Indefinites and their values Marco Degano Abstract: Imagine attending the PhD defence of the author of this dissertation and uttering the sentence 'Someone is reading this dissertation.'. You can use 'someone' to refer to a friend sitting in front of you, whom you know. But you can also use 'someone' to refer to a person in the audience, whom you do not know. Formal semantics studies the meaning of natural language, and it does so by means of formal logical accounts. This dissertation focuses on a seemingly tiny yet significant aspect of natural language: indefinites, such as the English 'someone'. In the example discussed, the value of 'someone' is fixed in the former case, while in the latter case its value varies according to all possible options you consider this person might be. Importantly, while English allows 'someone' in both cases, different languages employ dedicated forms of indefinites (marked indefinites) that can only be used if you know the referent and forms that can only be used if you do not know the referent. This dissertation focuses on these and similar contrasts, particularly on so-called scopal and epistemic specificity. In this domain, marked indefinites exhibit a variety of forms and meanings across languages, raising several questions and research goals. How can we formally account for these distinctions between indefinites? We develop a formal system, two-sorted team semantics (2TS), that draws from different traditions: team semantics, dependence logic, and two-sorted logic. An indefinite is associated with a variable over a set of variable assignments, a team, encoding its possible values. These values can have different dependency relationships with other operators in the sentence, reflecting the meaning and distribution of different indefinites. What are the attested types of (non-)specific indefinites cross-linguistically? We show how 2TS can explain why certain types of indefinites are attested while others are rare or unattested in terms of complexity and how marked indefinites form a convex meaning space. We discuss how the attested marked indefinites can be perspicuously represented by a Square of Opposition, called the Dependence Square of Opposition. Furthermore, we demonstrate how 2TS can adequately account for different classes of marked indefinites. What diachronic changes are possible among marked indefinites? We demonstrate how 2TS can adequately explain some attested diachronic paths and rule out others. The 2TS formalization transparently represents phenomena of semantic weakening in terms of entailment. We also analyse phenomena of grammaticalization involving free choice indefinites, accounting also for their distribution. How are indefinites realized beyond spoken language? We investigate the realization of indefinites in sign languages and argue for the suitability of 2TS in modelling the relevant phenomena. In conclusion, we have established how the formalization of indefinites and (non-)specificity provided by 2TS offers valuable insights into this linguistic domain. We hope that this dissertation has shown that the study of indefinites is anything but indefinite.