Uniform Lyndon Interpolation for Basic Non-normal Modal Logics
Publication date
2021
Authors
Iemhoff, Rosalie
Akbartabatabai, Seyedamirhossein
Jalali Keshavarz, Raheleh
Editors
Silva, Alexandra
Wassermann, Renata
de Queiroz, Ruy
Advisors
Supervisors
Document Type
Part of book
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License
taverne
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, Taverne
Citation
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