Core Competence evaluation is crucial for strategical choices in knowledge intensive companies. Such a process is usually manually performed by the management on the basis of subjective criteria, which can then cause non-optimal decisions, especially in wide companies. We propose here a semantic-based approach for the automatic evaluation of Core Competence, exploiting novel reasoning services in Description Logics, extracting commonalities in a collection of resource descriptions. Such inferences aim at identifying features shared at least by a significant portion of a collection of professional profiles formalized in accordance with a logic language. We are in fact not necessarily interested in competence shared by the whole company personnel.
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The process of individuating Core Competence is in fact usually characterized by
high complexity and low objectivity because of the intangibility of knowledge itself and
difficulties inherent in formalizing them. The automation of Core Competence
extraction process asks in fact for company know-how to be described according to a language
endowed with formal semantics. If employee profiles and organization knowledge are
formalized in a collection of concept descriptions according to a formal language
conveying semantics, the management could extract company Core Competence by
searching for features shared in such a collection. In particular, Description Logics [
Usefulness of LCSs has been shown in several different application fields, such as
the bottom-up construction of knowledge bases [
Noteworthy, all above introduced application scenarios share the need of individuating features which are common to all of the elements in a given collection.
In Core Competence evaluation, instead, the issue is determining commonalities of a significant portion of the collection rather than of the collection as a whole. The problem reverts then to finding a concept subsuming a significant number, or percentage, of elements in the collection. The degree of significance may be chosen by the management on the basis of organizational needs.
In order to perform such extraction process in a Knowledge Representation framework, we define concepts which are LCS of k elements in a collection of n descriptions, with k < n. We give the name k-Common Subsumers to such concepts.
The rest of this paper is organized as follows: in the next Section we briefly introduce the DL formalism we adopt; then we outline our motivational case study and its formalization in DLs. In Section 4 we detail k-Common Subsumers and three more specific reasoning services needed for the commonalities extraction process, provided in Section 5. Introduced services are illustrated in the motivating organizational context in Section 6, before closing the paper with conclusions. 2
We start recalling here basics of the formalism we adopt, based on Description Logics (DLs). DLs are a family of formalisms and reasoning services widely employed for knowledge representation in a decidable fragment of First Order Logic.
The alphabet of each DL is therefore made up by unary and binary predicates, denoted as Concepts Names and Role Names, respectively. The domain of interest is represented through more expressive and complex Concept Descriptions, involving constructors over concept and role names. The set of constructors allowed by a DL characterizes it in terms of expressiveness and reasoning complexity: of course the more a DL is expressive, the harder is inferring new knowledge on its descriptions.
Concept Definitions allow to assign an unique concept name to complex concept descriptions: the so called Unique Name Assumption (UNA) holds in every DL. Names associated to concept descriptions constitute the set of Defined Concepts, distinguished by Primitive Concepts not appearing on the left hand side of any concept definition and corresponding to the concept names.
Concept Inclusions detail instead specificity hierarchies among concepts, either defined or primitives. Role Inclusions are also aimed at detailing specificity hierarchies, but among roles.
The set of concepts inclusions and definitions represents the formal representation of the domain of interest, the intensional knowledge which takes the name TBox in DL systems and Ontology in the generic knowledge representation framework.
The motivating scenario we here propose needs at least the expressiveness of E LHN sublanguage of DLs for resources representation. E LHN allows of course for the constructors provided in every DL: conjunction of concepts(e.g.C++ u Java), negation of atomic concepts (:Skill), top concept(>, interpreted as the whole domain) and bottom concept (?, interpreted as the empty set). The following constructors are furthermore available: existential restriction (e.g. 9knowsLanguage.English), number restrictions (e.g. (· 2 knowsLanguage) and (¸ 3 hasExperienceYears)) and role inclusion (e.g. advancedKnowledge v basicKnowledge). 3
The investigations on the problem of evaluating Core Competence in knowledge intensive companies originate from a real need we faced in the implementation of IMPAKT, a novel and optimized semantic-based knowledge management system, which will be released late this year. by D.O.O.M. s.r.l.
IMPAKT is specifically aimed at semantic-based human resources management [
Hereafter we use Description Logics for knowledge representation and, for the sake of simplicity, assume that the only source of company know-how is company personnel. As a result, a company which needs to automatically extract its Core Competence has to formalize the knowledge profiles of employees according to the vocabulary provided by a TBox describing skill management domain.
An excerpt of the inclusions and the assertions composing the TBox at the basis of our case study is given in Figure 1 and Figure 2, respectively.
The extraction process is grounded on the reasonable assumption that Core Competence, although characterizing a company, has not necessarily to be held by the whole personnel, but at least by a significant portion of it. A competence shared by all of the employees could be in fact too generic, if the objective is, for example, identifying skills to invest on in long term strategy.
Consider the tiny organizational scenario in which the following employees are employed: Manager ´ 9advancedKnowledge.(ManagementTechniques u (¸ 8 hasExperienceYears)) AssetManager ´
Manager u 9advancedKnowledge.(AssetAllocation u (¸ 5 hasExperienceYears)) Engineer ´ 9advancedKnowledge.(Design u (¸ 5 hasExperienceYears)) u
9hasMasterDegree.Engineering u 9basicKnowledge.OperationsOptimization ManagerialEngineer ´ Engineer u 9basicKnowledge.ERPsystem u 9advancedKnowledge.(ProductionManagement u (¸ 3 hasExperienceYears)) u 9advancedKnowledge.(Process Management u (¸ 3 hasExperienceYears)) CSEngineer ´ Engineer u 9advancedKnowledge.OperatingSystems u 9advancedKnowledge.(Programming u (¸ 5 hasExperienceYears)) u 9advancedKnowledge.(SoftwareEngineering u (¸ 3 hasExperienceYears))
It is noteworthy that the employees competence descriptions need the full expressiveness of E LHN to convey all the embedded semantics. We therefore in the following
It is easy to observe that the only characteristic shared by the four employees of our tiny case study is ”an advanced knowledge about programming”. Such a feature might obviously be too generic to be considered for Core Competence identification. The management of a company needs instead to take into account features shared by significant subsets of the collection made up by the employees; the minimum required number of employees may be set by the management on the basis of a decisional process. As an example, if the management accepts that three employees have to hold some knowledge to consider it part of Core Competence, we can state that the company has advanced knowledge about object oriented programming as Core Competence. Such a result is more significant than the first one w.r.t. to the objective of determining the fields of excellence of the company.
Of course, the more the extracted knowledge is specific and unknown to the management, the more the automated process we propose is useful for achieving competitive advantage.
In the following we start recalling standard services we use in our approach and then proceed to introduce non-standard ones. The most important —and well-known— service characterizing reasoning in DL checks for specificity hierarchies, by determining whether a concept description is more specific than another one or, formally, if there is a subsumption relation between them.
Definition 1 (Subsumption) Given two concept descriptions C and D and a TBox T in a DL L, we say that D subsumes C w.r.t. T if for every model of T , CI ½ DI . We write C vT D, or simply C v D if we assume an empty TBox.
We recall Least Common Subsumer definition by Cohen and Hirsh [
Definition 2 (LCS) [
It is well known that, if the DL L admits conjunction of concepts “u”, then the LCS is unique up to concept equivalence (since if both E1 and E2 are common subsumers of C1; : : : ; Cn, then so is E1 u E2). Moreover, if union of concepts “t” is allowed in L, then for every set of concepts C1; : : : ; Cn 2 L, their LCS is C1 t ¢ ¢ ¢ t Cn. Hence, the study of LCS is limited to DLs not admitting union.
In order to deal with partial commonalities, we defined [
Definition 3 (k-CS) Let C1; : : : ; Cn be n concepts in a DL L, and let be k < n. A k-Common Subsumer (k-CS) of C1; : : : ; Cn is a concept D such that D is an LCS of k concepts among C1; : : : ; Cn.
By definition, LCSs are also k-CSs, for every k < n. For this reason we defined
[
We also defined [
The Least Common Subsumer, when not equivalent to the universal concept, is
of course the best common subsumer a collection may have: it subsumes the whole
collection. As a consequence, the computation of BCSs for collections admitting LCSs
not equivalent to > is meaningless. For such collections, we alternatively proposed [
In the following we show how to find commonalities in concept collections formalized in DL in accordance with outlined services.
In the computation of common subsumers of a collection of concept descriptions C1; : : : ; Cn we assume that all concepts Ci in the collection are consistent; hence Ci 6´ ? for every Ci 2 (C1; : : : ; Cn).
The reasoning services introduced in Section 4 ask for the concepts of the input collection to be written in components according to the following recursive definition: Definition 7 (Concept Components) Let C be a concept description in a DL L, with C written in a conjunction C1 u ¢ ¢ ¢ u Cm. The Concept Components of C are defined as follows: if Cj , with j = 1 : : : ; m is either a concept name, or a negated concept name, or a number restriction, then Cj is a Concept Component of C; if Cj = 9R.D , with j = 1 : : : ; m, then 9R.> is a Concept Component of C; if Cj = 8R.E, with j = 1 : : : ; m , then 8R.Ek is a Concept Component of C, for each Ek Concept Component of E.
Observe that we do not propagate universal restriction over existential restriction since existential restriction always simplify to a component of the form 9R.>. For the computation of the sets of k-CSs, IkCSs, BICSs and BCSs of a collection of concepts we define in the following a Subsumers Matrix, for the representation of the collection itself.
Definition 8 (Subsumers Matrix) Let C1; : : : ; Cn be a collection of concept descriptions Ci in a Description Logic L and let Dj 2 fD1; : : : ; Dmg be the Concept Components deriving from all concepts in the collection. We define the Subsumers Matrix S = (sij ) , with i = 1 : : : n and j = 1 : : : m, such that sij = 1 if the component Dj subsumes Ci, and sij = 0 if the component Dj does not subsume Ci. Definition 9 Referring to the Subsumers Matrix of C1; : : : ; Cn, we define: Concept Component Cardinality (TDj ) : cardinality of sigDj , that is, how many concepts among C1; : : : ; Cn are subsumed by Dj . Such a number is Pn i=1 sij ;
ponent cardinalities, that is, MS = maxfTD1 ; : : : TDm g;
cardinalities of concept components not subsuming all n concepts in the collection (P MS = maxfTDj jTDj < ng); by definition P MS < n;
Definition 8 hints that the computation of Subsumers Matrix includes an oracle to subsumption. As a consequence the following proposition holds: Proposition 2 Let L be a DL whose subsumption problem is decidable in polynomial time. Then Subsumers Matrix in L is computable in polynomial time too.
Such a result causes the computation of common subsumers in DLs with different complexities for subsumption to be treated separately. We therefore concentrate on the DL needed for modeling our case study, E LHN , even though some considerations are logic independent and preliminary to the determination of common subsumers in every DL.
Firstly, we define the solution sets for the introduced reasoning services, regardless of the DL employed for the representation of concepts in a given collection: BCS, set of BCSs; BICS, set of BICSs; ICSk, set of IkCSs of the collection, given k < n; CSk, set of k-CSs of the collection, given k < n.
Proposition 3 Given a DL L and a collection of concept descriptions in L, for each k < n the solution sets of the collection are such that ICSk µ CSk. If the collection admits only the universal concept as LCS, then B = BI also holds.
The commonalities extraction process in E LHN relies on computation results for
LCS computation. Baader et al. [
Theorem 1 The computation of the solution sets BCS, BICS, CSk, ICSk for a collection of concept descriptions in E LHN may be reduced to the problem of computing the LCS of the subsets of the collection.
Proof For computing CSk it is sufficient to compute for every subset fi1; : : : ; ikg µ f1; : : : ; ng the concept LCS(Ci1 ; : : : ; Cik ).
The same holds for ICSk, excluding those LCS(C1; : : : ; Ck) which are equivalent to
LCS(C1; : : : ; Cn). For the computation of the sets BCS and BICS, instead, we
provide Algorithm 1 that uses the one proposed by Kusters and Molitor [
Input : Subsumers Matrix S = (sij) for a collection of concepts Ci 2 fC1; : : : ; Cng in ELHN Output: BICS; BCS 1 if MS = n then 2 BCS := ;; 3 foreach Dj s.t. TDj = P MS do BICS := BICS [ LCSDj ; 4 else 5 foreach Dj s.t. TDj = MS do 6 BCS := BCS [ LCSDj ; 7 BICS := BCS; 8 return BCS , BICS;
Algorithm 1: An algorithm for Common Subsumers enumeration in E LHN 6
In order to better clarify the proposed services we apply the commonalities extraction process detailed in Section 5 to our tiny example scenario.
The input collection therefore is made up by the four profiles in Section 3. Let 50% be the required level of competence coverage set by company management to individuate Core Competence. We are hence interested in determining competence shared by at least two employees out of the four in the company.
In order to compute the set CS2, it is sufficient to compute the LCS of all subsets of cardinality 2: LCS(Antonio; Claudio) =
Engineer u 9advancedKnowledge.(Java u (¸ 2 hasExperienceYears)) u 9basicKnowledge.SoftwareEngineering u 9basicKnowledge.InformationSystems LCS(Antonio; Roberto) = 9advancedKnowledge.OOP LCS(Antonio; Daniele) = Engineer u 9advancedKnowledge.(Programming u
(¸ 5 hasExperienceYears)) u 9basicKnowledge.InformationSystems) LCS(Claudio; Roberto) = 9advancedKnowledge.OOP LCS(Claudio; Daniele) = Engineer u 9advancedKnowledge.(Programming u LCS(¸(R2obhearstEox;Dpearniieenlec)eY=ea9rasd)v)aunc9ebdaKsniocwKlneodwglee.Sdcgrei.IpntfLoarnmgautaigoensSystems
All elements in CS2 have to be investigated w.r.t. the LCS of the collection to identify Informative 2-Common Subsumers. We need then to compute such a concept: LCS = LCS(Antonio; Claudio; Roberto; Daniele) = 9advancedKnowledge.Programming . Each element in CS2 is more specific than LCS and then belongs also to ICS2.
We use instead Algorithm 1 for computing the sets BCS and BICS. The algorithm requires the concept collection Subsumers Matrix as input; so we have to compute it first. The concept components coming from the collection are computed according to Definition 7 and take into account TBox definitions in Figure 2. As a result we have the three concept components as in the following: D1 = 9hasMasterDegree.>, D2 = 9advancedKnowledge.>, D3 = 9basicKnowledge.>.
The collection subsumers matrix is shown in Figure 3 and is characterized by the following values: MS = 4, P MS = 3.
By applying Algorithm 1 we have that BCS := ; (line 2) and we need to compute, according to line 3, LCSD1 and LCSD3 . It is straightforward to notice that LCSD1 ´ LCSD3 , so the only BICS for the collection is: LCS(Antonio; Claudio; Daniele) = Engineer u 9advancedKnowledge.(Programming u (¸ 2 hasExperienceYears)) u 9basicKnowledge.InformationSystems
D1 D2 D3 Antonio x x x Claudio x x x Roberto x
Daniele x x x
Thanks to the commonalities extraction process proposed here, the company in our tiny case study discovered some new information about the fields of excellence characterizing its know-how. In particular, by computing the LCS of the collection of employee profiles, the company management may discover that the whole personnel knows Programming at an advanced level, which is quite a generic sort of information, probably well known by the company.
More significant and unknown commonalities may be found by computing the set of IkCSs: i) knowledge embedded in Engineer job title together with an advanced knowledge in Java, related to two years of working experience, and a basic knowledge in Information Systems and software engineering; ii) advanced knowledge about object oriented programming;iii) advanced knowledge about script languages. Such commonalities are therefore informative w.r.t. the objective of determining unknown fields of excellence in the company.
Moreover the company may discover, thanks to the computation of BICSs, that knowledge shared by the maximum number of employees in the company (excluding Programming which is shared by all employees) is an advanced knowledge of programming related to 2 years of experience, together with the knowledge embedded in Engineer job title and a basic knowledge in Information Systems.
In large knowledge intensive companies, like multinational ones, the proposed approach may hence help to detect hidden fields of excellence of a company, especially if out of the core business, thus representing a potential source of competitive advantage. 7
Motivated by the need to identify and extract so called Core Competence in knowledge intensive companies, and by the limits of LCS in such a framework, we have exploited informative common subsumers in Description Logics, useful in application fields where there is the need to extract significant informative commonalities in concept collections, and such commonalities are not shared by the entire collection. We have proposed definitions, algorithms to compute such informative common subsumers for E LHN and presented simple complexity results.
Obviously our approach requires competencies be modeled in accordance with an ontology, but as semantic-based languages and technologies gain momentum it is reasonable to assume that more and more companies will move towards a logic-based formalization of their skills and processes and be able to take advantage of proposed and other relevant non-standard services. This work has been supported in part by and Apulia Region funded projects PE 013 Innovative models for customer profiling, PS 092 DIPIS and PS 025 L’OrMaICT.