A Deep-Inference Sequent Calculus for Basic Propositional Team Logic (Without Delving Too Deep)
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866918121171845120 |
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| author | Anttila, Aleksi Iemhoff, Rosalie Yang, Fan |
| author_facet | Anttila, Aleksi Iemhoff, Rosalie Yang, Fan |
| contents | We introduce a sequent calculus for the propositional team logic with both the split disjunction and the inquisitive disjunction consisting of a Gentzen-style system (G3-like) for classical propositional logic together with two deep-inference rules for the inquisitive disjunction. We show that the system satisfies various desirable properties: it admits height-preserving weakening, contraction and inversion; it supports a procedure for constructing cutfree proofs and countermodels similar to that for G3cp; and cut elimination holds as a corollary of cut elimination for the G3-style subsystem together with a normal form theorem for cutfree derivations. We also prove a sequent interpolation theorem for the system that yields a novel Lyndon's interpolation theorem for the logic as a corollary. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_07509 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Deep-Inference Sequent Calculus for Basic Propositional Team Logic (Without Delving Too Deep) Anttila, Aleksi Iemhoff, Rosalie Yang, Fan Logic 03B60, 03F03 (Primary) 03F05, 03F07 (Secondary) We introduce a sequent calculus for the propositional team logic with both the split disjunction and the inquisitive disjunction consisting of a Gentzen-style system (G3-like) for classical propositional logic together with two deep-inference rules for the inquisitive disjunction. We show that the system satisfies various desirable properties: it admits height-preserving weakening, contraction and inversion; it supports a procedure for constructing cutfree proofs and countermodels similar to that for G3cp; and cut elimination holds as a corollary of cut elimination for the G3-style subsystem together with a normal form theorem for cutfree derivations. We also prove a sequent interpolation theorem for the system that yields a novel Lyndon's interpolation theorem for the logic as a corollary. |
| title | A Deep-Inference Sequent Calculus for Basic Propositional Team Logic (Without Delving Too Deep) |
| topic | Logic 03B60, 03F03 (Primary) 03F05, 03F07 (Secondary) |
| url | https://arxiv.org/abs/2508.07509 |