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Finite-Chain Graded Modal Logic

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Modality, Semantics and Interpretations

Part of the book series: Logic in Asia: Studia Logica Library ((LIAA))

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Abstract

Kripke frames are generalized to finite-chain graded frames. The minimal finite-chain graded modal logic is shown to be sound and complete with respect to the class of all finite-chain graded frames. Finite-chain algebras are defined for giving algebraic semantics for this modal logic. A Jónsson-Tarski style representation theorem for finite-chain algebras is proved. This new kind of multimodal logic differs from both classical normal modal logic and graded modal logic. Some results for extensions of the minimal finite-chain graded modal logic are also obtained.

Both authors are supported by the China National Fund for Social Sciences (No. 12CZX054), and Chongqing Funding of Social Sciences (No. 2013YBZX008).

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Notes

  1. 1.

    This definition of \(\sigma \) was first suggested by Katsuhiko Sano (Japan Advanced Institute of Science and Technology).

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Acknowledgments

We would like to give our thanks to the anonymous review for very insightful comments which led us to improve the paper. We also thank for the comments from Prof. Wojciech Buszkowski (Poland), Prof. Hiroakira Ono (Japan), and other audience on the occasion of the Second Asian Workshop on Philosophical Logic.

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Authors and Affiliations

  1. Institute for Logic and Intelligence, Southwest University, Tiansheng Road No.2, Beibei, Chongqing, China

    Minghui Ma

  2. School of Computer Science, Southwest University, Tiansheng Road No.2, Beibei, Chongqing, China

    Shanxia Wang

Authors
  1. Minghui Ma
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  2. Shanxia Wang
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Correspondence to Minghui Ma .

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Editors and Affiliations

  1. Institute of Logic and Cognition, Sun Yat-sen University, Guangzhou, China

    Shier Ju

  2. Institute of Logic and Cognition, Sun Yat-sen University, Guangzhou, China

    Hu Liu

  3. Japan Advanced Institute of Science and Technology, Ishikawa, Japan

    Hiroakira Ono

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Ma, M., Wang, S. (2015). Finite-Chain Graded Modal Logic. In: Ju, S., Liu, H., Ono, H. (eds) Modality, Semantics and Interpretations. Logic in Asia: Studia Logica Library. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-47197-5_4

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