Abstract
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 mathsf {ClAnt}—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.
Highlights
Inquisitive semantics (Ciardelli et al 2018) is a semantic framework that aims to represent statements and questions uniformly in a logical system and to analyze logical relations between them
The paper is organized as follows: In Sect. 2 we present InqBQ and some basic properties we will use throughout the paper; in Sect. 3 we introduce the ClAnt fragment of the logic; in Sect. 4 we study a deductive system suitable to capture entailment between ClAnt formulas and show some of its main properties; Sect. 5 is devoted to showing the main result of the paper, that is, the completeness of the deductive system introduced
In this paper we introduced the ClAnt fragment of InqBQ, extending the mentionsome and mention-all fragments
Summary
Inquisitive semantics (Ciardelli et al 2018) is a semantic framework that aims to represent statements and questions uniformly in a logical system and to analyze logical relations between them. Inquisitive first order logic InqBQ is the inquisitive counterpart of classical first order logic It extends the usual first order language by introducing question-forming operators to represent alternative questions (e.g., P Q, which stands for “Does P hold or does Q hold?”) and witness questions (e.g., ∃x.P(x), which stands for “What is an element with property P?”). This augmented language captures concepts specific to questions—such as answerhood and dependency between questions—through the entailment of the logic; and.
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