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The properties of metric Boolean algebras and their application to approximate reasoning in \(F(S)\). (Chinese. English summary) Zbl 1199.03052

Summary: The properties of metric Boolean algebras are discussed. The distance between an element and a filter of a metric Boolean algebra is given, and the distance between different filter is also given. As an application, the distance between a formula and a \(\varGamma\)-conclusion set and the different \(\varGamma\)-conclusion set of a logical metric space \( (F (S),\rho)\) is described.

MSC:

03G05 Logical aspects of Boolean algebras
03G25 Other algebras related to logic
68T37 Reasoning under uncertainty in the context of artificial intelligence
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