Three Etudes On Logical Dynamics And The Program Of Natural Logic

This chapter has three discussions related to one of Johan van Benthem's longstanding interests, the areas of interaction of logic and linguistics. We review much of what is known on the landscape of syllogistic logics. These are logics which correspond to fragments of language. The idea in this area is to have complete and decidable systems. Next we present a very simple form of dynamic logic, essentially a logic of two worlds with a back-and-forth arrow between them. This is then related to an issue in dynamic semantics, the logic of "and then". Our last discussion is related to an area which van Benthem again did so much to stimulate, the area of monotonicity reasoning in language. We connect the topic to reasoning in elementary mathematics. We formalize a monotonicity calculus following van Benthem and SanchezValencia, and we interpret this on hierarchies of preorders rather than sets.