Uniform Lyndon Interpolation for Basic Non-normal Modal Logics

Rosalie Iemhoff; Seyedamirhossein Akbartabatabai; Raheleh Jalali Keshavarz

doi:10.1007/978-3-030-88853-4_18

Uniform Lyndon Interpolation for Basic Non-normal Modal Logics

Rosalie Iemhoff, Seyedamirhossein Akbartabatabai, Raheleh Jalali Keshavarz

OFR - Theoretical Philosophy

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

Abstract

In this paper, a proof-theoretic method to prove uniform Lyndon interpolation for non-normal modal logics is introduced and applied to show that the logics E, M, MC, EN, MN have that property. In particular, these logics have uniform interpolation. Although for some of them the latter is known, the fact that they have uniform Lyndon interpolation is new. Also, the proof-theoretic proofs of these facts are new, as well as the constructive way to explicitly compute the interpolants that they provide. It is also shown that the non-normal modal logics EC and ECN do not have Craig interpolation, and whence no uniform (Lyndon) interpolation.

Original language	English
Title of host publication	Logic, Language, Information, and Computation
Subtitle of host publication	27th International Workshop, WoLLIC 2021, Virtual Event, October 5–8, 2021, Proceedings
Editors	Alexandra Silva, Renata Wassermann, Ruy de Queiroz
Publisher	Springer
Pages	287-301
Edition	1
ISBN (Electronic)	978-3-030-88853-4
ISBN (Print)	978-3-030-88852-7
DOIs	https://doi.org/10.1007/978-3-030-88853-4_18
Publication status	Published - 2021

Publication series

Name	Lecture Notes in Computer Science
Publisher	Springer
Volume	13038
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Keywords

Non-normal modal logics
Uniform interpolation
Uniform
Lyndon interpolation
Craig interpolation

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10.1007/978-3-030-88853-4_18

AkbarTabatabai2021_Chapter_UniformLyndonInterpolationForBFinal published version, 377 KBLicence: Taverne

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Iemhoff, R., Akbartabatabai, S., & Jalali Keshavarz, R. (2021). Uniform Lyndon Interpolation for Basic Non-normal Modal Logics. In A. Silva, R. Wassermann, & R. de Queiroz (Eds.), Logic, Language, Information, and Computation: 27th International Workshop, WoLLIC 2021, Virtual Event, October 5–8, 2021, Proceedings (1 ed., pp. 287-301). (Lecture Notes in Computer Science; Vol. 13038). Springer. https://doi.org/10.1007/978-3-030-88853-4_18

Iemhoff, Rosalie ; Akbartabatabai, Seyedamirhossein ; Jalali Keshavarz, Raheleh. / Uniform Lyndon Interpolation for Basic Non-normal Modal Logics. Logic, Language, Information, and Computation: 27th International Workshop, WoLLIC 2021, Virtual Event, October 5–8, 2021, Proceedings. editor / Alexandra Silva ; Renata Wassermann ; Ruy de Queiroz. 1. ed. Springer, 2021. pp. 287-301 (Lecture Notes in Computer Science).

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title = "Uniform Lyndon Interpolation for Basic Non-normal Modal Logics",

abstract = "In this paper, a proof-theoretic method to prove uniform Lyndon interpolation for non-normal modal logics is introduced and applied to show that the logics E, M, MC, EN, MN have that property. In particular, these logics have uniform interpolation. Although for some of them the latter is known, the fact that they have uniform Lyndon interpolation is new. Also, the proof-theoretic proofs of these facts are new, as well as the constructive way to explicitly compute the interpolants that they provide. It is also shown that the non-normal modal logics EC and ECN do not have Craig interpolation, and whence no uniform (Lyndon) interpolation.",

keywords = "Non-normal modal logics, Uniform interpolation, Uniform, Lyndon interpolation, Craig interpolation",

author = "Rosalie Iemhoff and Seyedamirhossein Akbartabatabai and {Jalali Keshavarz}, Raheleh",

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Iemhoff, R, Akbartabatabai, S & Jalali Keshavarz, R 2021, Uniform Lyndon Interpolation for Basic Non-normal Modal Logics. in A Silva, R Wassermann & R de Queiroz (eds), Logic, Language, Information, and Computation: 27th International Workshop, WoLLIC 2021, Virtual Event, October 5–8, 2021, Proceedings. 1 edn, Lecture Notes in Computer Science, vol. 13038, Springer, pp. 287-301. https://doi.org/10.1007/978-3-030-88853-4_18

Uniform Lyndon Interpolation for Basic Non-normal Modal Logics. / Iemhoff, Rosalie; Akbartabatabai, Seyedamirhossein; Jalali Keshavarz, Raheleh.
Logic, Language, Information, and Computation: 27th International Workshop, WoLLIC 2021, Virtual Event, October 5–8, 2021, Proceedings. ed. / Alexandra Silva; Renata Wassermann; Ruy de Queiroz. 1. ed. Springer, 2021. p. 287-301 (Lecture Notes in Computer Science; Vol. 13038).

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

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T1 - Uniform Lyndon Interpolation for Basic Non-normal Modal Logics

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AU - Akbartabatabai, Seyedamirhossein

AU - Jalali Keshavarz, Raheleh

PY - 2021

Y1 - 2021

N2 - In this paper, a proof-theoretic method to prove uniform Lyndon interpolation for non-normal modal logics is introduced and applied to show that the logics E, M, MC, EN, MN have that property. In particular, these logics have uniform interpolation. Although for some of them the latter is known, the fact that they have uniform Lyndon interpolation is new. Also, the proof-theoretic proofs of these facts are new, as well as the constructive way to explicitly compute the interpolants that they provide. It is also shown that the non-normal modal logics EC and ECN do not have Craig interpolation, and whence no uniform (Lyndon) interpolation.

AB - In this paper, a proof-theoretic method to prove uniform Lyndon interpolation for non-normal modal logics is introduced and applied to show that the logics E, M, MC, EN, MN have that property. In particular, these logics have uniform interpolation. Although for some of them the latter is known, the fact that they have uniform Lyndon interpolation is new. Also, the proof-theoretic proofs of these facts are new, as well as the constructive way to explicitly compute the interpolants that they provide. It is also shown that the non-normal modal logics EC and ECN do not have Craig interpolation, and whence no uniform (Lyndon) interpolation.

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KW - Uniform interpolation

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KW - Lyndon interpolation

KW - Craig interpolation

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Iemhoff R, Akbartabatabai S, Jalali Keshavarz R. Uniform Lyndon Interpolation for Basic Non-normal Modal Logics. In Silva A, Wassermann R, de Queiroz R, editors, Logic, Language, Information, and Computation: 27th International Workshop, WoLLIC 2021, Virtual Event, October 5–8, 2021, Proceedings. 1 ed. Springer. 2021. p. 287-301. (Lecture Notes in Computer Science). doi: 10.1007/978-3-030-88853-4_18

Uniform Lyndon Interpolation for Basic Non-normal Modal Logics

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