Completeness for the Classical Antecedent Fragment of Inquisitive First-Order Logic

Inquisitive first order logic is an extension of first order classical logic, introducing questions and studying the logical relations between questions and quantifiers. It is not known whether is recursively axiomatizable, even though an axiomatization has been found for fragments of the logic (Ciardelli, 2016). In this paper we define the ClAnt\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathsf {ClAnt}$$\end{document}—classical antecedent—fragment, together with an axiomatization and a proof of its strong completeness. This result extends the ones presented in the literature and introduces a new approach to study the axiomatization problem for fragments of the logic.