A proof-theoretical approach to some extensions of first order quantification
<|reference_start|>A proof-theoretical approach to some extensions of first order quantification: 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.<|reference_end|>
@article{allègre2024a,
    title={A proof-theoretical approach to some extensions of first order
  quantification},
    author={Lo"ic All`egre and Oph'elie Lacroix and Christian Retor'e},
    journal={arXiv preprint arXiv:2407.09865},
    year={2024},
    archivePrefix={arXiv},
    eprint={2407.09865},
    primaryClass={math.LO cs.LO}
}