Abstract
We give a general approach to characterizing minimal information in a modal context. Our modal treatment can be used for many applications, but is especially relevant under epistemic interpretations of the operator □. Relative to an arbitrary modal system, we give three characterizations of minimal information and provide conditions under which these characterizations are equivalent. We then study information orders based on bisimulations and Ehrenfeucht–Fraïssé games. Moving to the area of epistemic logics, we show that for one of these orders almost all systems trivialize the notion of minimal information. Another order which we present is much more promising as it permits to minimize with respect to positive knowledge. In S5, the resulting notion of minimal knowledge coincides with well‐established proposals. For S4 we compare the two orders.
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van der Hoek, W., Jaspars, J. & Thijsse, E. Persistence and minimality in epistemic logic. Annals of Mathematics and Artificial Intelligence 27, 25–47 (1999). https://doi.org/10.1023/A:1018967130652
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DOI: https://doi.org/10.1023/A:1018967130652