Inquisitive Semantics and Logic Salvador Mascarenhas Abstract: The first chapter introduces inquisitive semantics as a research program for the study of the semantics of natural language questions and disjunctions. The author begins by providing a brief outline of the necessary background on question semantics and erotetic logics, and then presents inquisitive semantics, by first laying out its main tenets and then defining a propositional logical system, InqL, that instantiates the inquisitive program. The second chapter presents the results of the author's investigations on the logical properties of the system defined in the previous chapter. The author begins with some informal remarks and then proceeds to introduce two crucial properties of the inquisitive system that have philosophical and linguistic relevance. The author then introduces an alternative formulation of the semantics of inquisitive logic in classical terms (that is, no update functions), which the author uses to present a sound and complete axiomatization of the system.