Metric Boolean Algebras and an Application to Propositional Logic
Boolean algebra, probability measure, size, similarity degree, approximate reasoning, propositional logic
Abstract
Let B be a Boolean algebra and Ω be the set of all homomorphisms from B into D, and μ be a probability measure on Ω . We introduce the concepts of sizes of elements of B and similarity degrees of pairs of elements of B by means of μ , and then define a metric on B . As an application, we propose a kind of approximate reasoning theory for propositional logic.
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References
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B Div(Γ) sup{d(A, B)|A, B ∈ D(Γ)} ≤ D(Γ).
Published
2011-07-11
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