Sequent Calculi for Data-Aware Modal Logics
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912623074738176 |
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| author | Areces, Carlos Cassano, Valentin Dutto, Danae Fervari, Raul |
| author_facet | Areces, Carlos Cassano, Valentin Dutto, Danae Fervari, Raul |
| contents | Data-aware modal logics offer a powerful formalism for reasoning about semi-structured queries in languages such as DataGL, XPath, and GQL. In brief, these logics can be viewed as modal systems capable of expressing both reachability statements and data-aware properties, such as value comparisons. One particularly expressive logic in this landscape is HXpathD, a hybrid modal logic that captures not only the navigational core of XPath but also data comparisons, node labels (keys), and key-based navigation operators. While previous work on HXpathD has primarily focused on its model-theoretic properties, in this paper we approach HXpathD from a proof-theoretic perspective. Concretely, we present a sound and complete Gentzen-style sequent calculus for HXpathD. Moreover, we show all rules in this calculus are invertible, and that it enjoys cut elimination. Our work contributes to the proof-theoretic foundations of data-aware modal logics, and enables a deeper logical analysis of query languages over graph-structured data. Moreover, our results lay the groundwork for extending proof-theoretic techniques to a broader class of modal systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_01868 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sequent Calculi for Data-Aware Modal Logics Areces, Carlos Cassano, Valentin Dutto, Danae Fervari, Raul Logic in Computer Science Logic in Computer Science Data-aware modal logics offer a powerful formalism for reasoning about semi-structured queries in languages such as DataGL, XPath, and GQL. In brief, these logics can be viewed as modal systems capable of expressing both reachability statements and data-aware properties, such as value comparisons. One particularly expressive logic in this landscape is HXpathD, a hybrid modal logic that captures not only the navigational core of XPath but also data comparisons, node labels (keys), and key-based navigation operators. While previous work on HXpathD has primarily focused on its model-theoretic properties, in this paper we approach HXpathD from a proof-theoretic perspective. Concretely, we present a sound and complete Gentzen-style sequent calculus for HXpathD. Moreover, we show all rules in this calculus are invertible, and that it enjoys cut elimination. Our work contributes to the proof-theoretic foundations of data-aware modal logics, and enables a deeper logical analysis of query languages over graph-structured data. Moreover, our results lay the groundwork for extending proof-theoretic techniques to a broader class of modal systems. |
| title | Sequent Calculi for Data-Aware Modal Logics |
| topic | Logic in Computer Science Logic in Computer Science |
| url | https://arxiv.org/abs/2510.01868 |