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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2508.13928 |
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| _version_ | 1866911111187529728 |
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| author | Petrukhin, Yaroslav |
| author_facet | Petrukhin, Yaroslav |
| contents | Definite descriptions are first-order expressions that denote unique objects. In this paper, we propose a second-order counterpart, designed to refer to unique relations between objects. We investigate this notion within the framework of Russell's theory of definite descriptions. While full second-order logic is incomplete, its fragment defined by Henkin's general models admits completeness. We develop our theory within this fragment and formalize it using a cut-free sequent calculus. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_13928 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On a Second-Order Version of Russellian Theory of Definite Descriptions Petrukhin, Yaroslav Logic in Computer Science Definite descriptions are first-order expressions that denote unique objects. In this paper, we propose a second-order counterpart, designed to refer to unique relations between objects. We investigate this notion within the framework of Russell's theory of definite descriptions. While full second-order logic is incomplete, its fragment defined by Henkin's general models admits completeness. We develop our theory within this fragment and formalize it using a cut-free sequent calculus. |
| title | On a Second-Order Version of Russellian Theory of Definite Descriptions |
| topic | Logic in Computer Science |
| url | https://arxiv.org/abs/2508.13928 |