A proof-theoretical approach to some extensions of first order quantification
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866909253846958080 |
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| author | Allègre, Loïc Lacroix, Ophélie Retoré, Christian |
| author_facet | Allègre, Loïc Lacroix, Ophélie Retoré, Christian |
| contents | Generalised quantifiers, which include Henkin's branching quantifiers, have been introduced by Mostowski and Lindström 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2407_09865 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A proof-theoretical approach to some extensions of first order quantification Allègre, Loïc Lacroix, Ophélie Retoré, Christian Logic Logic in Computer Science 03B16, 03B65, 03B70 Generalised quantifiers, which include Henkin's branching quantifiers, have been introduced by Mostowski and Lindström 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. |
| title | A proof-theoretical approach to some extensions of first order quantification |
| topic | Logic Logic in Computer Science 03B16, 03B65, 03B70 |
| url | https://arxiv.org/abs/2407.09865 |