Further Developments in the Terminological Theory of Data

1
Further Developments in the Terminological Theory
of Data

• Frank Farance
• Farance Inc
• Daniel Gillman
• US Bureau of Labor Statistics

2
Introduction

• Statistical Data
• Axioms
• Operations
• Datatypes
• Values
• Statistical Data (again)
• Ontologies

3
Statistical Data

• Categorical
• Nominal
• Sex categories
• Ordinal
• Preference Scale
• Quantitative
• Interval
• Temperature C (Celsius)
• Ratio
• Temperature K (Kelvin)

4
Axioms

• All Data Have Equality
• Nominal
• Exact, Non-numeric, Cardinality
• Ordinal
• Nominal Order
• Interval
• Numeric
• Ratio
• Interval Approximate

5
Operations

• Nominal
• Determine Equality, Cardinality No Arithmetic
• Ordinal
• Determine Equality, Cardinality, Order Averages
• Interval
• Equality Addition / Subtraction
• Ratio
• Equality Multiplication / Division

6
Datatypes

• Compare with Statistical Data Typology
• Assertions
• Axioms
• Characterizing Operations
• Operations
• Value Space
• ??

7
Values

• 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

8
Statistical Data (again)

• 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

9
Ontologies

• Specification of a Conceptualization
• Common definition
• Tom Gruber, 1994
• Concept system with an associated computational
  model
• Farance and Gillman, 2005
• Value space gt Concept System
• Assertions and Characterizing operations gt
  Computational model

10
Ontologies

• Datatype is an ontology
• Also, Concepts have roles
• Property
• Characteristic
• Values, Variables, Populations
• Concept system
• Computational Model
• Automatically create variables and associated
  allowed values

11
Ontologies

• Two ontologies for statistical survey work
• Datatypes (computational model for data)
• Variables (semantical model for data)
• How to tie these together?
• Values