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Switch to: References
Citations of:
A Proof Of Topological Completeness For S4 In
Annals of Pure and Applied Logic 133 (1-3):231-245 (2005)
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This chapter presents a new semantics for inductive empirical knowledge. The epistemic agent is represented concretely as a learner who processes new inputs through time and who forms new beliefs from those inputs by means of a concrete, computable learning program. The agent’s belief state is represented hyper-intensionally as a set of time-indexed sentences. Knowledge is interpreted as avoidance of error in the limit and as having converged to true belief from the present time onward. Familiar topics are re-examined within (...) |
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This paper brings together Dana Scottʼs measure-based semantics for the propositional modal logic S4, and recent work in Dynamic Topological Logic. In a series of recent talks, Scott showed that the language of S4 can be interpreted in the Lebesgue measure algebra, M, or algebra of Borel subsets of the real interval, [0,1], modulo sets of measure zero. Conjunctions, disjunctions and negations are interpreted via the Boolean structure of the algebra, and we add an interior operator on M that interprets (...) |
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This book offers a state-of-the-art introduction to the basic techniques and results of neighborhood semantics for modal logic. In addition to presenting the relevant technical background, it highlights both the pitfalls and potential uses of neighborhood models – an interesting class of mathematical structures that were originally introduced to provide a semantics for weak systems of modal logic. In addition, the book discusses a broad range of topics, including standard modal logic results ; bisimulations for neighborhood models and other model-theoretic (...) |
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In the topological semantics for modal logic, S4 is well-known to be complete for the rational line, for the real line, and for Cantor space: these are special cases of S4’s completeness for any dense-in-itself metric space. The construction used to prove completeness can be slightly amended to show that S4 is not only complete, but also strongly complete, for the rational line. But no similarly easy amendment is available for the real line or for Cantor space and the question (...) |
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Justification Logic is a family of epistemic logical systems obtained from modal logics of knowledge by adding a new type of formula t:F, which is read t is a justification for F. The principal epistemic modal logic S4 includes Tarski’s well-known topological interpretation, according to which the modality 2X is read the Interior of X in a topological space (the topological equivalent of the ‘knowable part of X’). In this paper, we extend Tarski’s topological interpretation from S4 to Justification Logic (...) |
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It is a landmark theorem of McKinsey and Tarski that if we interpret modal diamond as closure, then \ is the logic of any dense-in-itself metrizable space. The McKinsey–Tarski Theorem relies heavily on a metric that gives rise to the topology. We give a new and more topological proof of the theorem, utilizing Bing’s Metrization Theorem. |
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