
15The GuptαBelnαp Systems S and S* are not AxiomatisableNotre Dame Journal of Formal Logic 34 (4): 583596. 1993.

63On the complexity of propositional quantification in intuitionistic logicJournal of Symbolic Logic 62 (2): 529544. 1997.We define a propositionally quantified intuitionistic logic Hπ + by a natural extension of Kripke's semantics for propositional intutionistic logic. We then show that Hπ+ is recursively isomorphic to full second order classical logic. Hπ+ is the intuitionistic analogue of the modal systems S5π +, S4π +, S4.2π +, K4π +, Tπ +, Kπ + and Bπ +, studied by Fine

44Dynamic topological S5Annals of Pure and Applied Logic 160 (1): 96116. 2009.The topological semantics for modal logic interprets a standard modal propositional language in topological spaces rather than Kripke frames: the most general logic of topological spaces becomes S4. But other modal logics can be given a topological semantics by restricting attention to subclasses of topological spaces: in particular, S5 is logic of the class of almost discrete topological spaces, and also of trivial topological spaces. Dynamic Topological Logic interprets a modal language enrich…Read more

Axiomatizing the nextinterior fragment of dynamic topological logicBulletin of Symbolic Logic 3 376377. 1997.

25The GuptaBelnap systems ${\rm S}^\#$ and ${\rm S}^*$ are not axiomatisableNotre Dame Journal of Formal Logic 34 (4): 583596. 1993.

22The modal logic of continuous functions on cantor spaceArchive for Mathematical Logic 45 (8): 10211032. 2006.Let $\mathcal{L}$ be a propositional language with standard Boolean connectives plus two modalities: an S4ish 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

52Quantifying Over Propositions in Relevance Logic: Nonaxiomatisability of Primary Interpretations of $\forall p$ and $\exists p$Journal of Symbolic Logic 58 (1): 334349. 1993.

30John 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): 116118. 2004.

62Dunn's relevant predication, real properties and identityErkenntnis 47 (1): 3765. 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 remotivate 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

46The logical structure of linguistic commitment I: Four systems of nonrelevant commitment entailment (review)Journal of Philosophical Logic 23 (4). 1994.
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Areas of Specialization
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Modal Logic 
Quantified Modal Logic 
Semantics for Modal Logic 
Intuitionistic Logic 
Relevance Logic 
Liar Paradox 