Abstract
We introduce and study a modal logic wK4f that is related to the idea of minimal belief in much the same way as its strengthening, S4F, has been shown to be related to the idea of minimal knowledge. wK4f can be obtained by adding a weakened version of axiom F to the modal logic wK4. We show that, like S4F, wK4f is sound and complete with respect to the class of all minimal topological spaces ie topological spaces with only three open sets. We describe the rooted frames of wK4f by quadruples of natural numbers. Finally we characterise non-monotonic wK4f in terms of minimal models.
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Pearce, D., Uridia, L. (2010). Minimal Knowledge and Belief via Minimal Topology. In: Janhunen, T., Niemelä, I. (eds) Logics in Artificial Intelligence. JELIA 2010. Lecture Notes in Computer Science(), vol 6341. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15675-5_24
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DOI: https://doi.org/10.1007/978-3-642-15675-5_24
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