The fixed point and the Craig interpolation properties for sublogics of $$\textbf{IL}$$-Reference-Cited by-同舟云学术

The fixed point and the Craig interpolation properties for sublogics of $$\textbf{IL}$$

Published:2023-06-10 Issue:1-2 Volume:63 Page:1-37
ISSN:0933-5846
Container-title:Archive for Mathematical Logic
language:en
Short-container-title:Arch. Math. Logic

Author:

Iwata Sohei,Kurahashi Taishi^ORCID,Okawa Yuya

Abstract

AbstractWe study the fixed point property and the Craig interpolation property for sublogics of the interpretability logic

$$\textbf{IL}$$

IL . We provide a complete description of these sublogics concerning the uniqueness of fixed points, the fixed point property and the Craig interpolation property.

Funder

Japan Society for the Promotion of Science

Publisher

Springer Science and Business Media LLC

Subject

Logic,Philosophy

Link

https://link.springer.com/content/pdf/10.1007/s00153-023-00882-6.pdf

Reference17 articles.

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2. Bernardi, C.: The uniqueness of the fixed-point in every diagonalizable algebra. Stud. Logica. 35, 335–343 (1976)

3. Boolos, G.: The Unprovability of Consistency. An Essay in Modal Logic. Cambridge University Press, Cambridge (1979)

4. Boolos, G.: The Logic of Provability. Cambridge University Press, Cambridge (1993)

5. Ignatiev, K.N.: Partial conservativity and modal logics. ITLI Publication Series X-91-04 (1991)

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