A proof-theoretical approach to some extensions of first order quantification
Abstract
Generalised quantifiers, which include Henkin's branching quantifiers, have been introduced by Mostowski and Lindstr\"om and developed as a substantial topic application of logic, especially model theory, to linguistics with work by Barwise, Cooper, Keenan. In this paper, we mainly study the proof theory of some non-standard quantifiers as second order formulae . Our first example is the usual pair of first order quantifiers (for all / there exists) when individuals are viewed as individual concepts handled by second order deductive rules. Our second example is the study of a second order translation of the simplest branching quantifier: ``A member of each team and a member of each board of directors know each other", for which we propose a second order treatment.
Cite
@article{arxiv.2407.09865,
title = {A proof-theoretical approach to some extensions of first order quantification},
author = {Loïc Allègre and Ophélie Lacroix and Christian Retoré},
journal= {arXiv preprint arXiv:2407.09865},
year = {2024}
}