Abstract
This paper connects the following three apparently unrelated topics: an epistemic framework fighting logical omniscience, a class of generalized graphs without the arities of relations, and a family of non-normal modal logics rejecting the aggregative axiom. Through neighborhood frames as their meeting point, we show that, among many completeness results obtained in this paper, the limit of a family of weakly aggregative logics is both exactly the modal logic of hypergraphs and also the epistemic logic of local reasoning with veracity and positive introspection. The logics studied are shown to be decidable based on a filtration construction.
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Notes
- 1.
The graph is a variant of an example in [3], where hypergrphs are used to represent semi-public broadcasting channels for interacting agents.
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Acknowledgment
The authors thank the anonymous reviewers for pointing out some related work. Jixin Liu thanks China Postdoctoral Science Foundation (2020M683344) for support. Yanjing Wang gratefully acknowledges the support from NSSF (grant 19BZX135).
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Ding, Y., Liu, J., Wang, Y. (2021). Hypergraphs, Local Reasoning, and Weakly Aggregative Modal Logic. In: Ghosh, S., Icard, T. (eds) Logic, Rationality, and Interaction. LORI 2021. Lecture Notes in Computer Science(), vol 13039. Springer, Cham. https://doi.org/10.1007/978-3-030-88708-7_5
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