erally hard to understand and their integration with
explicit expressed knowledge (e.g. opinions) is often
impossible. The second group is the part of transpar-
ent diagnostic models (e.g. graphical models) (Cow-
ell et al., 2003), (Kohler and Friedman, 2009), which
structure and parameters may have own physical in-
terpretation or contractual meaning and which make it
easier to integrate knowledge from multiple sources.
In this paper we focus on transparent forms of knowl-
edge representation for complex objects treating only
black box models as a source of data reconstruction
or a source of preprocessed input data.
Aspects of diagnostic knowledge management
concerned with modeling, storaging, updating and
verification of consistency of modeled knowledge are
main objective of this paper. The general model-
ing process is conducted with the use of multimodal
statement networks introduced in (Cholewa, 2010),
including, inter alia, types of network layers, meth-
ods of layer interoperability, as well as construction
and development of models. Furthermore, methods
of verification of consistency of modeled knowledge
were addressed as well. Multimodal models enrich
the available range of methods (Cholewa, 2010). To
name a few, examples may include multiaspect mod-
els (Skupnik, 2009) or models with context inference
(Timofiejczuk, 2012).
Finally, the authors presented free software (REx)
(Cholewa et al., 2011), which provides a possibility to
perform actions described in this paper that are related
to modeling and management of diagnostic knowl-
edge.
2 MULTIMODAL STATEMENT
NETWORKS
One of the convenient methods of information rep-
resentation in expert systems includes a statement
which is equivalent to assertion on recognition of an
indicative expression resulting from observed facts,
or representing an opinion. One may distinguish be-
tween simple and complex statements. Simple state-
ments are presented in the form of a pair < c, v >,
where c is the content of the statement, and v is the
value (e.g. logical value) of the statement. Com-
plex statements, however, are presented in the form
of < c, v >, where c is a set of possible variants of
the statement content, and v is a set of values of sub-
sequent variants of its content. Provided the state-
ment content is constant, and that the set of variants
of statement content is an exhaustive set of mutually
excluding variants of statement content, then the com-
plex statements may be represented by means of ade-
quate sets of simple statements.
In a set of statements, one can observe a set of
statements with known values, and a set of statements
with unknown values. The statements of known val-
ues include primary statements whose values were di-
rectly determined by external processes, such as mea-
surement data or a user input, as well as constant
statements whose values were arbitrarily assumed by
e.g. a knowledge engineer. In turn, a set of state-
ments of unknown values includes secondary state-
ments whose values are strictly contingent on other
statement values, and are not directly defined by ex-
ternal processes as well as isolated statements inde-
pendent of other statements. The main purpose of
inference is to determine values of secondary state-
ments for desired values of primary statements. A di-
vision into the sets of primary and secondary state-
ments is subject to change depending on data avail-
able from external sources at a given moment of time.
For instance in the case of diagnosis process sec-
ondary statements are related mainly to fault or mal-
function and primary statements to observed process
variables or user input. In the case of root cause
recognition, the secondary statements are related to
the unknown causes of observed faults (primary state-
ments). Because the process of inference is bidirec-
tional the first case of inference and the second one
can be conducted in the same model.
Statements may be studied as approximate state-
ments provided their content and/or values are ap-
proximate. Approximate values of statements can be
defined as degrees of truth or degrees of belief in the
truth of statements. The value of approximate state-
ments s is to be considered as a point value b(s),
or as an interval value, e.g. b(s) = [0.6, 0.9]. Such
an approach also allows for considering the point
value as a special form of an interval value, e.g. for
b(s) = 0.3 the interval value shall be represented as
b(s) = [0.3, 0.3].
In (Cholewa, 2010) the author introduced con-
cepts of multimodal statement networks (multimodal
model) where selected nodes represent statements.
The network structure is a multilayer one and is de-
fined as a directed hypergraph described by ordered
triple:
< V, E, Γ >, (1)
where V is the set of all hypergraph vertices, E is the
set of hypergraph edges, and Γ is the set of hyper-
graph modes representing selected layers of the net-
work (Heath and Sioson, 2009). The network layers
are defined as
Γ
n
= {V
n
, E
n
}, Γ
m
= {V
m
, E
m
}, (2)
where V
n
⊂ V , V
m
⊂ V , E
m
⊂ E, E
n
⊂ E. It is as-
sumed that card(V
m
∩V
n
>
/
0) and it is estimated that
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