-
Axiomatizing the next-interior fragment of dynamic topological logicBulletin of Symbolic Logic 3 376-377. 1997.
-
32The Gupta-Belnap systems ${\rm S}^\#$ and ${\rm S}^*$ are not axiomatisableNotre Dame Journal of Formal Logic 34 (4): 583-596. 1993.
-
30The modal logic of continuous functions on cantor spaceArchive for Mathematical Logic 45 (8): 1021-1032. 2006.Let $\mathcal{L}$ be a propositional language with standard Boolean connectives plus two modalities: an S4-ish topological modality $\square$ and a temporal modality $\bigcirc$ , understood as ‘next’. We extend the topological semantic for S4 to a semantics for the language $\mathcal{L}$ by interpreting $\mathcal{L}$ in dynamic topological systems, i.e. ordered pairs $\langle X, f\rangle$ , where X is a topological space and f is a continuous function on X. Artemov, Davoren and Nerode have axiom…Read more
-
72Quantifying over propositions in relevance logic: nonaxiomatisability of primary interpretations of ∀ p_ and ∃ _pJournal of Symbolic Logic 58 (1): 334-349. 1993.A typical approach to semantics for relevance (and other) logics: specify a class of algebraic structures and take amodelto be one of these structures, α, together with some function or relation which associates with every formulaAa subset ofα. (This is the approach of, among others, Urquhart, Routley and Meyer and Fine.) In some cases there are restrictions on the class of subsets of α with which a formula can be associated: for example, in the semantics of Routley and Meyer [1973], a formula c…Read more
-
36John Woods. Paradox and paraconsistency: Conflict resolution in the abstract sciences, Cambridge University Press, Cambridge, New York, 2003, xviii+ 362 pp (review)Bulletin of Symbolic Logic 10 (1): 116-118. 2004.
-
82Dunn’s relevant predication, real properties and identityErkenntnis 47 (1): 37-65. 1997.We critically investigate and refine Dunn's relevant predication, his formalisation of the notion of a real property. We argue that Dunn's original dialectical moves presuppose some interpretation of relevant identity, though none is given. We then re-motivate the proposal in a broader context, considering the prospects for a classical formalisation of real properties, particularly of Geach's implicit distinction between real and ''Cambridge'' properties. After arguing against these prospects, w…Read more
-
63The logical structure of linguistic commitment I: Four systems of non-relevant commitment entailment (review)Journal of Philosophical Logic 23 (4). 1994.
-
49Shehtman introduced bimodal logics of the products of Kripke frames, thereby introducing frame products of unimodal logics. Van Benthem, Bezhanishvili, ten Cate and Sarenac generalize this idea to the bimodal logics of the products of topological spaces, thereby introducing topological products of unimodal logics. In particular, they show that the topological product of S4 and S4 is S4 ⊕ S4, i.e., the fusion of S4 and S4: this logic is strictly weaker than the frame product S4 × S4. Indeed, van …Read more
-
13On the Complexity of Propositional Quantification in Intuitionistic LogicJournal of Symbolic Logic 62 (2): 529-544. 1997.We define a propositionally quantified intuitionistic logic $\mathbf{H}\pi +$ by a natural extension of Kripke's semantics for propositional intutionistic logic. We then show that $\mathbf{H}\pi+$ is recursively isomorphic to full second order classical logic. $\mathbf{H}\pi+$ is the intuitionistic analogue of the modal systems $\mathbf{S}5\pi +, \mathbf{S}4\pi +, \mathbf{S}4.2\pi +, \mathbf{K}4\pi +, \mathbf{T}\pi +, \mathbf{K}\pi +$ and $\mathbf{B}\pi +$, studied by Fine.
-
118Comparing fixed-point and revision theories of truthJournal of Philosophical Logic 38 (4): 363-403. 2009.In response to the liar’s paradox, Kripke developed the fixed-point semantics for languages expressing their own truth concepts. Kripke’s work suggests a number of related fixed-point theories of truth for such languages. Gupta and Belnap develop their revision theory of truth in contrast to the fixed-point theories. The current paper considers three natural ways to compare the various resulting theories of truth, and establishes the resulting relationships among these theories. The point is to …Read more
-
164Relevant identityJournal of Philosophical Logic 28 (2): 199-222. 1999.We begin to fill a lacuna in the relevance logic enterprise by providing a foundational analysis of identity in relevance logic. We consider rival interpretations of identity in this context, settling on the relevant indiscernibility interpretation, an interpretation related to Dunn's relevant predication project. We propose a general test for the stability of an axiomatisation of identity, relative to this interpretation, and we put various axiomatisations to this test. We fill our discussion o…Read more
Toronto, Ontario, Canada
Areas of Specialization
1 more
Modal Logic |
Quantified Modal Logic |
Semantics for Modal Logic |
Intuitionistic Logic |
Relevance Logic |
Liar Paradox |