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arXiv · 2407.09865

A proof-theoretical approach to some extensions of first order quantification

Loïc Allègre·Ophélie Lacroix·Christian Retoré
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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.

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Loïc Allègre, Ophélie Lacroix, Christian Retoré. 2024-07-13. A proof-theoretical approach to some extensions of first order quantification. https://arxiv.org/abs/2407.09865

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