Disjunction and Existence Properties in Inquisitive First-Order Logic
Gianluca Grilletti · Studia Logica · 2018
Classical first-order logic $$\texttt {FO}$$ 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 $$\texttt {InqBQ}$$ InqBQ is a conservative extension of $$\texttt {FO}$$ FO which captures not only connections between statements, but also between questions. In this paper we prove the disjunction and existence properties for $$\texttt {InqBQ}$$ InqBQ relative to inquisitive disjunction and inquisitive existential quantifier $$\overline{\exists }$$ ∃ ¯ . Moreover we extend these results to several families of theories, among which the one in the language of $$\texttt {FO}$$ FO . To this end, we initiate a model-theoretic approach to the study of $$\texttt {InqBQ}$$ InqBQ . In particular, we develop a toolkit of basic constructions in order to transform and combine models of $$\texttt {InqBQ}$$ InqBQ .