1. Rob Nehmer Oakland University Rochester MI 6th University of Kansas International Conference on XBRL April 25 – 27, 2013 1

2.  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, 20132

3.  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, 20133

4.  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, 20134

5.  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, 20135

6.  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, 20136

7.  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, 20137

8. 8

9. 9 XBRL Abstract Model Conceptual Framework Ontology Qualitative Characteristics Conceptual Model Map Formalization/ conceptualization Design Must emphasize value adding activities

10.  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, 201310

11. 6th University of Kansas International Conference on XBRL April 25 – 27, 201311 Axioms Deduction s Derive d Theor y Ownership TransactAccount

12.  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(z i ) 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 = M i 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 M i. 6th University of Kansas International Conference on XBRL April 25 – 27, 201312

13.  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, 201313

14. 6th University of Kansas International Conference on XBRL April 25 – 27, 201314

15. 6th University of Kansas International Conference on XBRL April 25 – 27, 201315 1 2345 B C A φ1φ1 φ2φ2 1 4 9 EFG

16. 6th University of Kansas International Conference on XBRL April 25 – 27, 201316 1 2 34 5 0 -+/* B C A Risk Control φ1φ1 φ2φ2 φ3φ3

17. 6th University of Kansas International Conference on XBRL April 25 – 27, 201317 t f(t) h(t) g(t) f(x) f(x-1)f(x-2) g(x) g(x-1)g(x-2) φ1φ1 φ2φ2

18. 6th University of Kansas International Conference on XBRL April 25 – 27, 2013 18 1 2 34 5 0 -+/* Risk Control φ1φ1 φ2φ2 φ3φ3 φ4φ4

19. 6th University of Kansas International Conference on XBRL April 25 – 27, 201319 Applications Services Operating System BIOS CPU

20. 6th University of Kansas International Conference on XBRL April 25 – 27, 201320 Vending Machine Vendor Business Client A Business Client C Business Client B Internet Client 1 Internet Client 2 φ1φ1 φ2φ2

21. 6th University of Kansas International Conference on XBRL April 25 – 27, 201321