On the expressive power of inquisitive team logic and inquisitive first-order logic
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
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2026
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| _version_ | 1866912956105621504 |
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| author | Kontinen, Juha Ciardelli, Ivano |
| author_facet | Kontinen, Juha Ciardelli, Ivano |
| contents | Inquisitive team logic is a variant of inquisitive logic interpreted in team semantics, which has been argued to provide a natural setting for the regimentation of dependence claims. With respect to sentences, this logic is known to be expressively equivalent with first-order logic. In this article we show that, on the contrary, the expressive power of open formulas in this logic properly exceeds that of first-order logic. On the way to this result, we show that if inquisitive team logic is extended with the range-generating universal quantifier adopted in dependence logic, the resulting logic can express finiteness, and as a consequence, it is neither compact nor recursively axiomatizable. We further extend our results to standard inquisitive first-order logic, showing that some sentences of this logic express non first-order properties of models. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_08646 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the expressive power of inquisitive team logic and inquisitive first-order logic Kontinen, Juha Ciardelli, Ivano Logic Logic in Computer Science Inquisitive team logic is a variant of inquisitive logic interpreted in team semantics, which has been argued to provide a natural setting for the regimentation of dependence claims. With respect to sentences, this logic is known to be expressively equivalent with first-order logic. In this article we show that, on the contrary, the expressive power of open formulas in this logic properly exceeds that of first-order logic. On the way to this result, we show that if inquisitive team logic is extended with the range-generating universal quantifier adopted in dependence logic, the resulting logic can express finiteness, and as a consequence, it is neither compact nor recursively axiomatizable. We further extend our results to standard inquisitive first-order logic, showing that some sentences of this logic express non first-order properties of models. |
| title | On the expressive power of inquisitive team logic and inquisitive first-order logic |
| topic | Logic Logic in Computer Science |
| url | https://arxiv.org/abs/2603.08646 |