Abstract
Classical first-order logic texttt {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} is a conservative extension of texttt {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} 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}. To this end, we initiate a model-theoretic approach to the study of texttt {InqBQ}. In particular, we develop a toolkit of basic constructions in order to transform and combine models of texttt {InqBQ}.
Highlights
In this paper we prove the disjunction and existence properties for the logic InqBQ, solving a conjecture stated in [3] §4
Some of them are inspired by operations on intuitionistic Kripke-frames, others are based on constructions typical of classical logic
In this paper we briefly presented the logic InqBQ and gave a proof of a conjecture formulated in [3], namely that the disjunction and existence properties hold for every classical theory
Summary
In this paper we prove the disjunction and existence properties for the logic InqBQ, solving a conjecture stated in [3] §4. To this end, we develop several model-theoretic constructions to study InqBQ and its entailment relation. (b) “There exists an element with property P ”, clearly (a) implies (b), as witnessed by the entailment P (c) FO ∃x.P (x). In the rest of the paper we will assume to have fixed a countable set of variables Var and a signature Σ = {fi, Rj}i∈I,j∈J , that is a set of symbols divided between function symbols and relation symbols, each of them with a corresponding arity specified by the function ar : Σ → N. We take the syntax of FO to be given by the following grammar:
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
