Algebras of intervals and a logic of conditional assertions

Journal of Philosophical Logic 33 (5):497-548 (2004)
Intervals in boolean algebras enter into the study of conditional assertions (or events) in two ways: directly, either from intuitive arguments or from Goodman, Nguyen and Walker's representation theorem, as suitable mathematical entities to bear conditional probabilities, or indirectly, via a representation theorem for the family of algebras associated with de Finetti's three-valued logic of conditional assertions/events. Further representation theorems forge a connection with rough sets. The representation theorems and an equivalent of the boolean prime ideal theorem yield an algebraic completeness theorem for the three-valued logic. This in turn leads to a Henkin-style completeness theorem. Adequacy with respect to a family of Kripke models for de Finetti's logic, Łukasiewicz's three-valued logic and Priest's Logic of Paradox is demonstrated. The extension to first-order yields a short proof of adequacy for Körner's logic of inexact predicates
Keywords Philosophy
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DOI 10.1023/B:LOGI.0000046072.61596.32
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References found in this work BETA
Graham Priest (1979). Logic of Paradox. Journal of Philosophical Logic 8 (1):219-241.
Peter Milne (1997). Bruno de Finetti and the Logic of Conditional Events. British Journal for the Philosophy of Science 48 (2):195-232.

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