New Logical Perspectives on Monotonicity
Johan van Benthem, Fenrong Liu

Abstract:
Monotonicity-based inference is a fundamental notion in the logical semantics of natural language, and also in logic in general. Start- ing in generalized quantifier theory, we distinguish three senses of the notion, study their relations, and use these to connect monotonicity to logics of model change. At the end we return to natural language and consider monotonicity inference in linguistic settings with vocabulary for various forms of change. While we mostly raise issues in this paper, we do make a number of new observations backing up our distinctions.