Labelled calculi for lattice-based modal logics
Fuente:
arXiv
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| Autori principali: | , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866913199480111104 |
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| author | van der Berg, Ineke De Domenico, Andrea Greco, Giuseppe Manoorkar, Krishna Palmigiano, Alessandra Panettiere, Mattia |
| author_facet | van der Berg, Ineke De Domenico, Andrea Greco, Giuseppe Manoorkar, Krishna Palmigiano, Alessandra Panettiere, Mattia |
| contents | We introduce labelled sequent calculi for the basic normal non-distributive modal logic L and 31 of its axiomatic extensions, where the labels are atomic formulas of a first order language which is interpreted on the canonical extensions of the algebras in the variety corresponding to the logic L. Modular proofs are presented that these calculi are all sound, complete and conservative w.r.t. L, and enjoy cut elimination and the subformula property. The introduction of these calculi showcases a general methodology for introducing labelled calculi for the class of LE-logics and their analytic axiomatic extensions in a principled and uniform way. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_09887 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Labelled calculi for lattice-based modal logics van der Berg, Ineke De Domenico, Andrea Greco, Giuseppe Manoorkar, Krishna Palmigiano, Alessandra Panettiere, Mattia Logic We introduce labelled sequent calculi for the basic normal non-distributive modal logic L and 31 of its axiomatic extensions, where the labels are atomic formulas of a first order language which is interpreted on the canonical extensions of the algebras in the variety corresponding to the logic L. Modular proofs are presented that these calculi are all sound, complete and conservative w.r.t. L, and enjoy cut elimination and the subformula property. The introduction of these calculi showcases a general methodology for introducing labelled calculi for the class of LE-logics and their analytic axiomatic extensions in a principled and uniform way. |
| title | Labelled calculi for lattice-based modal logics |
| topic | Logic |
| url | https://arxiv.org/abs/2401.09887 |