A Fuzzy Approach to Temporal ModelBased Diagnosis for Intensive Care Units.

Article: Accounting for the Temporal Dimension in CaseBased Retrieval: A Framework for Medical Applications.
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ABSTRACT: Timevarying information embedded in cases has often been neglected and its role oversimplified in casebased reasoning systems. In several realworld problems, and in particular in medical applications, a case should capture the evolution of the observed phenomenon over time. To this end, we propose to represent temporal information at two levels: (1) at the case level, when some features are collected in the form of time series, because they describe parameters varying within a period of time (which corresponds to the case duration), and we aim at analyzing the system behavior within the case duration interval itself; (2) at the history level, when we are interested in reconstructing the evolution of the system by retrieving temporally related cases. In this paper, we describe a framework for case representation and retrieval that is able to take into account the temporal dimension, and is meant to be used in any time dependent domain, which is particularly well suited for medical applications. To support case retrieval, we provide an analysis of similaritybased time series retrieval techniques; to support history retrieval, we introduce possible ways to summarize the case content, together with the corresponding strategies for identifying similar instances in the knowledge base. A concrete application of our framework is represented byRhene, a system for intelligent retrieval in the hemodialysis domain.Computational Intelligence 01/2006; 22:208223. · 1.00 Impact Factor  SourceAvailable from: Stefania Montani01/2010: chapter Providing casebased retrieval as a decision support strategy in time dependent medical domains: pages 211228; Springer.
 SourceAvailable from: Giorgio Leonardi
Conference Paper: Multilevel Abstractions and Multidimensional Retrieval of Cases with Time Series Features.
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ABSTRACT: Time series retrieval is a critical issue in all domains in which the observed phenomenon dynamics have to be dealt with. In this paper, we propose a novel, domain independent time series retrieval framework, based on Temporal Abstractions (TA). Our framework allows for multilevel abstractions, according to two dimensions, namely a taxonomy of (trend or state) symbols, and a variety of time granularities. Moreover, we allow for flexible querying, where queries can be expressed at any level of detail in both dimensions, also in an interactive fashion, and ground cases as well as generalized ones can be retrieved. We also take advantage of multidimensional orthogonal index structures, which can be refined progressively and on demand. The framework in practice is illustrated by means of a case study in hemodialysis.CaseBased Reasoning Research and Development, 8th International Conference on CaseBased Reasoning, ICCBR 2009, Seattle, WA, USA, July 2023, 2009, Proceedings; 01/2009
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A Fuzzy Approach to Temporal ModelBased Diagnosis
for Intensive Care Units
Jos´ e Palma1and Jos´ e M. Ju´ arez1and Manuel Campos1and Roque Mar´ ın1
Abstract.
In the Intensive Care Unit (ICU) domain, temporal evolution of
diseases and patients’ contextual information are critical pieces of
knowledge that must be considered in the design of a diagnosis task.
The uncertainty inherent in the description of temporal information
associated to diseases requires a temporal representation and reason
ing framework. This temporal framework has to be flexible enough
to facilitate its integration in a behavioral model. This paper pro
poses a Temporal Behavioral Model (TBM) that makes this integ
ration possible and permits the specification of contextual inform
ation (that may modify the TBM). A diagnosis process is also pro
posed.ThisprocessusestemporalmodelbasedtechniquesandFuzzy
Temporal Constraints Networks (FTCN) as the underlying temporal
framework. Some heuristics, which affect not only the temporal reas
oning dimension but also the causal, have been designed in order to
compute solutions efficiently.
1INTRODUCTION
Physicians at intensive care units (ICUs) have to deal with an over
whelming amount of data provided not only by online monitoring
but also collected from patients’ records (e.g., laboratory results),
which are, in most cases, collected manually at different time in
stants. In order to provide efficient decision support systems and
medical research tools in the ICU domain, it is necessary to integrate
and analyse the information provided from these different sources.
These tools are focused on the analysis of patient’s evolution over
time. This kind of analysis may provide valuable information for
making decisions about patient treatments and for improving clin
ical guidelines.
A good analysis of patient evolutions lies in an efficient dia
gnosis process. The use of deep causal models together with model
based diagnosis techniques has proved its efficiency in the develop
ment of intelligent diagnosis systems [17]. Moreover, the ICUs do
main reveals the importance of the temporal component modelling
in capturing the temporal information associated to patient evolution
[13]. However, the inclusion of temporal representation techniques
in MBD has increased the complexity of the diagnosis process. Dif
ferent formalisms have been proposed to represent time in MBD,
ranging from totally qualitative approaches [11], based on Allen’s
interval logic [1], to totally quantitative approaches [9, 15, 16]. A
serious attempt to provide a general framework for temporal MDB
can be found in [3, 8], which presents a general characterization of
temporal MDB at knowledge level.
Our goal, therefore, is to present a general framework for Tem
poral MDB, along the lines of [3] but using an algebraic approach
1University of Murcia. Murcia, Spain. Contacting author jpalma@dif.um.es
based on Fuzzy Temporal Constraints Network framework (FCTN)
for temporal dimension representation.
The structure of the paper is as follows: the underlying temporal
framework is described in a concise manner in section 2. Section 3
presents the temporal behavioral model. The elements that constitute
the inputs and outputs of the algorithm are introduced in section 4.
The diagnosis process is analysed in section 5. Section 6 shows some
experimental results provided by a performance analysis. Finally, we
provide conclusions and future works.
2 TEMPORAL FRAMEWORK
In some proposals for Temporal MBD, the temporal dimension is
modelled by means of the socalled Fuzzy Temporal Constraint Net
work (FTCN) formalism [14]. A FTCN is a pair N =< T ,L >
consisting of a finite set of temporal variables, T = {T0,T1,...,Tn},
and a finite set of binary temporal constraints, L = {Lij, 0 ≤ i,j ≤
n} defined on the variables of T . A FTCN can be represented by
means of a directed constraint graph, where nodes represent temporal
variables and arcs represent binary temporal constraints.
Each binary constraint Lijon two temporal variables Tiand Tjis
defined by means of a convex possibility distribution πLij(π(v?) ≥
min{π(v),π(v?)};v ≤ v?≤ v??), whose discourse universe is Z,
and which restricts the possible values of the time elapsed between
both temporal variables. In the absence of other constraints, the as
signments Ti = tiand Tj = tj are possible if πLij(tj − ti) > 0 is
satisfied.
An ntuple S = (t1,...,tn) ∈ τnis a σpossible solution of a
FTCN network N if πSN= σ, where πSN= min{πLij(tj −
ti), 0 ≤ i,j ≤ n}. The possibility distribution πSNdefines the
fuzzy set SN of the σpossible solutions of the network, with σ ≥ 0.
A FTCN network N is consistent if and only if SN is greater than
a previously established threshold α, where α ∈ [0,1], with α = 1
being equivalent to the crisp case. The value of α is conditioned by
the context and is set up arbitrarily by the user.
This model has been implemented and extended in FuzzyTIME
[4], a general purpose temporal reasoner that provides high level
language and reasonings capabilities on fuzzy temporal constraints
between temporal variables which can represent intervals or time in
stants.
3TEMPORAL BEHAVIORAL MODEL
In this proposal, we opt for a Temporal Behavioral Model, TBM,
an abnormal behavioral model in which only the causal and tem
poral relations between hypotheses (diseases) and abnormal obser
vations caused by them are represented. These relations are defined
Page 2
by Diagnostic Fuzzy Temporal Patterns (DFTPs). Apart from the
abnormal behavioral model, a DFTP includes knowledge about
how the context affects the temporal behavioral model, referred to as
Contextual Metaknowledge (CTX). Hence, TBM = {DFTPk}.
Each DFTP can be formally defined by the tuple DFTP =
?H,IM,IH,Rdftp,CTX? where:
• H is the diagnostic hypothesis described by DFTP.
• IM = {imkk = 1,...,nim}, is the set of abnormal manifesta
tions implied by the hypothesis H.
• IH = {ihkk = 1,...,nih} is the set of hypotheses implied by
H (in medical domains, ihkis a disease caused by H).
• Rdftp= ?Tdftp,Ldftp? is a consistent FTCN, where tem
poral variables in Tdftpare associated to H, IM and IH,
Tdftp
poral constraints between them are defined in Ldftp, where
Ldftp= C(tH,tim
those constraints defined by the expert are instantiated, and a
subsequent process computes the minimal network of constraints
between all temporal variables.
• CTX = {CTXi} is the set of temporal contexts. A context
describes how the DFTP definition is modified when a con
text factor occurs (temporal or atemporal concepts). Formally
CTXi = ?ACi,TCi,Rct
– ACi is the set of possible atemporal concepts described in the
context (e.g. patient age, smoker).
=
{tH,tim
1 ,···,tim
nim,tih
1,···,tih
nih} and the tem
1 ,···,tim
nim,tih
1,···,tih
nih). Furthermore, only
i,MFi? where:
– TCi is the set of possible temporal concepts described in the
context (e.g. a drug was given at a certain time).
– Rct
with the temporal concepts TCi
– MFi = {mf1,...,mfm} is the set of modification functions
(mfi) that describes the DFTP modifications. These functions
create, delete and modify elements of the IM, IH sets, and the
Rdftpnetwork.
i is a FTCN that includes constraints in the hypothesis H
Theoretical descriptions of diseases are clearly shown in medical
manuals, however those descriptions are deeply conditioned by the
present situation of each particular patient. Temporal contexts are
therefore important aspects of diagnosis. The presence or absence
of manifestations can be explained by a given disease, but this could
change depending on patient contextual conditions. These conditions
affect existing manifestations, but they also could justify new symp
toms not gathered in the original DFTP. Other possible represent
ations of TBM are possible. However, the representation of context
knowledge and the behavior in medical environments is easily rep
resented by the model previously proposed in this work.
As an example, we present a (simplified) description of the acute
myocardial infarction (AIM) according to the TBM presented: The
AIM (Root Hypothesis: (AIM, t1)) is manifested by a precordial
pain, and moderate values of the ST levels (implied manifestations:
(pain, location,precordial,t2), (STlevel, intensity, moderate,t3)), the
second one more or less two minutes after the infarction (tem
poral constraint: t3 APPROX 2 MINS AFTER t1). The AIM could
also produce a mixed shock syndrome (implied hypothesis: (Mixed
ShockSyndrome, t4)).
4DIAGNOSIS ALGORITHM INPUTS AND
OUTPUTS
In order to provide a solution, the diagnosis process requires as in
puts (apart from the TBM) the patient’s observations (EV T−=
{evtii = 1,...,nobs}), the contextual observables (CTXobs =
{ctxii = 1,..,nctx}), and a consistent temporal network (Rinput),
whose temporal variables are associated to elements in EV T−and
CTX. In most cases, these temporal variables are specified as abso
lute time instants, which makes the reasoning process more efficient.
In our proposal, the diagnostic process output (i. e., the explan
ation provided) is composed not only of a set of abducibles, such
as in [3, 11], but by all the elements that conform the final instanti
ated causal network (physiopathological and ethiological diagnosis,
in medical domains). This kind of diagnosis explanation is neces
sary from the point of view of decision support system development.
Therefore, the diagnosis algorithm output can be formally defined
as the tuple EXP = ?CNexp,Rexp,DFTPexp,BLexp,ABexp?
where:
• CNexprepresents a directed graph describing the final causal net
work, where nodes represent observables and hypotheses in the
final explanation.
• Rexpis a FTCN where the temporal variables are associated to
the CNexpnodes.
• DFTPexpis the set of contextualized DFTP selected for explan
ation.
• BLexprepresents the binding list. It is a set of links between the
hypothesis nodes of the causal network and their corresponding
temporal patterns definitions.
• AB ⊂ DFTPexp is the set of abducibles generated by the dia
gnosis process.
In MBD, different interpretations of temporal diagnosis ex
planation have been proposed. On the one hand, there is totally
consistencybased diagnosis [10, 12], in which the explanation
provided should be consistent with all observations. On the other
hand, there is totally abductionbased diagnosis [7, 13], in which the
explanation should logically entail all the observations.
The same considerations can be made for temporal dimension. In
[3], a generic knowledge level model for temporal MDB is proposed
in which the definition of explanation has been parameterized. This
parameterization allows the definition of explanation to be moved
on the continuous line defined between totally consistent diagnosis
and totally abductive diagnosis. In our proposal we opt for an inter
mediate model in which an abductive component is applied to ab
normal events EV T−, and components consistency is applied for
thetemporaldimension.Thisintermediateinterpretationofdiagnosis
explanation can be formally stated as follows:
Definition 1 (Temporal Diagnosis). Given a Temporal Diagnostic
Problem TDP =< TBM,EV T,CTXevt,Rinput>, EXP =<
CNexp,Rexp,DFTPexp,BL,AB > is a possible explanation for
TDP iff:
1. DFTPexpSCTXevtSCTX = EV T−,
2. RinputSRexpis consistent.
5THE DIAGNOSIS PROCESS
Thediagnosisprocessinthisworkisdescribedbyanalgorithmbased
on the TBM described in Section 3. The following assumptions
have been made:
Multiple cardinality solution. Several hypotheses may be found
in a solution, which represent alternative or complementary solu
tions. Furthermore, different instances of the same hypothesis (the
same hypothesis located at different time instants) are possible in a
Page 3
solution. However, all hypotheses should be consistent with the con
text information.
Parsimonious covering based diagnosis. The proposed al
gorithm explains the abnormal event set EV T−
nious covering. New hypotheses are included in the final explana
tion if and only if events cannot be explained by the hypotheses
already instantiated. Of course, the solutions provided do not con
tradict either temporal or atemporal contextual concepts.
Acceptable efficiency of the process. Despite the fact that the
algorithm presents an exponential time execution, the algorithm in
cludes some heuristics (subsumption and temporal shifting) to im
prove efficiency. Experimental results,as we will see in Section 6,
point to an acceptable time response.
newthrough parsimo
5.1Subsumption
The aim of the subsumption process is to avoid an excessive prolifer
ation of temporally nearby hypotheses. Thus, before creating a new
instantiated pattern to explain a given event evti, the subsumption
process tries to include it in one of the already instantiated patterns,
particularly those patterns in DFTPexp which match with the pat
terns in TBM and which explain evti.
In order to subsume a given evti, with dftpk = evoke(evti), in
DFTP ∈ DFTPexp, the subsumption process checks if the tem
poral constraints defined in dftpk in which evti takes part are con
sistent with the temporal constraints of Rexp(the temporal constraint
network of the solution). In other words, the event evtiis included in
the solution and all temporal constraints related to this event in dftpk
are added to Rexp. After that, if Rexpis temporally consistent (that
is, if the consistency degree is greater than the previous established
threshold), the event evtiis subsumed. Furthermore, this event is ex
plained by the hypothesis of dftpkthat already explains other events
of the solution. This process is carried out by a temporal query to the
temporal reasoner using local propagation of the fuzzy constraints,
similar to the technique defined in [2].
Figure 1 shows how evt3 is subsumed in DFTP. Thus, on the
righthand side, the causal network of the pattern is represented,
where evt3is a cause of H1. On the lefthand side a part of the tem
poral constraint network of the solution is represented. Hence, the
new temporal constraints on the network can be observed, due to the
temporal variable associated to evt3.
The diagnosis algorithm tries to subsume an event in a pattern
when contextualization is not possible. We consider that contextu
alization is a process of characterizing a pattern for a given event in
a given context. Therefore, there is no sense in associating this event
within an existing pattern of the solution, because is is always as
sumed that any solution that can be framed in a context is better than
any other that can not.
However, subsumption usefulness refers to the time execution
factor. The subsumption process slows down the growth of instan
tiated hypotheses, which is exponential. Subsumption allows events
to be explained by instantiated hypotheses of the solution, avoiding
temporal nearby instances of hypotheses.
5.2Temporal Shifting
When subsumption is not possible, is a new pattern instantiation
enough?. The answer is no. When a given event cannot be sub
sumed, it is due to temporal inconsistencies in the instantiated pat
tern, DFTP. However, DFTP could possibly explain the new
event if temporal conditions were different.
Thus, we therefore propose including a new instance of the same
pattern and associating the event to it. If we reconsider the failed
subsumption, we will notice that only a few of the associated events
subsumed into it do not allow the new subsumption. According to
this, some of these events (already subsumed) can be subsumed by
the new instance of the pattern. In conclusion, a temporal shifting
process will produce two instances of the same pattern (at different
time instants), whose hypotheses explain at least one different event
and, perhaps, some common events.
evt1
evt1evt2evt3
H1
H1
evt3
evt4
evt4
evt2
H2
H2
R CN
exp
exp
new causal relation
old temporal constraints
new temporal constraints
Figure 1.
Subsunction.
In Figure 2, the temporal shifting of H1(H1) is represented when
the evt3 is explained. On the righthand side, the causal network is
represented. There, H1hypothesis can explain evt3when the hypo
thesis is shifted. On the lefthand side the temporal constraint net
work (Rexp) is represented. Note that a temporal constraint inhibits
the subsumption of evt3 in H1. Due to this, H1 is temporally shif
ted (H1). This new instance of the hypothesis does explain evt3.
Moreover, evt2could also be subsumed in H1.
consistent relation before temp.shift.
inconsistent relation
consistent relation after temp.shift.
evt1
H1
evt2evt3
H1
H1
H1
evt1evt2evt3
exp
exp
R CN
Figure 2.
Temporal Shifting.
The temporal shifting process is used when subsumption is not
possible.However,thisprocessreducesthealgorithm’sefficiencybe
cause of the large amount of calculi for temporal consistence check
ing, in spite of the local propagation process. Furthermore, this pro
cess could imply new subsumptions. In our opinion, this problem
could be partially reduced using some heuristics, which determine
whether the hypothesis must be shifted or not. In this work, we sug
gest the application of this shifting technique only with the latest
temporal instance of the pattern (last(D), line 10 of Algorithm 1).
This heuristic increases the probability of finding at least one hy
pothesis that can explain the event. Moreover, it avoids the combin
atorial explosion of explaining the hypothesis, because a single tem
Page 4
poral shifted hypothesis per event is guaranteed. We are currently
considering working with temporal intervals which provide a higher
level of abstraction. The use of intervals shows us how to associate a
concrete persistence to a DFTP. The definition of hypotheses per
sistence will allow the aggregation of nearby temporal hypotheses,
e.g. describing temporal influence interval on pattern instances. In
this case, it could be possible to aggregate those temporally shifted
hypotheses allocated in the same influence interval, so that a single
hypothesis substitutes all of them.
5.3The Diagnosis Algorithm
Once the selected event is explained and removed from EV Tnew
(initially EV Tnew = EV T−), its explaining hypothesis (hypo
theses) will be a new event to be explained, and therefore will be
included in EV Tnew. The algorithm finishes when it is not possible
to find a higher level hypothesis, abducibles of the solution, that can
explain any of the EV Tnew events. The diagnosis process can be
described, as follows:
1. An event e is selected from EV Tnew. The event e is possibly
associated to an evidence or a hypothesis.
2. The algorithm searches (evoke(), line 5) all possible patterns
D from TDM that can explain event e.
3.Finally, the algorithm tries to include each pattern of D found
in the solution as follows: 1)The algorithm considers temporal and
atemporal concepts from the context information input (CTXobs),
then the algorithm tries to contextualize (contextualized(), line 7)
the pattern. 2)If contextualization is not possible, the diagnosis pro
cess tries to subsume (subsume(), line 9) the event in any of the
already instantiated patterns that exist in the partial solution (see Sec
tion 5.1). 3)When subsumption is not possible either, the temporal
shifting process (see Section 5.2) is applied (temporal shifting(),
line 12). Due to the computational cost of this procedure, this process
mustfulfilsomeheuristicconditionslikethatproposedinsection5.2.
4)If non previousactions are possible, the diagnosis process will gen
erate an instance of the new pattern in the solution (generate new(),
line 17).
Function COVER (TBM, EV T−, CTXobs, Rinput) return EXP
1 : subsumed = FALSE
2 : EV Tnew= EV T−
3 :
while EV Tnew ?= ∅ do
4 :
for each evti ∈ EV Tnewdo
5 :D = evoke(evti)
6 :
for each dftpi ∈ D do
7 :
if not contextualized(dftpi,evti,EXP) then
8 :
if dftpi ∈ DFTPexpthen
9 :
if( not subsume(evti,dftpi,EXP) and
10:
not subsumed and last(D) = dftpi)then
11: subsumed = TRUE
12:
dftpnew= temporal shifting(evti,dftpi,EXP)
13:
evth= associateevent(dftpnew)
14:
EV Tnew= EV Tnew∪{evth}
15:
endif
16:
else
17:
dftpnew= generate new(evti,dftpi,EXP)
18:
evth= associate event (dftpnew)
19:
EV Tnew = EV Tnew∪ {evth}
20:
endif
21:
endif
22:
23:
24:
25:
endFunction
endfor
EV Tnew = EV Tnew?{evti}
endfor
endwhile
Algorithm 1: Parsimonious covering algorithm.
6 PERFORMANCE ANALYSIS.
In this work, we have focused our analysis on time execution factors,
trying to find the most relevant variables that influence the perform
ance of the diagnosis process. The objective of this analysis is to
ascertain the influence of different parameters of the input space on
the overall performance. The following factors are considered:
c)
d)
b)
a)
5000
10000
15000
20000
25000
30000
35000
40000
1.5 2 2.5 3
time (ms)
mean explain level
mean connectivity vs. time
"explainlevelmean.dat"
0
mean explain level vs. time
1
18000
20000
22000
24000
26000
28000
30000
32000
34000
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
time (ms)
"connectivitymean.dat"
mean connectivity
0.8
0
5000
10000
15000
20000
25000
30000
35000
0 1 2 3 4 5 6 7 8
"dftpnumber.dat"
time (ms)
dftp number vs. time
dftp number
5000
10000
15000
20000
25000
30000
35000
0 4 6 8 12 14
evidence number
evidence number vs. time
"evidencenumber.dat"
0
10 2
time (ms)
Figure 3.
Experimental results of the algorithm. Prototype: Java.
Proc:AMDAthlonXP Freq:1.53GHz RAM:256MB
• The Number of Input Events. Far from reducing the number
of conjectures, the increase of evidences, in medical domains
increases their possible explanations. This is mainly due to the
nature of clinical hypothesis, where the same evidence could be
explained by several hypotheses. The increase of evidences re
quires more time to complete the whole explanation process and,
therefore, the study considers only the time used to explain the
first hypothesis of each evidence. As is shown in Figure 6.a, the
executiontime presents an exponential behaviorof time, but this is
expected if we consider that the time spent for checking temporal
consistence (in temporal shifting and subsunctions) increases be
cause of the growth of temporal variables and events at each iter
ation.
• The Number of Patterns required to find a solution (Figure 6.b).
This parameter shows the influence of the number of DFTPs
considered in finding the solution, that is, how the depth of the
causal network affects the process performance.
• Mean Pattern Connectivity Degree (Km). Let us define con
nectivity (K) of a pattern (DFTP) in the TBM as follows:
Page 5
KDFTP = IH, that is, the number of implied hypotheses of
patterns. Then Kmcan be defined as:
P
• Mean Pattern Explanation Degree (Em): Explanation degree
(E) of a pattern (DFTP) in the TBM is defined as EDFTP =
IM + IH with IM ∧ IH ∈ DFTP, that is, the number of
causal links. The Emis defined as:
P
Km =
DFTP∈TBMKDFTP
 TBM 
(1)
Em =
∀DFTP∈TBMEDFTP
 TBM 
(2)
These last two factors, Kmand Em, can be considered as a meas
ure of the TBM complexity. Emcan be considered as an indication
of the complexity in covering the initial observations (Figure 6.c)
whereas Kmcan be associated to the complexity in building CNexp
upwards from the first hypotheses to abducibles (Figure 6.d).
This work is focuses on the capacity of the presented model to
represent causal and temporal knowledge, and the study of the per
formance analysis. Today, we are at the knowledge acquisition step,
so a causal and temporal knowledge acquisition tool (CATEKAT)
has been implemented for elaborating a complete TBM [5]. How
ever, this step is not finished yet. Thus, the input data set used in
this work has not been validated by the expert. In any case, we have
taken into account that the complexity of causal and constraints net
work in the testing bench is similar to a small set of already validated
patterns.
7 CONCLUSIONS AND FUTURE WORKS
This paper describes a general framework for temporal MDB which
tackles the problems of modelling complex interaction between deep
causal models and context knowledge and structure of explanations
(solutions) provided. The proposed framework demonstrates the suit
ability of FTCNs for time management. Following the general
framework proposed in [3], our proposal can be characterized in the
following terms: (a) the temporal phenomenon described in this pa
per can be considered a temporal behavior one in which the con
sequences of the fact that the system is in a given state (normal or
faulty) are observed after some time; (b) time is modelled by means
of a metric timeontology in which temporal information is repres
ented by FTCNs [4, 14]; and (c) with regard to the definition of the
explanation chosen, we demand that the explanation provided logic
ally entails all abnormal observations, and that its temporal inform
ation is consistent with the one observed. Therefore, we propose an
abductive approach for observations and a totally consistentbased
approach for temporal dimension.
The use of diagnostic temporal patterns proposed in this paper is
similar to that defined in [9], but our proposal makes it possible to
model causal relations between diagnostic patterns. Causal relations
between diagnostic patters allow us to define a causal network of dia
gnostic patterns. Another difference lies in the temporal representa
tion framework, since we use the Fuzzy Temporal Constraints Net
work formalism, while the diagnostic patterns defined in [9] make
use of a quantitative interval based approach.
One of the main differences between our approach and Brusoni et
al. [3] is related to the way that contextual knowledge is integrated in
the model. In Brusioni’s approach, contextual knowledge is defined
as a set of maximal episodes that can be used in the antecedent of
the logical formulae which conform the temporal behavioral model.
In our model, contextual knowledge is defined as a set of logical for
mulae which includes knowledge about temporal relations between
antecedents components, thus conforming a metaknowledge base
which defines how the context knowledge affects disease evolution
definition. In our model, therefore, contextual information is ortho
gonal to temporal behavior.
Future works will focus on the integration of this model with a
possibility theory based evaluation of hypothesis consistency (in or
der to provide a consistent explanation), and on the logical formula
tion in terms of temporal logic, like the one defined in [6].
8 Acknowledgement
This work is supported by the Spanish MCYT under the MEDICI
project (project number TIC200309400C04) and by the Spanish
MECD, under the FPU national plan (grant ref. AP20034476)
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