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  1. Jort M. Bergfeld, Kohei Kishida, Joshua Sack & Shengyang Zhong (forthcoming). Duality for the Logic of Quantum Actions. Studia Logica:1-25.
    In this paper we show a duality between two approaches to represent quantum structures abstractly and to model the logic and dynamics therein. One approach puts forward a “quantum dynamic frame” :2267–2282, 2005), a labelled transition system whose transition relations are intended to represent projections and unitaries on a Hilbert space. The other approach considers a “Piron lattice” , which characterizes the algebra of closed linear subspaces of a Hilbert space. We define categories of these two sorts of structures and (...)
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  2. Tomasz Placek, Nuel Belnap & Kohei Kishida (2013). On Topological Issues of Indeterminism. Erkenntnis:1-34.
    Indeterminism, understood as a notion that an event may be continued in a few alternative ways, invokes the question what a region of chanciness looks like. We concern ourselves with its topological and spatiotemporal aspects, abstracting from the nature or mechanism of chancy processes. We first argue that the question arises in Montague-Lewis-Earman conceptualization of indeterminism as well as in the branching tradition of Prior, Thomason and Belnap. As the resources of the former school are not rich enough to study (...)
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  3. Thomas Müller, Nuel Belnap & Kohei Kishida (2008). Funny Business in Branching Space-Times: Infinite Modal Correlations. Synthese 164 (1):141 - 159.
    The theory of branching space-times is designed as a rigorous framework for modelling indeterminism in a relativistically sound way. In that framework there is room for “funny business”, i.e., modal correlations such as occur through quantum-mechanical entanglement. This paper extends previous work by Belnap on notions of “funny business”. We provide two generalized definitions of “funny business”. Combinatorial funny business can be characterized as “absence of prima facie consistent scenarios”, while explanatory funny business characterizes situations in which no localized explanation (...)
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  4. Steve Awodey & Kohei Kishida, Topology and Modality: The Topological Interpretation of First-Order Modal Logic.
    As McKinsey and Tarksi showed, the Stone representation theorem for Boolean algebras extends to algebras with operators to give topological semantics for (classical) propositional modal logic, in which the "necessity" operation is modeled by taking the interior of an arbitrary subset of a topological space. in this paper the topological interpretation is extended in a natural way to arbitrary theories of full first-order logic. The resulting system of S4 first-order modal logic is complete with respect to such topological semantics.
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