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A Non-alethic Multi-agent Doxastic Logic as a Solution to Epistemic Conflicts

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Abstract

The non-alethic systems N1 of da Costa and A of Grana are both paraconsistent and paracomplete. Based on them, a multi-agent doxastic logic NADK can be obtained by logical expansion. The soundness and completeness of NADK are proved and its special theorems are also presented. In this logic, the belief version of the laws of contradiction and excluded middle, as well as the principle of explosion are all invalid. Therefore, it may provide a reliable logical basis for any theory which has paraconsistent or paracomplete epistemic conflicts, such as true contradictions, true contrarieties, and belief paradoxes. We also explain in detail how a non-alethic doxastic logic provides a reliable logical basis for tolerating these three types of epistemic conflicts. The present paper is the deepening and development of system N1 and A.

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Acknowledgements

The author thanks the helpful comments of anonymous reviewers, and thanks the authors of all the references, especially professor Grana, he sent his papers and book to me from Italy. Thanks professor da Costa, he answered me a lot of questions about paraconsistent logic. This paper was supported by the Major Program of the National Social Science Foundation of China (17ZDA026).

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  1. Department of Philosophy, East China Normal University, Shanghai, China

    Xudong Hao

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  1. Xudong Hao
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Correspondence to Xudong Hao.

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Hao, X. A Non-alethic Multi-agent Doxastic Logic as a Solution to Epistemic Conflicts. Axiomathes 32, 413–431 (2022). https://doi.org/10.1007/s10516-020-09530-7

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  • DOI: https://doi.org/10.1007/s10516-020-09530-7

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