Labelled Calculi for Lattice-Based Modal Logics

Ineke van der Berg; Andrea De Domenico; Giuseppe Greco; Krishna B. Manoorkar; Alessandra Palmigiano; Mattia Panettiere

doi:10.1007/978-3-031-26689-8_3

Labelled Calculi for Lattice-Based Modal Logics

Ineke van der Berg, Andrea De Domenico, Giuseppe Greco^*, Krishna B. Manoorkar, Alessandra Palmigiano, Mattia Panettiere

^*Corresponding author for this work

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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.

Original language	English
Title of host publication	Logic and Its Applications
Subtitle of host publication	10th Indian Conference, ICLA 2023, Indore, India, March 3–5, 2023, Proceedings
Editors	Mohua Banerjee, A.V. Sreejith
Publisher	Springer Science and Business Media Deutschland GmbH
Pages	23-47
Number of pages	25
ISBN (Electronic)	9783031266898
ISBN (Print)	9783031266881
DOIs	https://doi.org/10.1007/978-3-031-26689-8_3
Publication status	Published - 2023
Event	10th Indian Conference on Logic and Its Applications, ICLA 2023 - Indore, India Duration: 3 Mar 2023 → 5 Mar 2023

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	13963 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	10th Indian Conference on Logic and Its Applications, ICLA 2023
Country/Territory	India
City	Indore
Period	3/03/23 → 5/03/23

Bibliographical note

Publisher Copyright:
© 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.

Keywords

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

Access to Document

10.1007/978-3-031-26689-8_3

Labelled Calculi for Lattice-Based Modal LogicsFinal published version, 381 KBLicence: Article 25fa Dutch Copyright Act

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Cite this

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 (pp. 23-47). (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. https://doi.org/10.1007/978-3-031-26689-8_3

van der Berg, Ineke ; De Domenico, Andrea ; Greco, Giuseppe et al. / Labelled Calculi for Lattice-Based Modal Logics. Logic and Its Applications: 10th Indian Conference, ICLA 2023, Indore, India, March 3–5, 2023, Proceedings. editor / Mohua Banerjee ; A.V. Sreejith. Springer Science and Business Media Deutschland GmbH, 2023. pp. 23-47 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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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.",

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van der Berg, I , De Domenico, A , Greco, G , Manoorkar, KB , Palmigiano, A & Panettiere, M 2023, Labelled Calculi for Lattice-Based Modal Logics. in M Banerjee & AV 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

Labelled Calculi for Lattice-Based Modal Logics. / van der Berg, Ineke ; De Domenico, Andrea ; Greco, Giuseppe et al.
Logic and Its Applications: 10th Indian Conference, ICLA 2023, Indore, India, March 3–5, 2023, Proceedings. ed. / Mohua Banerjee; A.V. Sreejith. Springer Science and Business Media Deutschland GmbH, 2023. p. 23-47 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 13963 LNCS).

Research output: Chapter in Book / Report / Conference proceeding › Conference contribution › Academic › peer-review

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van der Berg I , De Domenico A , Greco G , Manoorkar KB , Palmigiano A , Panettiere M. Labelled Calculi for Lattice-Based Modal Logics. In Banerjee M, Sreejith AV, editors, Logic and Its Applications: 10th Indian Conference, ICLA 2023, Indore, India, March 3–5, 2023, Proceedings. Springer Science and Business Media Deutschland GmbH. 2023. p. 23-47. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). Epub 2023 Feb 22. doi: 10.1007/978-3-031-26689-8_3