Indefinites and their values

Formal semantics is a branch of linguistics and philosophy that studies the meaning of natural language using formal systems derived from logic and mathematics. This thesis investigates the formal semantics of indefinites, such as the English pronoun "someone". Indefinite pronouns can have a wide range of interpretations. For example, the sentence "John wants to listen to some song" can be understood in different ways, depending on how the indefinite "some song" is interpreted. It could refer to a specific song, whether known or unknown to the speaker, or it could have a non-specific reading, where any song would suffice. Across languages, different forms of indefinites are used, each suited to particular contexts or meanings. This thesis formally examines how indefinites in various languages convey different levels of scopal and epistemic specificity. It introduces a novel approach called two-sorted team semantics (2TS), which formalizes the interpretation of indefinites within a team semantics framework. Using dependence logic, a mathematical framework that can express relationships of dependencies among variable values, the thesis accounts for the formal semantics of different types of indefinites. The 2TS framework is applied to: (i) the cross-linguistic distribution of indefinites and related universal semantic patterns; (ii) the analysis of different indefinite types, including epistemic, non-specific, specific, and free choice indefinites; (iii) the diachronic development of indefinites; and (iv) the realization of indefinites in sign languages.