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We prove completeness of the propositional modal logic S4 for the measure algebra based on the Lebesgue-measurable subsets of the unit interval, [0, 1]. In recent talks, Dana Scott introduced a new measure-based semantics for the standard propositional modal language with Boolean connectives and necessity and possibility operators, and ♦. Propositional(More)
This paper explores the connection between fractal geometry and topological modal logic. In the early 1940’s, Tarski showed that the modal logic S4 can be interpreted in topological spaces. Since then, many interesting completeness results in the topological semantics have come to light, and renewed interest in this semantics can be seen in such recent(More)
xxx Working notes. Three main things remain to do. (1) Either include Tamar’s argument [now in separate document] for Theorem 5, or replace by some better construction for worst-case upper bound. (2) Put in the average-case lower bound calculus calculations needed in section 6. (3) General version of the worst-case lower bound method in section 7.3. A(More)
Consider a network linking the points of a rate-1 Poisson point process on the plane. Write ! (s) for the minimum possible mean length per unit area of such a network, subject to the constraint that the route-length between every pair of points is at most s times the Euclidean distance. We give upper and lower bounds on the function ! (s), and on the(More)
Dynamic Epistemic Logic (DEL) is an influential logical framework for reasoning about the dynamics of beliefs and knowledge. It has been related to older and more established logical frameworks but, despite these connections, DEL remains, arguably, a rather isolated logic in the vast realm of non-classical logics and modal logics. This is problematic if(More)