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Further Developments in the Terminological Theory of Data. Frank Farance Farance Inc Daniel Gillman US Bureau of Labor Statistics. Introduction. Statistical Data Axioms Operations Datatypes Values Statistical Data (again) Ontologies. Statistical Data. Categorical Nominal

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### Further Developments in the Terminological Theory of Data

Frank Farance

Farance Inc

Daniel Gillman

US Bureau of Labor Statistics

• Statistical Data

• Axioms

• Operations

• Datatypes

• Values

• Statistical Data (again)

• Ontologies

• Categorical

• Nominal

• Sex categories

• Ordinal

• Preference Scale

• Quantitative

• Interval

• Temperature ˚C (Celsius)

• Ratio

• Temperature ˚K (Kelvin)

• All Data Have Equality

• Nominal

• Exact, Non-numeric, Cardinality

• Ordinal

• Nominal + Order

• Interval

• Numeric

• Ratio

• Interval + Approximate

• Nominal

• Determine Equality, Cardinality; No Arithmetic

• Ordinal

• Determine Equality, Cardinality, Order; Averages

• Interval

• Ratio

• Equality; Multiplication / Division

• Compare with Statistical Data Typology

• Assertions

• Axioms

• Characterizing Operations

• Operations

• Value Space

• ??

• Value = Element of Value Space

• Share Notion of Equality

• Equality Differs Across Datatypes

• Compare Integer Versus Code

• Is a Concept

• Equality – i.e. compare concepts

• Integer

• Integer built from natural numbers

• Natural number built from sets

• Code

• Designation of (points to) concept

• Concept description stored in repository

• Population

• A concept

• Therefore, has characteristics

• Variables

• Not population characteristics

• Values

• Properties of characteristic

• Determinant (P) versus Determinable (Ch)

• What is determined (observed) about respondent

• Specification of a Conceptualization

• Common definition

• Tom Gruber, 1994

• Concept system with an associated computational model

• Farance and Gillman, 2005

• Value space => Concept System

• Assertions and Characterizing operations => Computational model

• Datatype is an ontology

• Also, Concepts have roles

• Property

• Characteristic

• Values, Variables, Populations

• Concept system

• Computational Model

• Automatically create variables and associated allowed values

• Two ontologies for statistical survey work

• Datatypes (computational model for data)

• Variables (semantical model for data)

• How to tie these together?

• Values