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- W4378650055 abstract "The first aim of this paper is to prove a topological completeness theorem for a weak version of Stalnaker’s logic KB of knowledge and belief. The weak version of KB is characterized by the assumption that the axioms and rules of KB have to be satisfied with the exception of the axiom (NI) of negative introspection. The proof of a topological completeness theorem for weak KB is based on the fact that nuclei (as defined in the framework of point-free topology) give rise to a profusion of topological belief operators that are compatible with the familiar topological knowledge operator Int. Thereby a canonical topological model for weak KB can be constructed. For this canonical model a truth lemma for the modal operators K and B holds such that a completeness theorem for weak KB can be proved in the familiar way. The second aim of this paper is to show that the topological interpretation of knowledge Int comes along with a complete Heyting algebra of belief operators N° that all fit the knowledge operator Int in the sense that the pairs (Int, N°) satisfy all axioms of weak KB. This amounts to a pluralistic relation between knowledge and belief: Knowledge does not fully determine belief, rather it designs a conceptual space for belief operators where different (competing) belief operators coexist that can be compared with each other." @default.
- W4378650055 created "2023-05-30" @default.
- W4378650055 creator A5066635576 @default.
- W4378650055 date "2023-05-29" @default.
- W4378650055 modified "2023-09-25" @default.
- W4378650055 title "Completeness and Doxastic Plurality for Topological Operators of Knowledge and Belief" @default.
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- W4378650055 doi "https://doi.org/10.1007/s10670-023-00666-7" @default.
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