•  10
    The logic of entailment and its history
    [Cambridge University Press]. 2024.
    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.
  •  9
    C. I. Lewis’s Intensional Semantics
    Notre Dame Journal of Formal Logic 64 (3): 329-352. 2023.
    This paper begins with a discussion of C. I. Lewis’s theory of meaning in his book, An Analysis of Knowledge and Valuation (1946) and his pragmatic theory of analyticity and necessity. I bring this theories together with some remarks that he makes in an appendix to the second edition of Symbolic Logic to construct an algebraic semantics for his logics S2 and S3. These logics and their semantics are compared and evaluated with regard to how well they implement Lewis’s theories of meaning and anal…Read more
  •  1967
    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. Th…Read more
  •  6
    Alasdair Urquhart on Nonclassical and Algebraic Logic and Complexity of Proofs (edited book)
    with Ivo Düntsch
    Springer Verlag. 2021.
    This book is dedicated to the work of Alasdair Urquhart. The book starts out with an introduction to and an overview of Urquhart’s work, and an autobiographical essay by Urquhart. This introductory section is followed by papers on algebraic logic and lattice theory, papers on the complexity of proofs, and papers on philosophical logic and history of logic. The final section of the book contains a response to the papers by Urquhart. Alasdair Urquhart has made extremely important contributions to …Read more
  •  1
    Relevance Logic
    In Dale Jacquette (ed.), A Companion to Philosophical Logic, Blackwell. 2006.
    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.
  •  209
    Logical Consequence and the Paradoxes
    Journal of Philosophical Logic 43 (2-3): 439-469. 2014.
    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…Read more
  •  320
    On the Ternary Relation and Conditionality
    with Jc Beall, Ross T. Brady, J. Michael Dunn, A. P. Hazen, Robert K. Meyer, Graham Priest, Greg Restall, David Ripley, John Slaney, and Richard Sylvan
    Journal of Philosophical Logic 41 (3). 2012.
    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 o…Read more
  •  52
    Guest editors' introduction
    Logic and Logical Philosophy 19 (1-2): 5-6. 2010.
    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
  •  6
    Relevance Domains and the Philosophy of Science
    In Ofer Arieli & Anna Zamansky (eds.), Arnon Avron on Semantics and Proof Theory of Non-Classical Logics, Springer Verlag. pp. 223-247. 2021.
    This paper uses Avron’s algebraic semantics for the logic RMI to model some ideas in the philosophy of science. Avron’s relevant disjunctive structures are each partitioned into relevance domains. Each relevance domain is a boolean algebra. I employ this semantics to act as a formal framework to represent what Nancy Cartwright calls the “dappled world”. On the dappled world hypothesis, local scientific theories each represent restricted aspects and regions of the universe. I use relevance domain…Read more
  •  206
    This important collection of essays details some of the more significant methodological and philosophical differences that have separated the two traditions, as ...
  •  5
  • Semantic Dialetheism
    In Graham Priest, J. C. Beall & Bradley Armour-Garb (eds.), The Law of Non-Contradiction: New Philosophical Essays, Clarendon Press. 2006.
    The doctrine of semantic dialetheism is set out and contrasted with metaphysical dialetheism. We find that there is a lot to be said in favour of semantic dialetheism. Semantic dlaietheism is given credence by the doctrine of partially defined predicates. To make sense of a partially defined predicate, Tappenden and Soames suggest that the seman tics of predicates should be given in terms of a set of conditions under which the predicate can be applied to things and a set of conditions under whic…Read more
  •  7
    From Iff to Is: Some New Thoughts on Identity in Relevant Logics
    In Can Başkent & Thomas Macaulay Ferguson (eds.), Graham Priest on Dialetheism and Paraconsistency, Springer Verlag. pp. 343-363. 2019.
    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.
  •  10
    Introduction to Special Issue in Honour of Robert Goldblatt
    Australasian Journal of Logic 17 (2): 81. 2020.
    This is a brief introduction to the special issue.
  •  9
    Advances in Modal Logic
    Bulletin of Symbolic Logic 8 (1): 95-97. 2002.
  •  9
    A General Semantics for Quantified Modal Logic
    with Robert Goldblatt
    In Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic, Csli Publications. pp. 227-246. 1998.
    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.
  •  18
    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…Read more
  •  7
    A General Semantic for Quantified Modal Logic
    with Robert Goldblatt
    In Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic, Csli Publications. pp. 227-246. 1998.
    In "An Alternative Semantics for Quantified Relevant Logic" (JSL 71 (2006)) we developed a semantics for quantified relevant logic that uses general frames. In this paper, we adapt that model theory to treat quantified modal logics, giving a complete semantics to the quantified extensions, both with and without the Barcan formula, of every proposi- tional modal logic S. If S is canonical our models are based on propositional frames that validate S. We employ frames in which not every set of worl…Read more
  •  20
    The Semantics of R4
    with Robert K. Meyer
    Journal of Philosophical Logic 22 (1): 95-110. 1993.
    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.
  •  2
    Truth and Meaning (review)
    Dialogue 39 (2): 412-413. 2000.
    I have found in teaching courses on philosophy of language that one can concentrate either on the problem of reference or the problem of meaning, not on both and still teach a coherent course. Kenneth Taylor’s Truth and Meaning provides further confirmation of this view. It is a very good textbook for a course on the theory of meaning and attempts to say relatively little about reference. It is clear and well written. It presents a wide range of rather difficult material perhaps as clearly and e…Read more
  • Semantics of Entailment 0
    with Robert K. Meyer
    In Peter Schroeder-Heister & Kosta Dosen (eds.), Substructural Logics, Oxford Science Publications. pp. 239-258. 1993.
  •  88
    Relevant Logic: A Philosophical Interpretation
    Cambridge University Press. 2004.
    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…Read more
  •  3
    Semantic Dialetheism
    In Graham Priest, J. C. Beall & Bradley Armour-Garb (eds.), The Law of Non-Contradiction, Clarendon Press. 2004.
    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…Read more
  •  6
    Relevant Logics
    with Robert K. Meyer
    In Lou Goble (ed.), The Blackwell Guide to Philosophical Logic, Blackwell. 2017.
    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 cle…Read more
  •  20
    Information, Negation, and Paraconsistency
    In Francesco Berto, Edwin Mares, Koji Tanaka & Francesco Paoli (eds.), Paraconsistency: Logic and Applications, Springer. pp. 43--55. 2013.