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

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XBRL Model Ontologies: Structuring Business Intelligence

Rob NehmerOakland University

Rochester MI

6th University of Kansas International Conference on XBRL April 25 – 27, 2013

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Formal Modeling and Ontology Development

Syntax and Semantics An Ontological Framework Model Theory Cases


Overview

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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



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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.



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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)



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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


Syntax and Semantics

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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


Syntax and Semantics

86th University of Kansas International Conference on XBRL

April 25 – 27, 2013

Syntax and Semantics in Teller (2008)


April 25 – 27, 2013

An Ontological Framework

XBRL Abstract Model

Conceptual Framework Ontology

Qualitative Characteristic

s

Conceptual Model

Map Map

Formalization/conceptualization

Design

Must emphasize value adding

activities

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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


Model Theory


April 25 – 27, 2013

Model Theory (cont.)

AxiomsDeduction

s

Derived

Theory

Language

Ownership

Transact

Account

InterpretationFunction

Real World

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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.



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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



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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 =




April 25 – 27, 2013

Case 1 – Disparate Semantics

1

2

34

5 B

C

ASyntactic Domains

Semantics

φ1 φ2

1

4

9

E F G


April 25 – 27, 2013

Case 2 –Homogenous Semantics

1

2

34

5

0

-

+

/

*B

C

ASyntactic Domains

Risk

Control

Semantics

φ1

φ2

φ3


April 25 – 27, 2013

Case 3 – Chained Semantics

t

f(t)

h(t)

g(t)

f(x)

f(x-1)

f(x-2)

g(x)

g(x-1)

g(x-2)

φ1

φ2


Case 4 – Mixed Models

1

2

34

5 0

-

+

/

*

Syntactic Domains

Risk

Control

Semantics

φ1

φ2

φ3φ4


April 25 – 27, 2013

Example – Classic Computer Architectures

Applications

Services

Operating System

BIOS

CPU


April 25 – 27, 2013

Example – Business Unit Unique IDs

Vending Machine Vendor

Business Client A

Business Client C

Business Client B

Internet Client 1

Internet Client 2

φ1

φ2


April 25 – 27, 2013

Questions?

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

Documents

accounting ontology

xbrl specs strings of

ontology development

ontology of ais

set of symbols

integer symbols

formal rep of accounting

formal modeling