Disjunction and Existence Properties in Inquisitive First-Order Logic

Classical first-order logic FO is commonly used to study logical connections between statements, that is sentences that in every context have an associated truth-value. Inquisitive first-order logic InqBQ is a conservative extension of FO which captures not only connections between statements, but also between questions. In this paper we prove the disjunction and existence properties for InqBQ relative to inquisitive disjunction and inquisitive existential quantifier ¯∃¯. Moreover we extend these results to several families of theories, among which the one in the language of FO. To this end, we initiate a model-theoretic approach to the study of InqBQ. In particular, we develop a toolkit of basic constructions in order to transform and combine models of InqBQ.