Modal Logic, measure algebras, and ‘gunky’ space

Tamar Lando

6 Dec 2013, 2pm-4pm, Oak Hall 408

Long before Kripke semantics became standard in modal logic, Tarski showed us that the basic propositional modal language can be interpreted in topological spaces. In Tarski’s semantics for the modal logic S4, each propositional variable is evaluated to an arbitrary subset of a fixed topological space. I develop a closely related, measure theoretic semantics for modal logics, in which modal formulas are interpreted in the Lebesgue measure algebra, or algebra of Borel subsets of the real interval [0,1], modulo sets of measure zero. This semantics was introduced by Dana Scott in the last several years. I discuss some of my own completeness results, and a philosophical application to the way we understand physical space.