Inquisitive Logic Consequence and Inference in the Realm of Questions

• Main Author: Ciardelli, Ivano (auth)
• Format: Electronic Book Chapter
• Language: English
• Published: Cham Springer Nature 2022
• Series: Trends in Logic
• Subjects: Philosophy: logic; Mathematical foundations; Logic of Questions; Inquisitive Logic; Information Semantics; Logic of Dependency; Dependence Logic; Intuitionistic Logic; Proofs-as-Programs; Information Types; role of questions in logic; Questions in propositional logic; reasoning with questions; Questions in first-order logic; Questions in modal logic; Connections with intuitionistic logic; Connections with dependence logic; how classical logic can be made inquisitive; connection inquisitive, intuitionistic, dependence logic
• Online Access: DOAB: download the publication; DOAB: description of the publication

This open access book makes a case for extending logic beyond its traditional boundaries, to encompass not only statements but also also questions. The motivations for this extension are examined in detail. It is shown that important notions, including logical answerhood and dependency, emerge as facets of the fundamental notion of entailment once logic is extended to questions, and can therefore be treated with the logician's toolkit, including model-theoretic constructions and proof systems. After motivating the enterprise, the book describes how classical propositional and predicate logic can be made inquisitive-i.e., extended conservatively with questions-and what the resulting logics look like in terms of meta-theoretic properties and proof systems. Finally, the book discusses the tight connections between inquisitive logic and dependence logic.