Topological semantics of the predicate modal calculus QGL extended with non-well-founded proofs

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Topological semantics of the predicate modal calculus QGL extended with non-well-founded proofs

P. 64–66.

Разумный П. М., Shamkanov D. S.

The paper investigates the predicate modal calculus QGL extended with non-well-founded proofs.

Language: English

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Keywords: Non-well-founded proofs

Publication based on the results of:

Доказательства и модели (2023)

In book

SCAN 2023 Semantical and Computational Aspects of Non-Classical Logics: Moscow + Online, June 13–17, 2023. Abstracts

M.: ., 2023.

On structural proof theory of the modal logic K+ extended with infinitary derivations

Shamkanov D. S., Logic Journal of the IGPL 2024 P. 1–46

We consider an extension of the modal logic of transitive closure K+ with certain infinitary derivations and present a sequent calculus for this extension, which allows non-well-founded proofs. We establish continuous cut-elimination for the given calculus using fixed-point theorems for contractive mappings. The infinitary derivations mentioned above are well founded and countably branching, while the non-well-founded proofs ...

Added: January 29, 2025

On structural proof theory of the modal logic K+ extended with infinitary derivations

Shamkanov D. S., / Series arXiv "math". 2023.

We consider an extension of the modal logic of transitive closure K+ with some inifinitary derivations and present a sequent calculus for this extension, which allows non-well-founded proofs. For the given calculus, we obtain the cut-elimination theorem following the lines of so called continuous cut elimination. Our consideration also covers ordinary proofs of K+ since ...

Added: November 14, 2023

Cut Elimination for the Weak Modal Grzegorczyk Logic via Non-well-Founded Proofs

Savateev Y., Shamkanov D. S., , in: Logic, Language, Information, and Computation: 26th International Workshop, WoLLIC 2019, Utrecht, The Netherlands, July 2-5, 2019, ProceedingsVol. 11541: Lecture Notes in Computer Science.: Berlin, Heidelberg: Springer, 2019. P. 569–583.

We present a sequent calculus for the weak Grzegorczyk logic 𝖦𝗈 allowing non-well-founded proofs and obtain the cut-elimination theorem for it by constructing a continuous cut-elimination mapping acting on these proofs. ...

Added: September 16, 2019

Non-well-founded proofs for the Grzegorczyk modal logic

Yury Savateev, Daniyar Shamkanov, Review of Symbolic Logic 2021 Vol. 14 No. 1 P. 22–50

We present a sequent calculus for the Grzegorczyk modal logic Grz allowing cyclic and other non-well-founded proofs and obtain the cut-elimination theorem for it by constructing a continuous cut-elimination mapping acting on these proofs. As an application, we establish the Lyndon interpolation property for the logic Grz proof-theoretically. ...

Added: February 26, 2018

Cut-elimination for the modal Grzegorczyk logic via non-well-founded proofs

Savateev Y., Shamkanov D. S., , in: Logic, Language, Information, and Computation: 24th International Workshop, WoLLIC 2017, London, UK, July 18-21, 2017, Proceedings.: Springer, 2017. P. 321–335.

We present a sequent calculus for the modal Grzegorczyk logic ...

Added: September 26, 2017