•  15
    The Guptα-Belnαp Systems S and S* are not Axiomatisable
    Notre Dame Journal of Formal Logic 34 (4): 583-596. 1993.
  •  63
    On the complexity of propositional quantification in intuitionistic logic
    Journal of Symbolic Logic 62 (2): 529-544. 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
  •  44
    Dynamic topological S5
    Annals of Pure and Applied Logic 160 (1): 96-116. 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 next-interior fragment of dynamic topological logic
    with Grigori Mints and V. Rybakov
    Bulletin of Symbolic Logic 3 376-377. 1997.
  •  22
    The modal logic of continuous functions on cantor space
    Archive 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
  •  62
    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
  •  20
    Montréal, Québec, Canada May 17–21, 2006
    with Jeremy Avigad, Sy Friedman, Akihiro Kanamori, Elisabeth Bouscaren, Claude Laflamme, Antonio Montalbán, Justin Moore, and Helmut Schwichtenberg
    Bulletin of Symbolic Logic 13 (1). 2007.
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