=Paper=
{{Paper
|id=Vol-1442/paper_32
|storemode=property
|title=An Ontology of Organizational Knowledge
|pdfUrl=https://ceur-ws.org/Vol-1442/paper_32.pdf
|volume=Vol-1442
|dblpUrl=https://dblp.org/rec/conf/ontobras/AraujoZA15
}}
==An Ontology of Organizational Knowledge==
<pdf width="1500px">https://ceur-ws.org/Vol-1442/paper_32.pdf</pdf>
<pre>
               An ontology of organizational knowledge
      Anderson Beraldo de Araújo1 , Mateus Zitelli1 , Vitor Gabriel de Araújo1
                            1
                                Federal University of ABC (UFABC)
                                  Santo André, São Paulo – Brazil
 anderson.araujo@ufabc.edu.br,{zitellimateus,araujo.vitorgabriel}@gmail.com


    Abstract. One of the main open problems in knowledge engineering is to un-
    derstand the nature of organizational knowledge. By using a representation of
    directed graphs in terms of first-order logical structures, we defined organiza-
    tional knowledge as integrated relevant information about relational structures.
    We provide an algorithm to measure the amount of organizational knowledge
    obtained via a research and exhibit empirical results about simulations of this
    algorithm. This preliminary analysis shows that the definition proposed is a
    fruitful ontological analysis of knowledge management.

1. Introduction
According to [1], Knowledge management (KM) has produced a bunch of definitions that
helps us to understand organizational knowledge, the kind of knowledge that we find in
organizations. Nonetheless, there is no universal approach to the different kind of defi-
nitions available. We are in need of an ontological analysis of organizational knowledge
that is capable to unify the different notion of knowledge relevant to bussiness.
        Indeed, organizational knowledge has been thought according to four fundamen-
tal types [3, 4]. The first one we can call the mental view of knowledge. According to
this standpoint, knowledge is a state of mind. In the mental view to manage knowledge
involves to regulate the provision of information controls and to improve individuals ca-
pacity of applying such a knowledge. The second view is the objectual view of knowledge.
Here knowledge is an object, something that we can store and manipulate. In the objec-
tual approach manage knowledge becomes a process of stock managing, in which we
could control the offers and the demands of individuals as parts of an integrated process
inside a company. To take knowledge as a procedural phenomenon of information is the
third approach, which we can call the procedural view of knowledge. In the procedural
perspective knowledge becomes a process of applying expertise, so to manage means to
manage the flows of information, such as creation process, conversion techniques, circu-
lation processes and carrying out processes. The fourth perspective is the credential view
of knowledge. In this approach knowledge is a credential for accessing information. In
this case, KM focus on how you manage the credentials to access and what you expect to
retrieve, granting the content as the result of a process.
       The credential view of knowledge is the standard approach that has been applied
in companies nowadays [5]. KM faces knowledge as the potential of influencing actions.
By doing so companies consider KM as a process of granting the right competences to the
chosen individuals. The focus is to provide the specific know-how to the realization of the
processes and to grant that every processes has its correspond knowledge unit correlated.
         In this paper we provide an logical method to quantify knowledge that can be used
in all the four views of organizational knowledge and present computational results about
them all. Quantitative indicators of knowledge can create benefits such as decreasing op-
erational cost, product cycle time and production time while increasing productivity, mar-
ket share, shareholder equity and patent income. They can drive decisions to invest on
employees skills, quality strategies, and define better core business processes. Moreover,
if applied to the customers, quantitative indicators can create an innovative communica-
tion platform, where the information of the clients can be quickly collected and processed
into relevant decision indicators in specific terms such as abandoning one line of product,
on the one hand, and investing, on the other [6, 7].
        One way to unify this different approaches to KM is to outline a minimal ontology
of business processes, in a Quinean sense. According to Quine, as it is well known, “to
be is to be the value of a variable” [8]. In other words, ontology is the collection of
entities admitted by a theory that is committed to their existence. In the present context,
we call minimal ontology the ontology shared by every theory that successfully describes
a processes as a organizational one. Our fundamental idea is to define organizational
structures, using the general concept of first-order logical structure (Section 2). Thus, we
propose a mathematical definition of information about organizational structures, based
on the abstract notion of information introduced here for the first time (Section 3). The
next step is to conceive organizational knowledge as justified relevant information about
organizational structures (Section 4). From this approach we formulate an algorithm and
simulate them (Section 5).

2. Organizational structures
We begin by some usual definitions in logic - more details can be found in [9]. The first
one is associated to the syntax of organizational structures.
Definition 2.1. A signature is a set of symbols S = C ∪ P ∪ R such that C = {c1 , . . . , ck }
is a set of constants, P = {P1 , . . . , Pm } is a set of property symbols, R = {R1 , . . . , Rn }
is a set of relation symbols. A formula over S is recursively defined in the following way:
    1. If τ, σ ∈ C, ρ ∈ P , δ ∈ R, then ρτ and δτ σ are formulas, called predicative
       formulas;
    2. If φ and ψ are formulas, then ¬φ, φ ∧ ψ, φ ∨ ψ, φ → ψ and φ ↔ ψ are formulas,
       called propositional formulas.
        A theory over S is just a set of formulas.
       Now we recall the general notion of first-order structure.
Definition 2.2. Given a signature S, a structure A over S is compounded of:
    1. A non-empty set dom(A), called the domain of A;
    2. For each constant τ in S, an element τ A in dom(A);
    3. For each property symbol ρ in S, a subset ρA of dom(A).
    4. For each relation symbol δ in S, a binary relation δ A on dom(A).
        We write A(φ) = 1 and A(φ) = 0 to indicate, respectively, that the formula φ
is true, false, in the structure A. Besides, we have the usual definitions of the logical
operators ¬φ, φ ∧ ψ, φ ∨ ψ, φ → ψ and φ ↔ ψ on a structure A. In particular, we say that
a theory T is correct about A if A(φ) = 1 for all φ ∈ T .
                                      Figure 1. Bussiness process


Definition 2.3. Given a signature S, an organizational structure AT over S is com-
pounded of a structure A over S, a theory T over S which is correct about A and ex-
presses facts about a business process.
         The idea inside the definition of organizational structures is that they are just log-
ical structures with a fundamental theory about how the processes works. In the propo-
sition 2.1, we show that business processes are indeed special cases of organizational
structures.
Proposition 2.1. Business processes are organizational structures.


Proof. According to [10], a business processes is a tuple (N, E, κ, λ), in which:

     1. N is the set of nodes;
     2. E ⊆ N × N is the set of edges;
     3. κ : N → T is a function that maps nodes to types T ;
     4. λ : N → L is a function that maps nodes to labels L.

       Let L = {l1 , . . . , lk } be the set of labels and T = {T1 , . . . , Tn } be the set of types.
Thus, we can define the organization structure A with domain dom(A) = {li : 1 ≤ i ≤
k}, subsets T1 , . . . , Tn of L and the relation E.

        In what follows, we write “α” = β to mean that the symbol β is a formal repre-
sentation of the expression α. Besides, Xβ is the interpretation of β in the structure A,
where X is a set over the domain of A. The elements of the domain dom(A) of a structure
A are indicated by bars above letters.
Example 2.1. Let S = C ∪ P ∪ R be the signature such that C = {i, f, o, r, s, v},
P = {E, A} and R = {L}, in which “initial” = i, “final” = f , “order” = o,
“receive goods” = r, “store goods” = s, “verify invoice” = v, “is event” = E,
“is activity” = A and “is linked to” = L. In this case, we can define the organizational
structure AT over S below, where T = :

     1. dom(A) = {ī, f¯, ō, r̄, s̄, v̄};
     2. iA = ī, f A = f¯, oA = ō, rA = r̄, sA = s̄, v A = v̄;
     3. E A = {ī, f¯} and AA = {ō, r̄, s̄, v̄};
     4. LA = {(ī, ō), (ō, r̄), (r̄, s̄), (r̄, v̄), (s̄, f¯), (v̄, f¯)}.

       The organizational structure AT defined above represents the bussiness process in
Figure 1.
                            Figure 2. Extended bussiness process


3. Structural information
We turn now to the fundamental notion associated to knowledge, namely, information.
The concept of information is polysemantic [11]. In this work we think of information
in semantic terms. Since we are going to define a notion of information about organiza-
tional structures, we will call it structural information. Roughly speaking, the structural
information of an organizational structure is the set of insertions and extractions that we
need to perform in order to create this structure.
Definition 3.1. Let AT be an organizational structure over S. An insertion of the symbol ω
into AT is an organizational structure ATi such that ATi is an structure over S 0 = S ∪ {ω}
with the following properties:

    1. ATi (τ ) = A(τ ) for all τ 6= ω such that τ ∈ S;
    2. If ω is a constant in S, then dom(ATi ) = dom(A) and ATi (ω) 6= A(ω), but if ω is
       a constant not in S, then dom(ATi ) = dom(A) ∪ {a} and ATi (ω) = a;
    3. If ω is a property symbol, then dom(ATi ) = dom(A) ∪ {a} and ATi (ω) = A(ω) ∪
       {a};
    4. If ω is a relation symbol, then dom(ATi ) = dom(A) ∪ {a1 , a2 } and ATi (ω) =
       A(ω) ∪ {(a1 , a2 )}.
Example 3.1. Consider the organizational structure AT over S from example 2.1. Define
the signature S 0 = C 0 ∪ P 0 ∪ R0 equals to S except by the fact that C 0 = C ∪ {t}, where
“transfer goods” = t. Thus, the organizational structure ATi defined below is an insertion
of t into AT :

    1. dom(Ai ) = dom(A) ∪ {t̄};
    2. tA = t̄ and τ Ai = τ A for τ ∈ C;
    3. E Ai = E A and AAi = AA ∪ {t̄};
    4. LAi = LA − {(ō, r̄)} ∪ {(ō, t̄), (t̄, r̄)}.

       The organizational structure ATi represents the business process in Figure 2.
Definition 3.2. Let A be an S-structure. An element a ∈ dom(A) is called free for the
symbol ω ∈ S if there is no constant τ ∈ S with A(τ ) = A(ω) neither a property symbol
α such that a ∈ A(α) and a = A(ω) nor a relation symbol β such that (a1 , a2 ) ∈ A(β)
and ai = A(ω) for i ∈ {1, 2}.
       If δ is a relation symbol, we write A(δ)i to denote element ai of (a1 , a2 ) ∈ A(δ).
Definition 3.3. Let AT be an organization structure over S. An extraction of the symbol
ω from AT is a database ATe such that ATe is an structure over S 0 = S − {ω} with the
following properties:

    1. ATe (τ ) = A(τ ) for all τ 6= ω such that τ ∈ S 0 ;
                           Figure 3. Contracted bussiness process


     2. If ω is a constant not in S, then dom(ATe ) = dom(A), but if ω is a constant in S,
        dom(ATe ) = dom(A) − {A(ω)} in the case of A(ω) being free for ω, otherwise,
        dom(ATe ) = dom(A);
     3. If ω is a property symbol not in S, then dom(ATe ) = dom(A), but if ω is a property
        symbol in S, then dom(ATe ) = dom(A) − {A(ω)}, where A(ω) is an element free
        for ω, and ATe (ω) = A(ω) − {A(ω)};
     4. If ω is a relational symbol not in S, then dom(ATe ) = dom(A), but if ω is a
        relational symbol in S, then dom(ATe ) = dom(A)−{A(ω)1 , A(ω)2 }, where A(ω)i
        is an element free for ω, and ATe (ω) = A(ω) − {(A(ω)1 , A(ω)2 )}.
Example 3.2. Consider the organizational structure AT over S from example 2.1. Define
the signature S 00 = C 00 ∪ P 00 ∪ R00 equals to S except by the fact that C 0 = C − {r}. Thus,
the organizational structure ATe defined below is an extraction of r from AT :
    1. dom(Ae ) = dom(A) − {r̄};
    2. τ Ae = τ A for τ ∈ C 00 ;
    3. E Ae = E A and AAe = AA − {r̄};
    4. LAe = LA − {(ō, r̄)} ∪ {(ō, s̄), (ō, v̄)}.
        The organizational structure AeT represents the business process in Figure 3.
         Strictly speaking, the organizational structure ATe in example 3.2 is not an extrac-
                                  e                                                          e
tion from AT . For example, LA = LA − {(ō, r̄)} ∪ {(ō, s̄), (ō, v̄)}, which means that LA
was made of insertions in AT as well. Since we are interested here in practical applica-
tions, we will not enter in such a subtle detail - we delegate that to a future mathematically
oriented article. This point is important because it shows that to build new organizational
structures from a given one is, in general, a process that use many steps. We explore this
idea to define a notion of structural information.
Definition 3.4. An update U A of an organizational structure AT over S is a finite se-
quence U A = (ATj : 0 ≤ j ≤ n) such that AT0 = AT and each ATj+1 is an insertion into or
an extraction from ATj . An update U A = (ATj : 0 ≤ j ≤ n) is satisfactory for a formula
φ if, and only if, either An (φ) = 1 or An (φ) = 0. In the case of a satisfactory update
U A for φ, we write U A (φ) = 1 to denote that An (φ) = 1 and U A (φ) = 0 to designate
that An (φ) = 0. A recipient over in organizational structure AT for a formula φ is a
non-empty collection of updates U of AT satisfactory for φ.
Example 3.3. Given the organizational structures AT , ATi and ATe from the previous
examples. The sequences (AT , ATi ) and (AT , ATe ) are updates of AT that generates, re-
spectively, the business processes in Figures 2 and 3.
Definition 3.5. Given a recipient U over a fixed organizational structure AT , the (struc-
tural) information of a sentence φ is the set

                              IU (φ) = {U A ∈ U : U A (φ) = 1}.
       Besides that, for a finite set of sentences Γ = {φ0 , φ1 , . . . , φn }, the (structural)
information of Γ is the set

                                                       n
                                                       [
                                           IU (Γ) =          IU (φi ).
                                                       i=0

Example 3.4. Consider the recipient U = {(AT , ATi ), (AT , AT2 )}. In this case, we have
the following:
      1. IU (Lrs ∨ Lrv) = {(AT , ATi )};
      2. IU (Lio) = U.

4. Organizational knowledge
Since we have a precise definition of information about organizational structures, we
can now define mathematically what is organizational knowledge. The intuition behind
our formal definition is that knowledge is information plus something else [12]. To be
specific, we defined organizational knowledge as justified relevant information about or-
ganizational structures.
Definition 4.1. Given an organizational structure AT over S = C ∪ P ∪ R such that
C = {c1 , . . . , ck }, P = {P1 , . . . , Pm }, and R = {R1 , . . . , Rn }, the organizational graph
associated to AT is the multi-graph GA = (V, {El }l<n ) such that:
    1. V = {(a, PjA ) ∈ dom(A) × ℘(dom(A)) : A(Pj (a)) = 1} for 1 ≤ j ≤ m;
    2. El = {(b, d) ∈ V 2 : b = (a, PjA )) ∈ V, d = (c, PkA )) ∈ V, A(Rl (a, c)) = 1} for
        1 ≤ l ≤ n.
Example 4.1. Let AT be the organizational structure from example 2.1. The organiza-
tional graph associated to AT is graph GA = (V, E) such that:
     1. V = {(ī, E A ), (f¯, E A ), (ō, AA ), (r̄, E A ), (s̄, E A ), (v̄, E A )};
     2. E                        =                            {((ī, E A ), (ō, AA )), ((ō, AA ), (r̄, E A )),
        ((r̄, E ), (s̄, E )), ((r̄, E ), (v̄, E )), ((s̄, E A ), (f¯, E A )), ((v̄, E A ), (f¯, E A ))}.
               A         A             A          A

Definition 4.2. Let R+ be set of non-negative real numbers. Given an organizational
graph G = (V, {Ei }i<n ) associated to an organizational structure AT over S, an ob-
jectual relevancy is a function d : V → R+ and a relational relevance is a function
D : {Ei }i<n → R+ such that
                                               d(a) ≤ [d]
and
                                               D(Ei ) ≤ [D],

         for all a ∈ V and i < n.
        The functions d and D represent the relevancy associated, respectively, to the
nodes and types of edges between nodes. Given that, we provide some axioms for func-
tions that every measure of organizational knowledge must satisfy.
Definition 4.3. We write UA (G) to indicate an update U A = (ATj : 0 ≤ j ≤ n) such that
AT0 = A and ATn = G. In special, UA (G) denotes the set of all updates UA (G). In this
way, we define that K : U(Gb ) × U(Gr ) → R+ is an knowledge function if, and only if:
    1. K(U (Gb ), U (Gr )) = K(U (Gr ), U (Gb ));
    2. If Gb = Gr then K(U (Gb ), U (Gr )) = 0;
    3. If Gb ∩ Gr = then K(U (Gb ), U (Gr )) = 1;
    4. If Gb ⊆ G then K(U (Gb ), U (Gr )) ≤ K(U (G), U (Gr ));
    5. If Gr ⊆ G then K(U (Gb ), U (Gr )) ≤ K(U (Gb ), U (G)).
        The first axiom expresses the symmetry between the knowledge base and the re-
search base. This is a consequence of the fact that insertions and extractions are dual
operations and so it does not matter whether we consider the order of the structures. The
second and third axioms are immediate and the forth and fifth represent the monotonicity
of the structural information.
Definition 4.4. Let AT be an organizational structure and K a knowledge function over
an organizational graph Gb = (Vb , {Ei }i<n ) associated to AT , called knowledge base,
and an organizational graph Gr = (Vr , {Ej }j<n ) associated to an organizational struc-
ture B T , called research base. Thus, the organizational knowledge of B T with respect to
AT and K is the number k such that

                        K = min{K(UGb ∩Gr (Gb ), UGb ∩Gr (Gr )) :

                               UGb ∩Gr ∈ U(Gb ) ∪ U(Gr )}.

5. Computational results
Our approach permits us to define the algorithm Organizational knowledge that calculates
organizational knowledge. We could provide a mathematical proof that this algorithm
computes an knowledge function, but we prefer to present empirical data about its exe-
cution - in a mathematical oriented article we will give all the details. The simulations
provided in this section were implemented in a program wrote in Python.
        The figure Fig. 4 is a graphic K × |V |, where |V | is the number of nodes of a
graph G = (V, {Ej }j<n ), generated with a number of nodes from 1 to 100 with step of
5 nodes, 5 types of edges with 10 possible values, i.e., with n = 5 and D : {Ej }j<n →
R+ with 10 possibles values. Each knowledge measure is a result of the mean of 10
trials. This graph shows that the variation in an research base with respect to nodes are
irrelevant to knowledge. This is in accordance with axiom 3. As we randomly choose new
organizational graphs bigger and bigger, the probability of finding completely different
graphs increase, and so knowledge approaches to 1.
       The figure Fig. 5 is a graphic K × |E|, where |E| is the number of edges of a
graph G = (V, {Ei }i<n ), generated with a number of nodes from 1 to 100 with step of 5
nodes, 5 types of edges with 10 possible values. Each knowledge measure is a result of
the mean of 10 trials. This graph shows that the variation in an research base with respect
to edges is relevant to knowledge. This is a sigmoid function, a special case of learning
curve [13]. Indeed, we have obtained the following function
                                                        √
                     K(x) = 1/(1 + 0.001010e−0.385636 x )1/0.000098 .

                         √
       The square root x is just due to the factor of redundancy 2.19721208941247
generated by the fact that we have chosen the graphs randomly. This redundancy implies
Algorithm 1 Organizational Knowledge
Require: GA = (VA , {Ek }k<m ), GB = (VB , {Ek }k<n )
Require: dA : VA → R+ , dB : VB → R+
Require: DA : {Ej }j<m → R+ , DB : {Ek }k<n → R+
 1: N := 0
 2: NA := 0
 3: NB := 0
 4: RA := 0
 5: RB := 0
 6: K := 0
 7: for (x, y) ∈ GA or (x, y) ∈ GB do
 8:   if (x, y) ∈ GA and (x, y) ∈ GB then
 9:      N := N + 1
10:   else if (x, y) ∈ GA then
11:      for (x, y) ∈ Ej do
12:         NA := NA + 1
13:         RA := RA + D[D A (Ei ) dA (x)
                              A]
                                  ( 2[dA ] + d2[d
                                               A (y)
                                                  A]
                                                     )
14:      end for
15:   else
16:      for (x, y) ∈ Ek do
17:         NB := NB + 1
18:         RB := RB + D[D B (Ei ) dB (x)
                              B]
                                  ( 2[dB ] + d2[d
                                               B (y)
                                                  B]
                                                     )
19:      end for
20:   end if
21: end for
22: K := 1 − N +N RN +N R
                    A A   B B
23: return K




          Figure 4. Knowledge between random graphs with variation of nodes
              Figure 5. Knowledge between random graphs with variation of edges


    a decreasing in the growing of knowledge. This is a very important result because, first, it
    shows a clear connection between our definition of knowledge and the usual empirical ap-
    proaches to learning and, besides that, it is evidence that knowledge is indeed a relational
    property of organizational structures, as it have been sustained, for example, [5].

    6. Conclusion
    The main focus of the quantitative measure discussed in this paper is to use dynamic
    data taken from research methods about knowledge management. Our results shows that
    knowledge is a relational property of organizational structures. Nonetheless, much more
    should be done in order to understand the consequences of these results. At first, the
    organizational knowledge management techniques comprehend aspects of how to under-
    stand knowledge, using the right attitudes to the right environments. Once the knowledge
    meaning is defined, the knowledge sharing behaviour should be identified in order to ap-
    ply quantitative measures and then driving the KM process toward a more certain path
    [14]. We also need to analyse how the measurement of knowledge given here can be used
    for these purposes. We relegate that to future works.

    Acknowledgment
    Omitted for the sake of double-blind evaluation.

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