Representation theory treatment of measurement semantics for ratio, ordinal and nominal scales

Within the scope of the representational theory a formal framework for description of semantic aspects of measurement on different scales is proposed. This is done by means of a first-order formal logical system consisting of a set of empirical predicates which play the part of a data structure in the framework, a set of operations by means of which syntactically correct statements can be formed; a set of axioms being true statements and a set of numerical statements which is an aggregation of potential measurement results carrying a meaningful load. On this basis the notation of semantic information on various scales is introduced and some common claims about the measurement semantic information are derived. The proposed framework can be used for the development of concepts, principles and guidelines which can support decision making in the arrangement of design and the application of measurement information systems.