Information overload is a common problem in current Information and Knowledge Based Systems. The Web, being the largest public available information source, is particularly a ected by this issue, so several approaches to deal with it are being developed by Semantic Web researchers. Most of them are based on using context knowledge to delimit which information is signi cant to a user, such as the CDR ontology design pattern, our previous contribution to handle relevance depending on context in OWL ontologies. In this work, we extend this proposal with fuzzy Description Logics formalisms in order to represent vague knowledge about context and application-speci c facts, and to manage the degree of importance of a relevance relation. A main advantage of our proposal is that current (non-fuzzy) standards and inference engines can be used.
Anyone who has been staring at his computer screen {INSPEC database, Google
Scholar and ScienceDirect on the web browser, in addition to Zotero with
selected papers and a couple of seven hundred pages pdf les with the last ESWC
proceedings{, hastening to nd the right reference to complete a submission one
hour before the deadline, has an idea of what information overload is. This state
is more precisely de ned in Information Systems [
Warding o this situation is one of the purposes of Semantic Web technologies. Agents in the Semantic Web use metadata to locate, discover and integrate di erent information sources, which will drive eventually to provide users with a considerable amount of data. Clearly, semantic agents must implement mechanisms that reduce the amount of information delivered to users, in such a way that they supply just the just amount of data to them {these which users are really interested in{, in order to avoid information overload. That means that, when retrieving information to support users, only those segments of ontologies which are relevant or signi cant with respect to the current task should be considered. This is known as selective activation of knowledge.
Hence it is necessary to represent which pieces of the available information are relevant to carry out a task. In that regard, what is important depends on (i) which is the problem to be solved, and (ii) other factors, somehow extrinsic, as user environment, preferences, previous actions. etc. All these elements make up, in a wide sense, the context of use of the system. In Semantic Web systems, where knowledge is represented using ontologies, this context can be as well represented using an ontology.
In a previous work, we developed an ontology design pattern to represent in
OWL this notion of relevance dependent on context [
The relevance ontology resulting from applying the CDR pattern has two main lacks. First of them, de nitions of complex context concepts (respectively for de nitions of complex domain concepts) are crisp, which results in having a context description either included or not in another context description. As a result, it is not possible to represent directly vague contexts, e.g. \the patient is slightly unconscious", and partial similarity between contexts, e.g. \anaphylaxis is quite similar to sepsis". On the other hand, the relevance ontology only allows the developer to associate which concrete information is interesting in a scenario, but it does not measure how important this connection is, which is convenient in some applications. Recalling the example of our doctor, it can be realized that electronic registers about previous adverse drug events are more important in this case and should be presented rstly to the doctor: avoiding an anaphylactic shock is a major priority and medical protocols prevent the doctor from being in contact with patients' blood. Ranking the relevance relations would allow system responses to be ordered by precedence and a threshold to be xed in order to retrieve only the top k most relevant domains.
In this paper, we propose an extension of the CDR design pattern to deal with vague contexts and domains and to quantify relevance relations. Our approach relies on Fuzzy Description Logics (fuzzy DLs), a logical formalism proposed in the literature which combines Fuzzy Logic theory and classical Description Logics in order to de ne a sound framework to represent and reason with imprecise and vague knowledge in ontologies.
The contributions of this paper are the following. Firstly, we reassess the
original de nition of the CDR pattern and, as a novelty, we demonstrate that
the reasoning procedure is complete. Secondly, as the main contribution, we
formulate an extension of the pattern which results in a fuzzy ontology. This
extension allows imprecise context and domain descriptions to be represented and
relevance relations to be weighted. Though the fuzzy CDR ontology is not OWL
compliant, previous results can be applied to reduce it to a crisp representation
in order to use existing inference engines [
The paper is structured as follows. Section 2 recalls the CDR design
pattern from [
2.1
We will use in this paper DLs notation, which can be directly translated to
XMLbased OWL syntax. An introduction to DLs is provided next; further details can
be found in [
The signature (or vocabulary) of a description logic contains the symbols used in it. Formally, the signature is the disjoint union S = R ] C ] I, being R = fRAg the set of atomic roles (or properties), C = fCAg the set of atomic concepts (or classes), and I = fa; b; : : :g the set of individuals (or instances). From these atomic elements in S, new complex roles (noted Rol(S) = fRig), concepts (Con(S) = fCig), and axioms (Ax(S) = fOig) can be composed (subscripts will not be used when disambiguation is not needed). By extension, the signature S(O) of an axiom (respectively for roles and concepts) is the set of atomic elements of S which are included in O. Several logics are distinguished in DLs depending on the constructors allowed to create new complex expressions; each one is named using capital letters which denote the valid operators. Generally, having more constructors in a logic means that it is more expressive and, consequently, the computational complexity of reasoning processes is higher.
A DL ontology is a triple K = hT ; R; Ai, where T (the TBox) contains axioms about concepts, R (the RBox) axioms about roles, and A (the ABox) axioms about individuals. The signature of an ontology S(K) is the union of all the signatures S(O) of the axioms in K. The set of concepts (resp. roles) de ned in an ontology is noted Con(K) (resp. Rol(K)). Hereafter, we will use the basic DL ALC unless otherwise indicated.
A TBox T consists of a nite set of general concept inclusion (GCI) axioms of the form C1 v C2, which means that concept C1 is more speci c than C2, i.e. C2 subsumes C1. A concept de nition C1 C2 (C1 and C2 are equivalent) is an abbreviation of the pair of axioms C1 v C2 and C2 v C1. Concept expressions for C1 and C2 can be derived inductively from atomic primitives using concept constructors. Table 1 shows the constructors allowed for concepts and roles in ALC. In more complex DLs, a RBox R consists of a nite set of role axioms stating role properties such as inclusion, transitivity, etc. However, in ALC the RBox is assumed to be empty and complex role expressions cannot be used in concept and instance axioms. An ABox A consists of a nite set of axioms about individuals. These axioms describe an individual with respect to a concept (a : C, which means that a is an instance of C) or a pair of individuals with respect to a role ((a; b) : R, which means that (a; b) is an instance of R).
An interpretation I of an ontology K is a pair I = ( I ; I ) where I , the domain of the interpretation, is a non-empty set, and I is a function which maps every individual a onto an element aI 2 I , each concept in K with a subset of I , and each role in K with a subset of I I . This interpretation is conveniently extended for complex concepts.
An ALC interpretation I is a model of: { a : C i aI 2 CI , { (a; b) : R i (aI ; bI ) 2 RI , { C1 v C2 i C1I C2I , { a KB K = hT ; R; Ai i it satis es each element in T , R and A.
One of the main reasoning tasks in DLs is subsumption checking: C2 subsumes C1 w.r.t. K (noted as K j= C1 v C2) i C1I C2I is veri ed for every model I of K. Classifying an ontology K consists of computing for each pair of concepts C1; C2 2 Con(K) if K j= C1 v C2. 2.2
The CDR design pattern de nes constructively how to develop a new ontology {the relevance or CDR ontology{ built upon the domain-speci c and the context vocabulary sub-models.
The domain sub-ontology KD contains the knowledge required to solve the concrete problem that the system is facing. We will use the notation Dj (\complex domain") to name concept expressions built using elements in KD (and ontology constructs); that is, S(Dj ) S(KD). The context ontology KC contains the knowledge required to express the circumstances or the surroundings under which the domain knowledge will be used; it can be seen as a formal vocabulary to describe these situations. We will use the notation Ci (\complex context") to name concept expressions de ned using elements of KC (and ontology constructs); that is, S(Ci) S(KC ).
Note that Dj and Ci are not part of the domain and the context ontology.
Actually, they are de ned in the CDR ontology (KR), which is a new ontology where Ci, Dj , and links between them are de ned. These links, named pro les, state that the domain-speci c knowledge Dj ought to be considered in situation Ci. A pro le concept is a new concept representing a pro le-connection, and is de ned with existential restrictions on the complex context and the complex domain that it links (via properties R1 and R2). Then, the relevance ontology KR contains new classes (the so called \pro les") which relate complex contexts Ci and complex domains Dj through quanti ed roles: De nition 1. Let KD and KC be, respectively, the domain and the context subontologies, Ci a complex context such that S(Ci) S(KC ) and Dj a complex domain such that S(Dj ) S(KD). The relevance ontology or CDR ontology which relates the set of pairs f(Ci; Dj )g (i.e. states that Dj is interesting when Ci happens) is a consistent ontology KR = hT R; RR; ARi where T R includes de nitions for the concepts P>; C>; D>; Ci; Dj ; Pi;j , and satis es: 1. P>; C>; D> are the superclasses Pro le, Context and Domain: { Pi;j v P>, Ci v C>, Dj v D> 2. R1 is the (new) bridge property linking pro les and complex contexts: { P> v 8R1:C> 3. R2 is the (new) bridge property linking pro les and complex domains: { P> v 8R2:D> 4. Pi;j is the pro le linking the named context Ci and the named domain Dj : { Pi;j
9R1:Ci u 9R2:Dj
Notice that none of Ci and Dj are part of the domain and the context submodels, respectively, but they are de ned in the new ontology KR. Therefore, S(KC ) [ S(KD) S(KR), i.e. KR must import the axioms stated in KC and KD to preserve the semantics of Ci and Dj .
Proposition 1. Let KR be a CDR ontology, Ci and Ci0 complex contexts dened in T R, and Dj and Dj0 complex domains de ned in T R. The ontology KR satis es the property: Ci v Ci0 ^ Dj v Dj0 ) Pi;j v Pi0;j0
This proposition re ects the intuition that if a context and a domain are connected through a pro le, more general (i.e. subsuming) contexts and domains will be connected through a more general pro le.
Proof. The proof is immediate from the forth condition in De nition 1. tu Dj0 .
In general, the reciprocal is not true. This formulation allows a consistent relevance ontology to be created with Pi;j v Pi0;j0 , but Ci 6v Ci0 and/or Dj 6v
The main reasoning task involving a relevance ontology consists on nding all the concepts in the domain ontology which are worth to be considered in a given context, that is, the domains that are associated through pro les with a complex context expressed using the context vocabulary.
De nition 2. Given the ontologies KR, KD and KC (with their respective signatures S KR ; S KD ; S KC ) and a complex context E (S (E) S KC ), the restricted domain of the scenario E w.r.t. KR, noted as D E; KR , consists of the concepts I in KD such as:
D E; KR
= I j I 2 Con(KD) ^ (E v Cn) ^ (Pn;m v P>) ^ (I v Dm)
E; KR can be computed in practice as follows: 1. fCng = fCn v C>j E v Cng 2. fPk;lg = fPk;l v P> j (Pk;l v 9R1:Ck) ^ (Cn 3. fDmg = fDm v D> j (Pk;l v 9R2:Dl) ^ (Dm 4. D E; KR = I 2 Con(KD) j I v Dm Ck)g Dl)g
The nal output of the algorithm to the user is the set of simple domain
concepts of KD which are relevant to the query context E. Due to length
restrictions, we refer the reader to our previous work in [
Proposition 2. Algorithm 1 is complete, i.e. it nds all the concepts I related with E through pro les.
Proof. From the expressions in the steps 1-4 of Algorithm 1, it can be trivially realized that every Pk;l subsuming the (hypothetical) pro le PE;I linking E and I is retrieved. By de nition, E v Cn v Ck 8n; k and I v Dm v Dl 8m; l. Recalling Proposition 1, we get directly that PE;I v Pn;m v Pk;l. tu
The computational complexity of Algorithm 1 is asymptotically bounded by
ontology classi cation, which depends on the expressivity of KR. Since pro le
declarations (from De nition 1) are included in ALC, KR complexity is
conditioned by complexity of Ci and Dj expressions and, subsequently, by complexity
of KC and KD ontologies. In the simplest case, that is KR, KC and KD are in ALC
(with general TBoxes), concept satis ability in KR is ExpTime-complete [
Fuzzy Sets theory and Fuzzy Logic are aimed at managing imprecise and vague
knowledge [
In a fuzzy DL we can de ne, for instance, T omF avouriteGroups as the set of bands that Tom (from MySpace) likes, with radiohead completely belonging to it (degree equals to 1), while the cardigans may also belong but with less degree (equals to 0.7). Similarly, two individuals can be partially related through a role: radiohead isSimilarT o the cardigans with degree 0.6. Other axioms may be as well fuzzi ed, e.g. GCIs: AcidJ azz is a subset of F unk with degree 0.7; then, an AcidJ azz-lover (an individual with membership degree equal to 1) can be inferred to be interested in F unk to some extent (degree equal to 0.7).
In [
As mentioned in Section 2.2, in the crisp case, the new pro le classes of the relevance ontology are ALC concepts, whereas no special restrictions are considered for Ci and Dj {at the most, they are expected to be in SHOIN (D). Consequently, in this fuzzy extension we will consider f ALC to de ne the new fuzzy pro les; additionally, more complex fuzzy DLs for Ci and Dj expressions may be contemplated, for instance these f SHOIN and f SROIQ. Next, the fuzzy DL f ALC is reviewed.
Let B = f ; >g, C = f ; <g, and 2 [0; 1]. A f ALC TBox consists of fuzzy GCIs, which constrain the truth value of a GCI, i.e. they are expressions of the form hC vB Di. A f ALC RBox is empty. A f ALC ABox consists of a nite set of fuzzy assertions. A fuzzy assertion can be an expression of the form ha : C B i, ha : C C i or h(a; b) : R B i. Note that negative GCIs or negative role membership axioms are not allowed.
A f ALC interpretation maps every individual a onto an element aI 2 I , every concept C onto a function CI : I ! [0; 1], and every role R onto a function RI : I I ! [0; 1]. For a t-norm , a t-conorm , a negation function and an implication function ), Table 2 summarizes the syntax and the semantics of the interpretation of concept, roles and axioms. We will use Godel implication for GCIs: ) = f1; if jj ; if > g; and Zadeh family of functions for the remaining operators: t-norm = minf ; g, t-conorm = maxf ; g, Lukasiewicz negation = 1 .
A fuzzy interpretation I satis es (is a model of): { ha : C B i i CI (aI ) B , { ha : C C i i CI (aI ) C , { h(a; b) : R B i i RI (aI ; bI ) B , { hC vB Di i infx2 I fCI (x) ) DI (x)g B , { a fKB f K = hT ; R; Ai i it satis es each element in T , R and A.
We assume that there are not fuzzy axioms of the form 0, 1 (which are tautologies), > 1 and < 0 (which are obvious inconsistencies).
An axiom is a logical consequence of a knowledge base K, denoted K j= i every model of K satis es . The greatest lower bound (glb) of a fuzzy axiom is de ned as the supf : K j= h ig. 3.2
The fuzzy CDR ontology extends the original proposal by letting contexts, domains and pro les to be de ned using fuzzy GCIs. Thus, complex context and domain concepts can be stated to be partially similar using fuzzy GCIs, whereas the degree of subsumption in a pro le de nition represents the importance value of the connection between the involved context and domain.
De nition 3. Let KD and KC be, respectively, the domain and the context subontologies, Ci a complex context such as S(Ci) S(KC ) and Dj a complex domain such as S(Dj ) S(KD). The fuzzy relevance ontology which relates the set of pairs f(Ci; Dj )g with degree i;j (i.e. states that Dj is interesting with rank i;j when Ci happens) is a consistent fuzzy ontology f KR = hT R; RR; ARi where T R includes (non-exclusively) de nitions for the fuzzy concepts P>; C>; D>; Ci; Dj ; Pi;j , and satis es: 1. P>; C>; D> are the superclasses Pro le, Context and Domain: { Pi;j v 1 P>, Ci v 1 C>, Dj v 1 D> 2. R1 is the (fuzzy) bridge property linking pro les and complex contexts: { P> v 1 8R1:C> 3. R2 is the (fuzzy) bridge property linking pro les and complex domains: { P> v 1 8R2:D> 4. Pi;j is the (fuzzy) pro le which links the named context Ci and the named context Dj : { Pi;j v
i;j 9R1:Ci u 9R2:Dj
It is interesting to note that the context ontology KC and the domain ontology KD may be fuzzy or not. However, both Ci and Dj are fuzzy concepts de ned with fuzzy GCIs. The example in Section 3.3 shows a fuzzy relevance ontology built upon two crisp ontologies KC and KD.
By extension of the crisp case, the domain restricted by a context w.r.t. a fuzzy relevance ontology contains all the (fuzzy or crisp) concepts of the domain sub-ontology which are relevant in a given (fuzzy) context and the degree of interest. It is formally de ned as a set of pairs (domain concept, degree), where \domain concepts" are the domains relevant to the context of the query (i.e. related through pro les) and \degree" is a number computed on i;j values. De nition 4. Given the ontologies f KR, KD y KC (with their respective signatures S f KR ; S KD ; S KC ) and a complex context E ((S (E) S KC ), the ranked restricted domain of the scenario E w.r.t. f KR, noted as D E; f KR , consists of the pairs (I; i;j ) such as: { I 2 Con(KD) ^ (E v>0 Cn) ^ (Pn;m v>0 9R1:Cn u 9R2:Dm) ^ (Iv>0Dm) { i;j = glb(E v Cn) glb(Pn;m v 9R1:Cn u 9R2:Dm) glb(I v Dm)
The algorithm to calculate the ranked restricted domain of a scenario is a fuzzy extension of Algorithm 1.
E; f KR can be computed in practice as follows: 1. Get the complex contexts subsuming the query context (and their degree):
Z1 = f(Cn; n) j (E v>0 Cn) ^ ( n = glb(E v Cn))g 2. Get the pro les which involve the retrieved contexts (and their degree): Z2 = f(Ck; Pk;l; k) j (Pk;l v>0 9R1:Ck) ^ ( k = glb(Pk;l v 9R1:Ck)) ^ (Ck Cn[Z1])g 3. Get the complex domains involved by the retrieved pro les (and their degree):
Z3 = f(Pk;l; Dl; l) j (Pk[Z;l2] v>0 9R2:Dl) ^ ( l = glb(Pk;l v 9R2:Dl))g 4. Combine the partial degrees of the retrieved pro les using a : Z4 = f(Ck; Dl; k;l) j ((Ck; Pk;l; k) 2 Z2) ^ ((Pk;l; Dl; l) 2 Z3) ^ ( k;l = k l)g 5. Aggregate all the degrees which a domain has been retrieved with using a :
Z5 = f(Dm; m) j ( m = L(Ck;Dm; k;l)2Z4 ( k;l n))g 6. Get the I 2 Con(KD) more speci c than the retrieved complex domains (and their degree): D(E; f KR) = f(I; i;j ) j (I v Dm) ^ ( i;j = m glb(I v Dm[Z5]))g (for simplicity, we assume that Cn; Ck v C>; Pk;l v P>; Dm; Dl v D>) The output of the algorithm is a set of pairs containing all the I v Dm and their degree of importance. A concept I can be retrieved with more than a degree through di erent pro les, so these values should be conveniently aggregated, using a t-conorm , in order to provide the user with an only nal relevance value. Therefore, the nal output of the algorithm to the user will be a set of pairs (simple domain concept, degree) which are the concepts of the domain relevant to the context of the query.
Proposition 3. Algorithm 2 is complete, i.e. it nds all the concepts I related with E through pro les and the degree of this connection.
Proof. From the expressions of Algorithm 2, it can be realized that the retrieved Pk;l; Cn; Dm are the same as in the crisp case. The only di erence with the previous algorithm is the computation of values.
Therefore, based on proof of Algorithm 1 and De nition 4, we have just to prove that k;l = k l is equal to glb(Pk;l v 9R1:Ck u 9R2:Dl), the degree of the relevance relation between Ck (a superclass of E) and Dl (a superclass of I).
Using the properties of fuzzy sets, we know that (A ) B C) implies (A ) B) and (A ) C) , for some t-norm and its residuum-based implication (for example, for min t-norm and Godel implication). Applying this expression to our GCI, Pk;lv k;l 9R1:Ck u 9R2:Dl ) Pk;lv 1 9R1:Ck( 1 k;l) and Pk;lv 2 9R2:Dl( 2 k;l). From Algorithm 2, we have the glbs k and l. Since they are the greatest lower bounds, k 1 k;l and l 2 k;l. Consequently, k k;l ) k;l k 0, for any 0, and l k;l ) k;l l 00, for any 00. On the other hand, for min t-norm and Godel implication, (A ) B) 1 and (A ) C) 2 imply (A ) B C) 1 2. Applying this ewxephreasvseioPnkt;lovthek G ClI9sRo1f:CAklguor9itRh2m:D2l., BPyk;ldve nkit9ioRn1,:Ckk;land kPk;lvl. l 9R2:Dl, Consequently, k;l k l and k;l k l, so necessarily k;l= k
An upper bound for the computational complexity of the reasoning
procedure can be deduced from the works [
Besides subsumption tests, Algorithm 2 also calculates a considerable number
of glbs (exactly, one for each retrieved concept in Steps 1-4), needing each of them
at most log(N ) (being N the number of degrees) additional subsumption tests [
Currently, we are using the CDR design pattern to build a relevance ontology
for a medical application [
In this application, we have clearly separated the context and the domain
ontologies, being both of them crisp. The context ontology is a vocabulary to
describe clinical situations of the patients. There exist several medical ontologies
which can be reused for this purpose; our context ontology is strongly based on
the OWL translation of the Galen ontology1, a well-known and sound
terminology intended to be used in the implementation of clinical decision support
systems [
The (fuzzy) pro les in the relevance ontology connects (vague) descriptions of patient clinical states and (concrete) descriptions of datasets of the HIS, asserting which registers should we be checked in each situation. The degree of importance of each of these associations is represented by using fuzzy GCIs. 1 http://www.co-ode.org/galen/full-galen.owl
The following fuzzy relevance ontology f KR is an excerpt of our test
knowledge base. This is indeed an f SROIQ ontology, so it includes some additional
constructors to the f ALC described in this paper {e.g., number restrictions, used
in this example. This fuzzy DL is more extensively studied in [
Axioms which extend Galen ontology hAnaphylaxis v 0:7 Shocki hSepticShock v 0:5 Anaphylaxisi hShock u 1hasComplication v 0:8 EpinephrineAdministrationi De nition of complex contexts hC1 v 1 9hasComplication:Elderlyi hC2 v 1 Anaphylaxisi hC3 v 1 EpinephrineAdministrationi De nition of complex domains hD1 v 1 EHRCurrentP rescriptioni hD2 v 1 EHRCurrentP rescription t EHRDrugIntollerancei hD3 v 1 EHRAntidepressivesi hD3 v 1 D1i De nition of relations (for convenience) hR1 relSymptomi hR2 relRegisteri De nition of pro les hP1;1 v 0:6 9R1:C1 u 9R2:D1i hP3;3 v 0:9 9R1:C3 u 9R2:D3i Mandatory axioms
hP2;2 v 0:5 9R1:C2 u 9R2:D2i hC1 v 1 C>i, hC2 v 1 C>i, hD1 v 1 D>i, hD2 v 1 C>i, hP1;1 v 1 P>i, hP2;2 v 1 P>i, hP> v 1 8R1:C>i, hP> v 1 8R2:D>i
Let us suppose the query context Anaphylaxis u 9hasComplication:Elderly. Using Algorithm 2, we can retrieve the domains asserted to be interesting in this context, that is, D Anaphylaxis u 9hasComplication:Elderly; f KR . { Step 1
Anaphylaxis u 9hasComplication:Elderly v 1 Anaphylaxis v 0:7 Shock, Anaphylaxis u 9hasComplication:Elderly v 1 1hasComplication ) Anaphylaxis u 9hasComplication:Elderly v 0:7 Shocku 1hasComplication Anaphylaxis u 9hasComplication:Elderly v 0:7 Shocku 1hasComplication, Shocku 1hasComplication v 0:8 EpinephrineAdministration ) Anaphylaxis u 9hasComplication:Elderly v 0:7 EpinephrineAdministration Z1 = f(C1; 1); (C2; 1); (C3; 0:7)g { Step 2 { Step 3
P1;1 v 0:6 9R1:C1 u 9R2:D1 ) P1;1 v 0:6 9R1:C1 P2;2 v 0:5 9R1:C2 u 9R2:D2 ) P2;2 v 0:5 9R1:C2 P3;3 v 0:9 9R1:C3 u 9R2:D3 ) P3;3 v 0:9 9R1:C3 Z2 = f(C1; P1;1; 0:6); (C2; P2;2; 0:5); (C3; P3;3; 0:9)g P1;1 v 0:6 9R1:C1 u 9R2:D1 ) P1;1 v 0:6 9R2:D1 P1;1 v 0:6 9R2:D1 v 1 9R2:D2 ) P1;1 v 0:6 9R2:D2 P2;2 v 0:5 9R1:C2 u 9R2:D2 ) P2;2 v 0:5 9R2:D2 P3;3 v 0:9 9R1:C3 u 9R2:D3 ) P3;3 v 0:9 9R2:D3 P3;3 v 0:9 9R2:D3 v 1 9R2:D1 ) P1;1 v 0:9 9R2:D1 P3;3 v 0:9 9R2:D1 v 1 9R2:D2 ) P3;3 v 0:9 9R2:D2 Z3 = f(P1;1; D1; 0:6); (P1;1; D2; 0:6); (P2;2; D2; 0:5); (P3;3; D3; 0:9); (P3;3; D1; 0:9); (P3;3; D2; 0:9)g { Step 4
Z4 = f(C1; D1; min(0:6; 0:6) = 0:6); (C1; D2; min(0:6; 0:6) = 0:6); (C2; D2; min(0:5; 0:5) = 0:5); (C3; D1; min(0:9; 0:9) = 0:9); (C3; D2; min(0:9, 0:9) = 0:9); (C3; D3; min(0:9; 0:9) = 0:9)g { Step 5
Z5 = f(D1; max(min(0:6; 1); min(0:9; 0:7)) = 0:7); (D2; max(min(0:6; 1); min(0:5; 1); min(0:9; 0:7)) = 0:7); (D3; min(0:9; 0:7) = 0:7)g { Step 6
D E; f KR = f (EHRCurrentP rescription; min(0:7; 1) = 0:7); (EHRCurrentP rescription; min(0:7; 1) = 0:7); (EHRAntidepressives; min(0:7; 1) = 0:7); (EHRDrugIntolerance; min(0:7; 1) = 0:7); (EHRAntidepressives; min(0:7; 1) = 0:7); (EHRAntidepressives; min(0:7; 1) = 0:7)g
If the outputs of the algorithm are aggregated, the nal results provided to the user are (EHRCurrentP rescription; max(0:7; 0:7) = 0:7), (EHRDrugIntollerance; 0:7), (EHRAntidepressives; max(0:7; 0:7; 0:7) = 0:7).
These results mean that the system alerts the doctor to check the patient information about current prescriptions, especially those concerning antidepressive drugs, and past diagnoses about drug intolerance; all the recommendations are equally important with degree 0.7. Moreover, these data could be retrieved automatically from the hospital database, once the patient is identi ed, and the doctor would know directly this information. 4
Ontology design patterns are concise guidelines which identify common
knowledge representation issues and propose advices to solve them. The work [
Regarding to representation of relevance, a review of di erent perspectives
about implementation of context-sensitivity is presented in [
More general is the idea of contextualization of ontologies, which concerns
models which are satis able or not (instead of relevant) depending on some
circumstances. C-OWL is an extension to OWL to de ne mappings between
locally-interpreted and globally-valid ontologies [
Several fuzzy DLs can be found in the literature (some examples are
enumerated in [
In this work, we have reviewed the formulation of the CDR design pattern, which de nes a schema to represent relevance in OWL ontologies and a reasoning algorithm to retrieve the domain information relevant to a concept. As a novelty, this algorithm has been proved formally to be complete.
Based on this approach, this paper concentrates on an extension of the design pattern which allows imprecise context and speci c-domain knowledge to be managed {fuzzy concepts, relations and axioms may be used in context and domain expressions{, as well as connections between contexts and domains to have a ranking degree. This extension relies on fuzzy DLs, a formalism that provides a complete and sound framework to manage imprecise and vague knowledge in ontologies. Previous contributions describing procedures to reduce reasoning with fuzzy representations to reasoning with crisp ontologies are remarked in the paper, since they avoid to implement new inference engines.
Pattern use is depicted with an example in the healthcare domain, which
corresponds to a real application being developed currently in a research project
at the University of Granada. Therefore, the main direction for future work is to
test the utility of the pattern in this real application in order to show its
feasibility and to improve it, taking into account that the complexity of the reasoning
algorithm is quite high. Using the pattern in other domains and comparing it
with existing similar approaches will be studied as well. Development of
supporting tools is also a remarkable e ort which will be faced. In this sense, a tight
integration with current and future versions of DeLorean [