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 decidablesystems.Nextwepresentaverysimpleformofdynamiclogic,essentiallya logicoftwoworldswithaback-and-fortharrowbetweenthem.Thisisthenrelatedto anissueindynamicsemantics,thelogicof"andthen".Ourlastdiscussionisrelatedto an area which van Benthem again did so much to stimulate, the area of monotonicity reasoninginlanguage.Weconnectthetopictoreasoninginelementarymathematics. WeformalizeamonotonicitycalculusfollowingvanBenthemandSanchezValencia, and we interpret this on hierarchies of preorders rather than sets.