Affiliation:
1. Graduate School of Science and Engineering, Chiba University, 1-33 Yayoi-cho, Inage-ku, Chiba-shi, Chiba, 263-8522, Japan
Abstract
Abstract
We investigate the fixed point properties for sublogics of the interpretability logic $\textbf {IL}$. In our previous work, it was proved that a sublogic $\textbf {IL}^{-}(\textbf {J 2}_+, \textbf {J 5})$ has the fixed point property (FPP) and that a sublogic $\textbf {IL}^{-}(\textbf {J 4}, \textbf {J 5})$ has a newly introduced weaker property $\ell $FPP. In this paper, we provide countably many sublogics of $\textbf {IL}^{-}(\textbf {J 2}_{+}, \textbf {J 5})$ (resp. $\textbf {IL}^{-}(\textbf {J 4}, \textbf {J 5})$) having FPP (resp. $\ell $FPP).
Publisher
Oxford University Press (OUP)
Subject
Logic,Hardware and Architecture,Arts and Humanities (miscellaneous),Software,Theoretical Computer Science
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3. Modal completeness of sublogics of the interpretability logic IL;Kurahashi;Mathematical Logic Quarterly,2021
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