A universal theory of measure and integral on valuation spaces with respect to diverse implication operators

摘要

Vluation spaces with respect to diverse implication operators areinvestigated in a unified way where the Lebesgue measure is acommonly used measure, and it is proved that all the logic for- mulasare measurable functions with respect to popularly used implicationoperations. The comcept of t- (α-tautology) is introduced and rulesof generalized modus ponens (MP) and hypothetic syllogism (HS) areestablished in the sense of semantics.