Abstract
A weighted graph extends a standard Kripke frame for modal logic with a weight on each of its edges. Distance and similarity measures can be imposed so that the edges stand for the dissimilairty/similarity relation between nodes (in particular, we focus on the distance and similarity metrics introduced in [5]). Models based on these types of weighted graphs give a simple and flexible way of formally interpreting knowledge. We study proof systems and computational complexity of the resulting logics, partially by correspondence to normal modal logics interpreted in Kripke semantics.
Supported by the National Social Science Fund of China (Grant No. 20 &ZD047).
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Notes
- 1.
A weighted epistemic logic over similarities defined as such is studied in [7].
- 2.
The axiomatic system \(\textbf{K}\) is \(\textbf{KS}\) without the axiom (S); see Fig. 3 for details. By adding the axiom schemes (B) and (T), i.e., \(K_a\varphi \rightarrow \varphi \) for the latter, to the system \(\textbf{K}\), we get the axiomatic system \(\textbf{KTB}\).
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Liang, X., Wáng, Y.N. (2022). Epistemic Logic via Distance and Similarity. In: Khanna, S., Cao, J., Bai, Q., Xu, G. (eds) PRICAI 2022: Trends in Artificial Intelligence. PRICAI 2022. Lecture Notes in Computer Science, vol 13629. Springer, Cham. https://doi.org/10.1007/978-3-031-20862-1_3
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