Works by Edwin Mares
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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 (...) presenting some interesting open problems. It will be of interest to a range of readers including advanced students of logic, philosophical and mathematical logicians, and computer scientists. (shrink)
- 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, (...) and can be cleared up by adopting a particular substructural logic in place of classical logic. We then argue that our perspective can be justified via an informational semantics of contraction-free substructural logics. (shrink)
- On the Ternary Relation and Conditionality.Jc Beall,Ross T. Brady,J. Michael Dunn,A. P. Hazen,Edwin D. 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 (...) a general conception of conditionality that may unify the three given conceptions. (shrink)
- 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.
- 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 (...) B) -> (A V for all xB). with x not free in A. Validity of EC requires an additional model condition involving the boolean difference of propositions. A QR-model falsifying EC is constructed by forming the disjoint union of two natural arithmetical structures in which negation is interpreted by the minus operation. (shrink)
- Realism and Anti-Realism.Stuart Brock &Edwin David 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 (...) sense objective and mind-independent. The authors carefully set out and explain the different realist and anti-realist positions and arguments that occur in five key domains: science, ethics, mathematics, modality and fictional objects. For each area the authors examine the various styles of argument in support of and against realism and anti-realism, show how these different positions and arguments arise in very different domains, evaluate their success within these fields, and draw general conclusions about these assorted strategies. Error theory, fictionalism, non-cognitivism, relativism and response-dependence are taken as the most important positions in opposition to the realist and these are explored in depth. Suitable for advanced level undergraduates, the book offers readers a clear introduction to a subject central to much contemporary work in metaphysics, epistemology and philosophy of language. (shrink)
- Relevant Logics.Edwin D. Mares &Robert K. Meyer -2001 - In Lou Goble,The Blackwell Guide to Philosophical Logic. Malden, Mass.: Wiley-Blackwell. pp. 280–308.Once upon a time, modal logic was castigated because it ‘had no semantics.’ Kripke, Hintikka, Kanger, and others changed all that. In a similar way, when Relevant Logic was introduced by Anderson and Belnap, it too was castigated for ‘having no semantics.’ The present overview marks a culmination of that effort. The semantic approach described here brings together a number of hitherto disparate efforts to set out formal systems for logics of relevant implication and entailment. It also makes clear (despite (...) some of our hopes and utterances) that the One True Logic does not exist. This is as true for relevant logics as Kripke et al., showed it to be for modal logics. In both cases, subtle (and not so subtle) variations on semantical postulates produce different logics in the same family. The question of which semantical postulates are correct makes no sense without further context, i.e., the questioner needs to answer the question: Correct for what? The question that does remain is: What motivates the relevant family of logics? And this is the question that is the main job for this chapter to investigate. (shrink)
- General information in relevant logic.Edwin D. Mares -2009 -Synthese 167 (2):343-362.This paper sets out a philosophical interpretation of the model theory of Mares and Goldblatt (The Journal of Symbolic Logic 71, 2006). This interpretation distinguishes between truth conditions and information conditions. Whereas the usual Tarskian truth condition holds for universally quantified statements, their information condition is quite different. The information condition utilizes general propositions . The present paper gives a philosophical explanation of general propositions and argues that these are needed to give an adequate theory of general information.
- Relevant logic and the theory of information.Edwin Mares -1996 -Synthese 109 (3):345 - 360.This paper provides an interpretation of the Routley-Meyer semantics for a weak negation-free relevant logic using Israel and Perry's theory of information. In particular, Routley and Meyer's ternary accessibility relation is given an interpretation in information-theoretic terms.
- Paraconsistency: Logic and Applications.Francesco Berto,Edwin Mares,Koji Tanaka &Francesco Paoli (eds.) -2012 - Dordrecht, Netherland: 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 (...) this situation. The book includes almost every major author currently working in the field. The papers are on the cutting edge of the literature some of which discuss current debates and others present important new ideas. The editors have avoided papers about technical details of paraconsistent logic, but instead concentrated upon works that discuss more 'big picture' ideas. Different treatments of paradoxes takes centre stage in many of the papers, but also there are several papers on how to interpret paraconistent logic and some on how it can be applied to philosophy of mathematics, the philosophy of language, and metaphysics. (shrink)
- 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.
- 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 (...) the nature of misinformation. A form of relevant logic—called "LOI" for "logic of objective information"—is presented and the relationship between the justification of its proof theory and the semantics is discussed. This relationship is rather reciprocal. Intuitive features of the logic are used to interpret and justify aspects of the model theory and intuitive aspects of the model theory are used to interpret and justify features of the logic. Information conditions are presented for the connectives and the way that they fit into the theory of information is discussed. (shrink)
- The logic of entailment and its history.Edwin Mares -2024 - [New York]: [Cambridge University Press].This book provides a new philosophical, semantical and historical analysis of and justification for the relevant logic of entailment. Its fresh and original perspective on the logic of entailment will be valuable for all who want to know more about the historical and philosophical origins of modern symbolic logic.No categories
- Introduction: Post-analytic and meta-continental philosophy.Jack Reynolds,James Chase,James Williams &Edwin Mares -2010 - In James Williams, Edwin Mares, James Chase & Jack Reynolds,Postanalytic and Metacontinental: Crossing Philosophical Divides. New York: 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'.
- (1 other version)Semantic Dialetheism.Edwin Mares -2004 - In Graham Priest, Jc Beall & Bradley P. Armour-Garb,The law of non-contradiction : new philosophical essays. New York: Oxford University Press. pp. 264–275.Approaches to paraconsistency can be arranged on a spectrum similar to the way in which approaches to vagueness are often understood. On the left are the metaphysical realists; those who think that there are real contradictory facts, that are mind and language independent. On the right are those who think that although we can have inconsistent beliefs and inconsistent theories — and we need a paraconsistent logic to deal with them — the world itself is perfectly consistent. In the middle (...) are the semantic dialetheists, who claim that there are true contradictions, but that these come about because of particular features of our use of language. This chapter outlines a particular version of semantic dialetheism based on a four-valued logic. It contends that although we need such a logic to deal with our current language, we could regiment our uses of predicates (and other expressions) to eliminate all true contradictions. (shrink)
- 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.
- 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)).
- Molinist Conditionals.Edwin Mares &Ken Perszyk -2011 - In Ken Perszyk,Molinism: The Contemporary Debate. Oxford, GB: Oxford University Press. pp. 96--117.
- Propositional function.Edwin Mares -2014 -Stanford Encyclopedia of Philosophy.
- Conditionals, probability, and nontriviality.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 (...) trivialize the semantics. (shrink)
- Informational Semantics as a Third Alternative?Patrick Allo &Edwin Mares -2011 -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 (...) of the premises. We show that this basic platitude can be used to characterise the extension of classical as well as non-classical consequence relations. The distinctive trait of an informational semantics is that truth-conditions are replaced by information-conditions. The latter leads to an inversion of the usual order of explanation: Considerations about logical discrimination (how finely propositions are individuated) are conceptually prior to considerations about deductive strength. Because this allows us to bypass considerations about truth, an informational semantics provides an attractive and metaphysically unencumbered account of logical consequence, non-classical logics, logical rivalry and pluralism about logical consequence. (shrink)
- 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.
- 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.
- 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.
- 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. -/- .
- An informational interpretation of weak relevant logic and relevant property theory.Edwin Mares -2017 -Synthese 199 (Suppl 3):547-569.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 (...) set theories that are based on them. (shrink)
- Postanalytic and Metacontinental: Crossing Philosophical Divides.James Williams,Edwin Mares,James Chase &Jack Reynolds (eds.) -2010 - New York: Continuum.This important collection of essays details some of the more significant methodological and philosophical differences that have separated the two traditions, as ...
- 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.
- (1 other version)Relevance Logic.Edwin D. Mares -2002 - In Dale Jacquette,A Companion to Philosophical Logic. Malden, MA, USA: Wiley-Blackwell. pp. 607–627.This chapter contains sections titled: Non‐Sequiturs are Bad The Real Use of Premises Implication From Proof Theory to Semantics Adding Conjunction The Problem of Disjunction Routley and Meyer's Ternary Relation Rules for Disjunction The Semantics of Negation Rules for Negation Disjunctive Syllogism Logics Stronger than R Logics Weaker than R Relevant Logics and Natural Language Conditionals Theory of Properties Summary.
- The Semantic Completeness Of Rk.Edwin Mares -1992 -Reports on Mathematical Logic:3-10.This paper extends the argument of Mares, ``Classically Complete Modal Relevant Logics'' Zeitschrift fur mathematische Logik und Grundlagen der Mathematik, to show that the system RK is complete over an Extension of the Routley-Meyer semantics.
- Belief Revision, Probabilism, and Logic Choice.Edwin Mares -2014 -Review of Symbolic Logic 7 (4):647-670.This paper presents a probabilist paraconsistent theory of belief revision. This theory is based on a very general theory of probability, that fits with a wide range of classical and nonclassical logics. The theory incorporates a version of Jeffrey conditionalisation as its method of updating. A Dutch book argument is given, and the theory is applied to the problem of choosing a logical system.
- “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.
- Paraconsistent probability theory and paraconsistent bayesianism.Edwin Mares -1997 -Logique Et Analyse 160:375-84.This paper presents a theory of probability based on the paraconsistent logic D4. The resulting probability functions are then used to define two sorts of Bayesian updating. One sort of updating merely uses the simple rule of conditionalisation. The other sort adds a wrinkle to the simple rule so that agents' beliefs become more consistent as well as more complete through updating.
- Semantics of Entailment 0.Robert K. Meyer &Edwin D. Mares -1993 - In Peter Joseph Schroeder-Heister & Kosta Došen,Substructural Logics. Oxford, England: Oxford University Press on Demand. pp. 239-258.
- Halldén-Completeness and Modal Relevant Logic.Edwin Mares -2003 -Logique Et Analyse 46.
- A General Semantics for Quantified Modal Logic.Robert Goldblatt &Edwin D. Mares -1998 - In Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev,Advances in Modal Logic. CSLI Publications. pp. 227-246.This paper uses an "admissible set semantics" to treat quantification in quantified modal logics. The truth condition for the universal quantifier states that a universally quantified statement (x)A(x) is true at a world w if and only if there is some proposition true at that world that entails every instance of A(x). It is shown that, for any canonical propositional modal logic the corresponding admissible set semantics characterises the quantified version of that modal logic.
- 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.
- 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 (...) over three versions of the semantics. We call the strongest of these logics DWE for Doing Well Enough. (shrink)
- Andersonian deontic logic.Edwin D. Mares -1992 -Theoria 58 (1):1-2.
- 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.
- Maxwell John (‘Max’) Cresswell, 1939–2024.Robert Goldblatt &Edwin Mares -forthcoming -Australasian Journal of Philosophy.No categories
- Logical Modalities from Aristotle to Carnap: The Story of Necessity.Adriane Rini,Edwin Mares &Max Cresswell (eds.) -2016 - New York: Cambridge University Press.Interest in the metaphysics and logic of possible worlds goes back at least as far as Aristotle, but few books address the history of these important concepts. This volume offers new essays on the theories about the logical modalities held by leading philosophers from Aristotle in ancient Greece to Rudolf Carnap in the twentieth century. The story begins with an illuminating discussion of Aristotle's views on the connection between logic and metaphysics, continues through the Stoic and mediaeval traditions, and then (...) moves to the early modern period with particular attention to Locke and Leibniz. The views of Kant, Peirce, C. I. Lewis and Carnap complete the volume. Many of the essays illuminate the connection between the historical figures studied, and recent or current work in the philosophy of modality. The result is a rich and wide-ranging picture of the history of the logical modalities. (shrink)
- 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.
- Boolean Conservative Extension Results for some Modal Relevant Logics.Edwin D. Mares &Koji Tanaka -2010 -Australasian Journal of Logic 8 (5):31-49.This paper shows that a collection of modal relevant logics are conservatively extended by the addition of Boolean negation.
- Curitorial Introduction: Hartry Field, ‘Properties, Propositions and Conditionals’.Edwin Mares -2020 -Australasian Philosophical Review 4 (2):105-111.
- Symmetry and Completeness in Relevant Epistemic Logic.Shawn Standefer &Edwin Mares -forthcoming -Journal of Philosophical Logic:1-22.In this paper, we provide an axiom system for the relevant logic of equivalence relation frames and prove completeness for it. This provides a partial answer to the longstanding open problem of axiomatizing frames for relevant modal logics where the modal accessibility relation is symmetric. Following this, we show that the logic enjoys Halldén completeness and that a related logic enjoys the disjunction property.
- 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.
- From Iff to Is: Some New Thoughts on Identity in Relevant Logics.Edwin Mares -2019 - In Can Başkent & Thomas Macaulay Ferguson,Graham Priest on Dialetheism and Paraconsistency. Cham, Switzerland: Springer Verlag. pp. 343-363.In this paper, I set out a semantics for identity in relevant logic that is based on an analogy between the biconditional and identity. This analogy supports the semantics that Priest has set out for identity in basic relevant logic and it motivates a version of the Routley–Meyer semantics in which identities can be viewed as constraints on the ternary relation that is used to treat implication.
- Relevant logic, probabilistic information, and conditionals.Edwin Mares -2006 -Logique Et Analyse 49:399-411.
- 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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James Chase
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Jonathan Ichikawa
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Øystein Linnebo
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