' theory of causation, Lewis'' dyadic deontic logic, and Chellas'' dyadic deontic logic.
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  37.  4
    The Semantics of R4.Edwin D. Mares & Robert K. Meyer - 1993 - Journal of Philosophical Logic 22 (1):95-110.
    The Logic R4 is obtained by adding the axiom □ → to the modal relevant logic NR. We produce a model theory for this logic and show completeness. We also show that there is a natural embedding of a Kripke model for S4 in each R4 model structure.
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  38.  7
    An Informational Interpretation of Weak Relevant Logic and Relevant Property Theory.Edwin Mares - forthcoming - Synthese:1-23.
    This paper extends the theory of situated inference from Mares to treat two weak relevant logics, B and DJ. These logics are interesting because they can be used as bases for consistent naïve theories, such as naïve set theory. The concepts of a situation and of information that are employed by the theory of situated inference are used to justify various aspects of these logics and to give an interpretation of the notion of set that is represented in the naïve (...)
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  39.  54
    Special-Issue Book Review.Edwin D. Mares - 1996 - Philosophia Mathematica 4 (2):198-202.
  40.  51
    Relevant Logic and the Philosophy of Mathematics.Edwin Mares - 2012 - Philosophy Compass 7 (7):481-494.
    This paper sets out three programmes that attempt to use relevant logic as the basis for a philosophy of mathematics. Although these three programmes do not exhaust the possible approaches to mathematics through relevant logic, they are fairly representative of the current state of the field. The three programmes are compared and their relative strengths and weaknesses set out. At the end of the paper I examine the consequences of adopting each programme for the realist debate about mathematical objects.
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  41.  38
    Completeness Results for Some Two-Dimensional Logics of Actuality.David R. Gilbert & Edwin D. Mares - 2012 - Review of Symbolic Logic 5 (2):239-258.
    We provide a Hilbert-style axiomatization of the logic of , as well as a two-dimensional semantics with respect to which our logics are sound and complete. Our completeness results are quite general, pertaining to all such actuality logics that extend a normal and canonical modal basis. We also show that our logics have the strong finite model property and permit straightforward first-order extensions.
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  42.  31
    Andersonian deontic logic.Edwin D. Mares - 1992 - Theoria 58 (1):1-2.
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  43. Semantics of Entailment 0.Robert K. Meyer & Edwin D. Mares - 1993 - In Peter Schroeder-Heister & Kosta Dosen (eds.), Substructural Logics. Oxford Science Publications. pp. 239-258.
  44.  49
    On S.André Fuhrmann & Edwin D. Mares - 1994 - Studia Logica 53 (1):75 - 91.
    The sentential logic S extends classical logic by an implication-like connective. The logic was first presented by Chellas as the smallest system modelled by contraining the Stalnaker-Lewis semantics for counterfactual conditionals such that the conditional is effectively evaluated as in the ternary relations semantics for relevant logics. The resulting logic occupies a key position among modal and substructural logics. We prove completeness results and study conditions for proceeding from one family of logics to another.
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  45. Halldén-Completeness and Modal Relevant Logic.Edwin Mares - 2003 - Logique Et Analyse 46.
  46.  22
    Guest Editors' Introduction.Koji Tanaka, Francesco Berto, Edwin Mares & Francesco Paoli - 2010 - Logic and Logical Philosophy 19 (1-2):5-6.
    A logic is said to be paraconsistent if it doesn’t license you to infer everything from a contradiction. To be precise, let |= be a relation of logical consequence. We call |= explosive if it validates the inference rule: {A,¬A} |= B for every A and B. Classical logic and most other standard logics, including intuitionist logic, are explosive. Instead of licensing you to infer everything from a contradiction, paraconsistent logic allows you to sensibly deal with the contradiction.
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  47.  10
    Advances in Modal Logic, Volume 1, Edited by Kracht Marcus, de Rijke Maarten, Wansing Heinrich, and Zakharyaschev Michael, CSLI Lecture Notes, No. 87, Center for the Study of Language and Information, Stanford 1998, Also Distributed by Cambridge University Press, New York, Xvi+ 392 Pp. [REVIEW]Edwin D. Mares - 2002 - Bulletin of Symbolic Logic 8 (1):95-97.
  48.  10
    Review: Marcus Kracht, Maarten de Rijke, Heinrich Wansing, Michael Zakharyaschev, Advances in Modal Logic. [REVIEW]Edwin D. Mares - 2002 - Bulletin of Symbolic Logic 8 (1):95-97.
  49.  15
    The Fact Semantics for Ramified Type Theory and the Axiom of Reducibility.Edwin D. Mares - 2007 - Notre Dame Journal of Formal Logic 48 (2):237-251.
    This paper uses an atomistic ontology of universals, individuals, and facts to provide a semantics for ramified type theory. It is shown that with some natural constraints on the sort of universals and facts admitted into a model, the axiom of reducibility is made valid.
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  50.  9
    The Incompleteness of RGL.Edwin D. Mares - 2000 - Studia Logica 65 (3):315-322.
    RGLis a version of the modal logic GLbased on the relevant logic R. It is shown that the class of RKframes that verify all theorems of RGLalso verify a scheme that we call (!). If RGLhas (!) as a theorem, however, it is not a relevant logic. I go on to show that not all instances of (!) are theorems of RGL, hence this logic is not complete over any class of RKframes.
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