XBRL Model Ontologies: Structuring Business Intelligence

1. XBRL Model Ontologies: Structuring Business Intelligence Rob Nehmer Oakland University Rochester MI 6th University of Kansas International Conference on XBRL April 25 – 27, 2013

2. Overview • Formal Modeling and Ontology Development • Syntax and Semantics • An Ontological Framework • Model Theory • Cases 6th University of Kansas International Conference on XBRL April 25 – 27, 2013

3. Formal Modeling and Ontology Development • Teller (2008) – XBRL as a formal rep of accounting? No, just to store data • Swanson and Freeze (2009) • Ontology: rendering unstructured contexts into structured frameworks • Combine FASB conceptual framework, presentation (statement), and GAAP codification • Value chain (internal) vs. valuation model (external) • No XBRL 6th University of Kansas International Conference on XBRL April 25 – 27, 2013

4. Formal Modeling and Ontology Development • Lupasc et al (2010) – REA framework as ontology of AIS, add value chain • Geerts and McCarthy (1999) – OO and semantic approach which introduces ontology as a future development to include enterprise knowledge management • Guan et al (2006) – limitations of REA wrt ontology. Suggest adding Bunge-Wand-Weber modeling constructs to it. 6th University of Kansas International Conference on XBRL April 25 – 27, 2013

5. Formal Modeling and Ontology Development • Sugumaran and Storey (2002) – prototype an ontology management system • Chou et al (2008) • Operationalize Sugumaran and Storey in accounting context in five stages • Collect accounting information from enterprise • Analyze the collected items • Create accounting taxonomy • Use DB Schema to implement items and relationships between them • Generate accounting ontology (not done) 6th University of Kansas International Conference on XBRL April 25 – 27, 2013

6. Syntax and Semantics • Formalizations (including the XBRL specs) • Strings of symbols comprise the language of the formalization • Syntax • Manipulation of strings by inference, parsing and validation tools • Purely formal • Concerned with the production of valid sentences, i.e., strings of symbols 6th University of Kansas International Conference on XBRL April 25 – 27, 2013

7. Syntax and Semantics • Semantics • “Meanings” attached to the strings • Formally: the meanings and an interpretation function mapping the formalism (syntax) to the meaning (semantics) • Natural/hermeneutic: interpreting the meaning and mapping dynamically back to the formal representation in syntax 6th University of Kansas International Conference on XBRL April 25 – 27, 2013

8. Syntax and Semantics in Teller (2008) 6th University of Kansas International Conference on XBRL April 25 – 27, 2013

9. An Ontological Framework Conceptual Framework Ontology XBRL Abstract Model Qualitative Characteristics Map Map Design Formalization/ conceptualization Conceptual Model Must emphasize value adding activities 6th University of Kansas International Conference on XBRL April 25 – 27, 2013

10. Model Theory • A branch of mathematics concerned with constructing models with a concrete operationalization of semantic truth • Includes: • The symbols of a formal syntactic language, L • A set of objects about which the language has meaningful thing to say, M • An interpretation function, φ, between the symbols of L and the objects of M 6th University of Kansas International Conference on XBRL April 25 – 27, 2013

11. Model Theory (cont.) Language Derived Theory Interpretation Function Axioms Deductions Real World 6th University of Kansas International Conference on XBRL April 25 – 27, 2013

12. Model Theory (cont.) • Example: Primary Mappings • Map the set of symbols for constants in L, the integer symbols and symbols for vectors of integers to, for example, φ(zi) in M. • The functions are mapped from the set of symbols for functions in L, that is, f and θ, of degree i to, for example, φ(f) on M X M X...X M = Mi with meanings in M as in 1 above. • The predicates are mapped from the set of symbols for predicates in L of degree i to a subset contained in Mi. 6th University of Kansas International Conference on XBRL April 25 – 27, 2013

13. Model Theory (cont.) • Process • Create/discover the semantical system including the interrelationships between its components • Create the syntactic language to describe the semantical system • Create the interpretation functions between the semantical and syntactic systems 6th University of Kansas International Conference on XBRL April 25 – 27, 2013

14. Model Theory (cont.) • Example: Truth Function of the Interpretation • φ maps relation symbols of a semantical system with degree i from each predicate in a predicate calculus with the same degree. • φ maps the constants of the semantical system from each individual of the predicate calculus. • σ˅τ = 6th University of Kansas International Conference on XBRL April 25 – 27, 2013

15. Case 1 – Disparate Semantics Syntactic Domains φ1 φ2 Semantics 6th University of Kansas International Conference on XBRL April 25 – 27, 2013

16. Case 2 –Homogenous Semantics Syntactic Domains φ1 φ3 φ2 Semantics 6th University of Kansas International Conference on XBRL April 25 – 27, 2013

17. Case 3 – Chained Semantics φ1 φ2 6th University of Kansas International Conference on XBRL April 25 – 27, 2013

18. Case 4 – Mixed Models Syntactic Domains φ2 φ4 φ3 φ1 Semantics 6th University of Kansas International Conference on XBRL April 25 – 27, 2013

19. Example – Classic Computer Architectures 6th University of Kansas International Conference on XBRL April 25 – 27, 2013

20. Example – Business Unit Unique IDs Vending Machine Vendor φ1 Business Client A Business Client B Business Client C φ2 Internet Client 1 Internet Client 2 6th University of Kansas International Conference on XBRL April 25 – 27, 2013

21. Questions? 6th University of Kansas International Conference on XBRL April 25 – 27, 2013