Abstract
We introduce a type of weighted modal logic with explicit weights both in the language and in the models. The framework has its applications in epistemic logic for reasoning about agents’ knowledge based on their capability, and in deontic logic for agents’ choices based on their deontic capability or utilities. We make use of weighted Kripke models with the weights understood epistemically as a similarity measure between states and deontically as a measure of expected utilities. We present sound and complete axiomatizations for the logics, and discuss variants and possible extensions.
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Acknowledgments
We would like to thank the two referees of LORI 2021 for their valuable remarks and comments. Huimin Dong acknowledges funding support by the National Social Science Fund of China (20CZX051) and Yì N. Wáng acknowledges funding support by the National Social Science Fund of China (18ZDA290, 20&ZD047).
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Dong, H., Li, X., Wáng, Y.N. (2021). Weighted Modal Logic in Epistemic and Deontic Contexts. 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_6
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