Speaker: Adam Bjorndahl
Date and Time: Thursday, June 4th 2020, 16:30-18:00, Amsterdam time.
In standard possible worlds style semantics for modal logics, a model consists in a set of worlds W together with some additional structure (e.g., a relation, a topology, a (set of) function(s), etc.). And a formula is defined to be valid in such a model if it is true at each and every world in W. In this talk, we consider the idea of relaxing this definition of validity: instead of requiring truth at all worlds in W, what happens if we only ask for truth at “almost all” worlds? Of course, this depends on just what we mean by “almost all”. Natural closure conditions on the corresponding notion of “almost-validity” yield some constraints, but of course do not determine a unique definition of “almost all”. On the other hand, well-known topological and measure-theoretic notions of “large” sets (and, dually, “negligible” sets) provide appealing candidates for making this notion precise; each determines a corresponding class of “almost-valid” formulas, with some surprising and familiar axiomatizations to explore.