Symmetric Contingency Logic with Unlimitedly Many Modalities


The completeness of the axiomatization of contingency logic over symmetric frames has been thought of as a nontrivial job, the unimodal case of which cannot be generalized to the finitely multimodal case, which in turn cannot be generalized to the infinitely multimodal case. This paper deals with the completeness of symmetric contingency logic with unlimitedly many modalities, no matter whether the set of modalities is finite or infinite.

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This research is supported by the project 17CZX053 of National Social Science Fundation of China. We would like to acknowledge an anonymous referee for his/her insightful comments.

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Correspondence to Jie Fan.

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Fan, J. Symmetric Contingency Logic with Unlimitedly Many Modalities. J Philos Logic 48, 851–866 (2019).

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  • Contingency
  • Symmetric frames
  • Axiomatization
  • Completeness
  • Unlimitedly many modalities