Abstract
With the idea of analyzing awareness as potential for knowledge, we propose a novel semantics for awareness logic. Expressivities of languages with different combinations of modalities for this semantics are investigated. We explore the properties of our semantics and compare our model with Fagin & Halpern model and the model by Heifetz et al. in partitional settings. A series of equivalence results are established from the comparison. Finally, we provide two axiomatizations for implicit knowledge and explicit knowledge, respectively, and prove soundness and completeness for them.
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Acknowledgements
This research was supported by the Key Project of National Social Science Foundation of China (No. 16AZX017). This paper rebuilds and extends the previous work “A Two-Layer Partition Awareness Structure”, in the proceedings of the 7th LORI. The authors would like to thank Professor Joseph Y. Halpern for his valuable comments on earlier versions of this paper during his visit to Sun Yat-sen University. Thank the editors for giving us more time to revise the paper. Great gratitude is paid to the anonymous reviewer for the exceptionally detailed comments and suggestions. The latter is crucial and indispensable for all the substantial improvements of this paper.
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Song, P., Xiong, W. Awareness as Potential for Knowledge. J Philos Logic 52, 669–703 (2023). https://doi.org/10.1007/s10992-022-09684-2
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DOI: https://doi.org/10.1007/s10992-022-09684-2