Rob Nehmer
Oakland 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
6th University of Kansas International Conference on XBRL
April 25 – 27, 2013
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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
6th University of Kansas International Conference on XBRL
April 25 – 27, 2013
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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-WandWeber modeling constructs to it.
6th University of Kansas International Conference on XBRL
April 25 – 27, 2013
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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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6th University of Kansas International Conference on XBRL
April 25 – 27, 2013
5
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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
6th University of Kansas International Conference on XBRL
April 25 – 27, 2013
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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
6th University of Kansas International Conference on XBRL
April 25 – 27, 2013
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6th University of Kansas International Conference on XBRL
April 25 – 27, 2013
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XBRL
Abstract
Model
Map
Conceptual
Framework
Ontology
Map
Qualitative
Characteristics
Design
Must
emphasize
value
adding
activities
Conceptual
Model
Formalization/
conceptualization
6th University of Kansas International Conference on XBRL
April 25 – 27, 2013
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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
6th University of Kansas International Conference on XBRL
April 25 – 27, 2013
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Axioms
Deduction
s
Derive
d
Theor
y
Account
Transact
Ownership
6th University of Kansas International Conference on XBRL
April 25 – 27, 2013
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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.
6th University of Kansas International Conference on XBRL
April 25 – 27, 2013
12
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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
6th University of Kansas International Conference on XBRL
April 25 – 27, 2013
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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 =
𝐹 𝑖𝑓 𝜎 𝑎𝑛𝑑 𝜏 𝑎𝑟𝑒 𝑏𝑜𝑡ℎ 𝑓𝑎𝑙𝑠𝑒 𝑓𝑜𝑟 𝑆𝑆
𝑇 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒
6th University of Kansas International Conference on XBRL
April 25 – 27, 2013
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A
1
C
5
B
2
4
3
φ1
φ2
1
E
4
F
G
9
6th University of Kansas International Conference on XBRL
April 25 – 27, 2013
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A
1
5
-
2
4
*
3
C
0
B
+
/
φ1
φ3
φ2
Risk
Control
6th University of Kansas International Conference on XBRL
April 25 – 27, 2013
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φ1
t
g(t)
f(t)
h(t)
f(x)
g(x)
f(x-1)
g(x-1)
f(x-2)
g(x-2)
φ2
6th University of Kansas International Conference on XBRL
April 25 – 27, 2013
17
-
1
5
2
4
φ3
*
3
0
+
/
φ2
φ4
φ1
Risk
Control
6th University of Kansas International Conference on XBRL
April 25 – 27, 2013
18
Applications
Services
Operating System
BIOS
CPU
6th University of Kansas International Conference on XBRL
April 25 – 27, 2013
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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
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6th University of Kansas International Conference on XBRL
April 25 – 27, 2013
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