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Labelled Calculi for Lattice-Based Modal Logics

Authors :
van der Berg, Ineke
De Domenico, Andrea
Greco, Giuseppe
Manoorkar, Krishna B.
Palmigiano, Alessandra
Panettiere, Mattia
Banerjee, Mohua
Sreejith, A.V.
Banerjee, Mohua
Sreejith, A.V.
Ethics, Governance and Society
Source :
van der Berg, I, De Domenico, A, Greco, G, Manoorkar, K B, Palmigiano, A & Panettiere, M 2023, Labelled Calculi for Lattice-Based Modal Logics . in M Banerjee & A V Sreejith (eds), Logic and Its Applications : 10th Indian Conference, ICLA 2023, Indore, India, March 3–5, 2023, Proceedings . Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 13963 LNCS, Springer Science and Business Media Deutschland GmbH, pp. 23-47, 10th Indian Conference on Logic and Its Applications, ICLA 2023, Indore, India, 3/03/23 . https://doi.org/10.1007/978-3-031-26689-8_3, Logic and Its Applications: 10th Indian Conference, ICLA 2023, Indore, India, March 3–5, 2023, Proceedings, 23-47, STARTPAGE=23;ENDPAGE=47;TITLE=Logic and Its Applications, Logic and Its Applications ISBN: 9783031266881
Publication Year :
2023
Publisher :
Springer Science and Business Media Deutschland GmbH, 2023.

Abstract

We introduce labelled sequent calculi for the basic normal non-distri-butive modal logic 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. Modular proofs are presented that these calculi are all sound, complete and conservative w.r.t, 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.

Subjects

Subjects :
Algorithmic correspondence theory
Non-distributive modal logic
Algorithmic proof theory
Labelled calculi

Details

Language :
English
ISBN :
978-3-031-26688-1
ISBNs :
9783031266881
Database :
OpenAIRE
Journal :
van der Berg, I, De Domenico, A, Greco, G, Manoorkar, K B, Palmigiano, A & Panettiere, M 2023, Labelled Calculi for Lattice-Based Modal Logics . in M Banerjee & A V Sreejith (eds), Logic and Its Applications : 10th Indian Conference, ICLA 2023, Indore, India, March 3–5, 2023, Proceedings . Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 13963 LNCS, Springer Science and Business Media Deutschland GmbH, pp. 23-47, 10th Indian Conference on Logic and Its Applications, ICLA 2023, Indore, India, 3/03/23 . https://doi.org/10.1007/978-3-031-26689-8_3, Logic and Its Applications: 10th Indian Conference, ICLA 2023, Indore, India, March 3–5, 2023, Proceedings, 23-47, STARTPAGE=23;ENDPAGE=47;TITLE=Logic and Its Applications, Logic and Its Applications ISBN: 9783031266881
Accession number :
edsair.doi.dedup.....30959edd3a9877d132b70ef04f08099a

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