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During the second half of the 19th century, in the field of physiological optics, there was a strong controversy between Hermann von Helmholtz and Ewald Hering. This controversy has been usually characterized as “empiricism” vs. “nativism”. In the field of physiology of visual perception, several subjects demanded attention, among them, color vision. Helmholtz and Hering suggested different theories for the physiological correlate of color sensation and different color spaces to give an account of the relationships between colors. In this article, (...) I will argue that the controversy between the two authors could be understood as differences between styles of reasoning, and these different styles express different presuppositions. More specifically, I want to suggest that the disagreements could be linked to the discussions on how vital phenomena should be studied. (shrink)

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As they are conventionally formulated, Boolean games assume that players make their choices in ignorance of the choices being made by other players – they are games of simultaneous moves. For many settings, this is clearly unrealistic. In this paper, we show how Boolean games can be enriched by dependency graphs which explicitly represent the informational dependencies between variables in a game. More precisely, dependency graphs play two roles. First, when we say that variable x depends on variable y, then (...) we mean that when a strategy assigns a value to variable x, it can be informed by the value that has been assigned to y. Second, and as a consequence of the first property, they capture a richer and more plausible model of concurrency than the simultaneous-action model implicit in conventional Boolean games. Dependency graphs implicitly define a partial ordering of the run-time events in a game: if x is dependent on y, then the assignment of a value to y must precede the assignment of a value to x; if x and y are independent, however, then we can say nothing about the ordering of assignments to these variables—the assignments may occur concurrently. We refer to Boolean games with dependency graphs as partial-order Boolean games. After motivating and presenting the partial-order Boolean games model, we explore its properties. We show that while some problems associated with our new games have the same complexity as in conventional Boolean games, for others the complexity blows up dramatically. We also show that the concurrency in partial-order Boolean games can be modelled using a closure-operator semantics, and conclude by considering the relationship of our model to Independence-Friendly logic. (shrink)

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Neil Tennant’s core logic is a type of bilateralist natural deduction system based on proofs and refutations. We present a proof system for propositional core logic, explain its connections to bilateralism, and explore the possibility of using it as a type theory, in the same kind of way intuitionistic logic is often used as a type theory. Our proof system is not Tennant’s own, but it is very closely related, and determines the same consequence relation. The difference, however, matters for (...) our purposes, and we discuss this. We then turn to the question of strong normalization, showing that although Tennant’s proof system for core logic is not strongly normalizing, our modified system is. (shrink)

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Review by: Julian Gutierrez The Bulletin of Symbolic Logic, Volume 19, Issue 1, Page 108-110, March 2013.

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