• 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
  •  46
  •  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.
  •  44
    Shehtman 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
  •  13
    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 $\mathbf{H}\pi +$ 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.
  •  14
    Editorial Introduction
    Journal of Philosophical Logic 39 (4): 341-344. 2010.
  •  92
    Comparing fixed-point and revision theories of truth
    Journal 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