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Some apparently valid arguments crucially rely on context change. To take a kind of example first discussed by Frege, ‘Tomorrow, it’ll be sunny’ taken on a day seems to entail ‘Today, it’s sunny’ taken on the next day, but the first sentence taken on a day sadly does not seem to entail the second sentence taken on the second next day. Mid-argument context change has not been accounted for by the tradition that has extensively studied the distinctive logical properties of (...) |
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To sentential language we add an operator C to be read as ‘it changes that…’ and present an axiomatic system in the frame of classical logic to catch some meaning of the term ‘change’. A typical axiom is e.g.: CA implies, a basic rule is: from A it may be inferred (theorems do not change). So this system is not regular. On the semantic level we introduce stages (of the development of some world, of some agents’ convictions or of some (...) |
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In this paper the class of minimal models C ZI for Kiczuk's system of physical change ZI is provided and soundness and completeness proofs of ZI with respect to these models are given. ZI logic consists of propositional logic von Wright's And Then and six specific axioms characterizing the meaning of unary propositional operator "Zm", read "there is a change in the fact that". ZI is intended to be a logic which provides a formal account for describing two kinds of (...) |
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The paper deals with the problem of axiomatizing a system T1 of discrete tense logic, where one thinks of time as the set Z of all the integers together with the operations +1 ("immediate successor") and-1 ("immediate predecessor"). T1 is like the Segerberg-Sundholm system WI in working with so-called infinitary inference ruldes; on the other hand, it differs from W I with respect to (i) proof-theoretical setting, (ii) presence of past tense operators and a "now" operator, and, most importantly, with (...) |
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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 axiomatized a logic S4C, and have shown (...) |
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Dynamic topological logic provides a context for studying the confluence of the topological semantics for S4, topological dynamics, and temporal logic. The topological semantics for S4 is based on topological spaces rather than Kripke frames. In this semantics, □ is interpreted as topological interior. Thus S4 can be understood as the logic of topological spaces, and □ can be understood as a topological modality. Topological dynamics studies the asymptotic properties of continuous maps on topological spaces. Let a dynamic topological system (...) |
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An explanatorily powerful approach to the modal dimension of knowledge is Robert Nozick’s idea that knowledge stands in a tracking relation to the world. However, pinning down a specific modal condition has proved elusive. In this paper, I offer a diagnosis and a positive proposal. The root of the problem, I argue, is the unquestioned assumption that tracking is a matter of directly preserving conformity between what is believed and what is the case in certain possible worlds. My proposal is (...) |
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We argue that the view that we misperceive time as passing is self-undermining. |
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Dynamic topological logic provides a context for studying the confluence of the topological semantics for S4, topological dynamics, and temporal logic. The topological semantics for S4 is based on topological spaces rather than Kripke frames. In this semantics, is interpreted as topological interior. Thus S4 can be understood as the logic of topological spaces, and can be understood as a topological modality. Topological dynamics studies the asymptotic properties of continuous maps on topological spaces. Let a dynamic topological system be a (...) |
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