Łukasiewicz logic and the foundations of measurement

Studia Logica 40 (3):209 - 225 (1981)
The logic of inexactness, presented in this paper, is a version of the Łukasiewicz logic with predicates valued in [0, ∞). We axiomatize multi-valued models of equality and ordering in this logic guaranteeing their imbeddibility in the real line. Our axioms of equality and ordering, when interpreted as axioms of proximity and dominance, can be applied to the foundations of measurement (especially in the social sciences). In two-valued logic they provide theories of ratio scale measurement. In multivalued logic they enable us to treat formally errors arising in nominal and ordinal measurements.
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    References found in this work BETA
    M. Katz (1980). Inexact Geometry. Notre Dame Journal of Formal Logic 21 (3):521-535.
    Fred S. Roberts (1973). Tolerance Geometry. Notre Dame Journal of Formal Logic 14 (1):68-76.
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