Research Article Abstract Computation in Schizophrenia

Research ArticleAbstract Computation in Schizophrenia Detection throughArtificial Neural Network Based Systems

L Cardoso1 F Marins1 R Magalhatildees23 N Marins4 T Oliveira1 H Vicente5

A Abelha1 J Machado1 and J Neves1

1University of Minho CCTC 4710-057 Braga Portugal2Life and Health Sciences Research Institute (ICVS) School of Health Sciences University of Minho 4710-057 Braga Portugal3ICVS3Brsquos PT Government Associate Laboratory Guimaraes 4710-057 Braga Portugal4Centro Hospitalar Conde de Ferreira 4200-227 Porto Portugal5Department of Chemistry and Evora Chemistry Centre School of Science and Technology University of Evora7004-516 Evora Portugal

Correspondence should be addressed to J Neves jnevesdiuminhopt

Received 22 July 2014 Revised 17 September 2014 Accepted 28 September 2014

Academic Editor Xiangfeng Luo

Copyright copy 2015 L Cardoso et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Schizophrenia stands for a long-lasting state of mental uncertainty that may bring to an end the relation among behavior thoughtand emotion that is it may lead to unreliable perception not suitable actions and feelings and a sense of mental fragmentationIndeed its diagnosis is done over a large period of time continuos signs of the disturbance persist for at least 6 (six) monthsOnce detected the psychiatrist diagnosis is made through the clinical interview and a series of psychic tests addressed mainlyto avoid the diagnosis of other mental states or diseases Undeniably the main problem with identifying schizophrenia is thedifficulty to distinguish its symptoms from those associated to different untidiness or roles Therefore this work will focus onthe development of a diagnostic support system in terms of its knowledge representation and reasoning procedures based on ablended of Logic Programming and Artificial Neural Networks approaches to computing taking advantage of a novel approach toknowledge representation and reasoning which aims to solve the problems associated in the handling (ie to stand for and reason)of defective information

1 Introduction

Schizophrenia is a brain disorder that strikes people as theyare entering the prime of their life and in many cases mayrun a recurrent and ultimately chronic course that will lead tosubstantial disability Indeed this highly destructive mentalillness affects the essence of what makes people human thatis their personality and intellect [1]

The incidence of this disease is roughly one new patientper year per ten thousand human beings In the one handit occurs in all cultures in spite of more schizophrenicones appearing in the lower socioeconomic classes of theindustrialized countries on the other hand the admissionrates for schizophrenia are higher in the urban areas than in

the rural onesThe gender distribution is approximately equalin both sexes and the peak of incidence is situated between 15and 25 years inmales and between 25 and 35 years in females[1 2]

There are also several risk factors that must be consid-ered namely the genetic ones like predisposing pregnancyand birth complications Indeed and to some extent someprecipitating circumstances such as family interactions (egdysfunctional families and expressed emotion a kind ofbehavior with overt criticism and hostility) life events (eghappenings that provokes a high level of stress) or drugabuse must also be object of attention [2]

When working on the diagnosis of schizophrenia thechallenging question with which practitioners are met relies

Hindawi Publishing Corporatione Scientific World JournalVolume 2015 Article ID 467178 10 pageshttpdxdoiorg1011552015467178

2 The Scientific World Journal

on the similarity between the signs and symptoms amongpsychic diseases and states Typically the earliest act forthe diagnosis of schizophrenia proceeds from the detectionof a specific outbreak ordinarily evinced by hallucinationsdelusions disorganized speech catatonic behavior abolitionand social separation or even additional personality disor-ders The psychiatric diagnosis is made through the clinicalinterview based on psychopathology but the problem isthat knowledge of psychopathology of anthology dependson the training and experience of the psychiatrist Theselimitations ldquoopen the doorrdquo to mistake and doubt From herethe practitioners may perform psychic exams intended todetect cognitive flaws delusional perception and abnormalchanges or thoughts among others [1 2]

Above any kind of dispute the main problem with thediagnosis of schizophrenia comes from the large numberof different mental diseases and states that may mimic itssigns such as epilepsy drug-induced psychosis affective psy-choses (eg bipolar major depressive disorders) Aspergersyndrome schizoaffective disorder and Wilsonrsquos disease Toface this situation the practitioner is forced to order extraexams namely toxicological tests electroencephalography(EEG) and brain computed tomography (CT)rsquos [1] Also thispinpointing is usually done over a large period of time (at least6months) therefore generating a huge amount of data whichhas to be treated and interpreted by the practitioner(s)

Facing such a large amount of facts even experiencedpsychiatrists have difficulties to make a precise diagnosisand distinguishing between this and other diseases Unfortu-nately there is not toomuchwork done in the area ofMedicalInformatics to help in this process although Strous et al [3]worked on a system that uses the differences on writing todiagnose schizophrenia

With this paper we make a start on the developmentof an unusual or original diagnosis assistance system forschizophrenia We will present a logic programming basedapproach in order to represent the knowledge and rea-soning with a focus on the Degree of Confidence (DoC)of the attributes set that makes a function or a predicate[4]

2 Related Work

Many studies presenting the concept of uncertainty andorldquoimperfect datardquo like [5ndash8] show that there is an emergentinterest in the problem of uncertainty as compared toaccuracy or error in data [9 10] The notion of uncer-tainty is broader than error or accuracy and includes thesemore restricted concepts While accuracy is the closenessof measurements or computations to their ldquotruerdquo value orsome value agreed to be the ldquotruthrdquo uncertainty can beconsidered any aspect of the data that results in less thanperfect knowledge about the phenomena being studied [11ndash13]

The consequences of the uncertainty in the data and inthe data quality to user exploring modelling visualizing and

querying have been also referred to in many studies [6 8 14ndash18] On the one hand it is consensual that when the dataare uncertain a different representation and uncertaintywhich can be reduced by ldquoacquiring additional informationor improving the quality of the information availablerdquo [6] isneeded that is in almost all decisions that one may take theinformation is not always exact but indeed imperfect in thesense thatwe handle estimated values probabilisticmeasuresor degrees of uncertainty [19 20] On the other handknowledge and belief are generally incomplete contradictoryor even error sensitive It is advisable the use of formaltools to deal with the problems that arise with the use ofpartial contradictory ambiguous imperfect nebulous ormissing information [13 21ndash23] Some general models havebeen presented [8 16 24] where uncertainty is associatedto the application of Probability Theory [16 17] Fuzzy SetTheory [25] Similarities [26 27] Other approaches forknowledge representation and reasoning have been proposedusing the Logic Programming (LP) paradigm namely inthe area of Model Theory [28ndash30] and Proof Theory [29 3132] Qualitative models and qualitative reasoning have beenaround in Artificial Intelligence research for some time [1433] in particular due to the growing need to offer support indecision-making processesThe evaluation of knowledge thatstems out from logic programs becomes a point of researchIn this sense the evaluation of knowledge that stems out fromlogic programs becomes a point of research Shi et al [15] andSchneider [25] work is a good example of quality evaluationusing logic They used abduction [14] and temporal logic forquality-checking of medical guidelines proposing a methodto diagnose potential problems in a guideline regarding thefulfillment of general medical quality criteria at a metalevelcharacterization They explored an approach which uses arelational translation to map the temporal logic formulas tofirst-order logic and a resolution-based theorem prover [25]In another research line the Quality-of-Information concept(QoI) [6 7 26 34] demonstrated their applicability in manydynamic environments and for decision making purposesThe objective is to build a quantification process of the QoIand an assessment of the argument values of a given predicatewith relation to their domains (here understood as Degree-of-Confidence (DoC)) which stems from a logic program ortheory during the evolutive process of searching solutions inorder to solve a problem in environments with default dataOur main contribution relies on the fact that at the end theinitial extensions of the predicates that make the universe ofdiscourse are given in terms of DoCs predicates that stand foronersquos confidence that the initial predicates arguments valuesof the predicates that make the universe of discourse fit intotheir respective domainsThis approach potentiates the use ofdiverse computational paradigms like Case Based Reasoning[35] Artificial Neural Networks (ANN) [36 37] and ParticleSwarm [38] just to name a few It also encapsulates initself a new vision of Multivalue Logics once a proof of atheorem in a conventional way is evaluated to the interval[0 1] Following these studies good results were achieved fordifferent purposes namely inHealthcare [27] Civil Law [39]

The Scientific World Journal 3

Multiagent Systems [40] Virtual Entities [34] AmbientAssisted Living [41] and Decision Making Environments[30] Indeed some interesting results have been obtainednamely in the fields of Coronary Risk Evaluation [42]Hyperactivity Disorder [43] and Length ofHospital Stay [44]among others which fit the case studies insufficiency that arecommon in this area of research and applications

3 Knowledge Representation and Reasoning

We follow the proof theoretical approach and an extensionto the LP language [31] to knowledge representation andreasoning An Extended Logic Program (ELP) stands for afinite set of clauses in the form

119902 larr997888 1199011

and 119901119899

and not1199021

and sdot sdot sdot and not119902119898

(1199011

and sdot sdot sdot and 119901119899

and not1199021


) (119899 119898 ge 0)

(1)

where is a domain atom denoting falsity and the 119901119894 119902119895

and 119901 are classical ground literals that is either positiveatoms or atoms preceded by the classical negation sign not

[32] Under this representation formalism every program isassociated with a set of abducibles [28 30] given here inthe form of exceptions to the extensions of the predicatesthat make the program Once again LP has emerged asan attractive formalism for knowledge representation andreasoning tasks introducing an efficient search mechanismfor problem solving Due to the growing need to offer usersupport in decision-making processes some studies havebeen presented [45 46] related to the qualitative models andqualitative reasoning in Database Theory and in ArtificialIntelligence (AI) research With respect to the problem ofknowledge representation and reasoning mechanisms in LPa measure of the Quality of Information (QoI) of suchprograms has been object of some work with promisingresults [47ndash49] that is the QoI denotes onersquos confidence thata particular term of a predicate that makes the universe ofdiscourse belongs to its extension Indeed theQoI indeed [31]with respect to the extension of a predicate 119894 will be given by atruth-value in the interval [0 1] that is if the information isknown (positive) or false (negative) the QoI for the extensionof predicate 119894 is 1 For situations where the information isunknown the QoI is given by

QoI119894

= lim119873rarrinfin

1

119873= 0 (119873 ≫ 0) (2)

where 119873 denotes the cardinality of the set of terms orclauses of the extension of predicate 119894 that stand for theincompleteness under consideration For situations where

the extension of predicate 119894 is unknown but can be taken froma set of values the QoI is given by

QoI119894

=1

Card (3)

where Card denotes the cardinality of the abducibles set for119894 if the abducibles set is disjoint If the abducibles set is notdisjoint the QoI is given by

QoI119894

=1

(119862Card1

+ sdot sdot sdot + 119862CardCard)

(4)

where 119862CardCard is a card-combination subset with Card ele-

ments The next element of the model to be considered isthe relative importance that a predicate assigns to each of itsattributes under observation that is 119908

119896

119894 which stands for the

relevance of attribute 119896 in the extension of predicate119894 It is

also assumed that the weights of all the attribute predicatesare normalized that is

sum1le119896le119899

119908119896

119894= 1 forall

119894 (5)

where forall denotes the universal quantifier It is now possibleto define a predicate

119894scoring function 119881

119894(119909) so that for a

value 119909 = (1199091 119909

119899) defined in terms of the attributes of

predicate119894 one may have

119881119894

(119909) = sum1le119896le119899

119908119896

119894timesQoI119894

(119909)

119899 (6)

It is now feasible to rewrite the extensions of the predicatereferred to above according to productions of the type

predicate119894

(1199091 119909

119899) QoI DoC (7)

and evaluate the Degree of Confidence (DoC) given byDoC = 119881

119894(1199091 119909

119899)119899 which denotes onersquos confidence that

the argument values of predicate119894fit into its domain values To

bemore general let us suppose that theUniverse ofDiscourseis described by the extension of the predicates

1198861

(sdot sdot sdot ) 1198862


(sdot sdot sdot ) (119899 ge 0) (8)


Therefore one may have (where perp denotes an argumentvalue of the type unknown the values of the others argumentsstand for themselves)

not1198861

(1199091 1199101 1199111) larr997888 not 119886

1(1199091 1199101 1199111)

1198861

(perp [10 20] 15) 1 DoC

[5 10] [5 30] [10 20]⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟attributesrsquos domains for 119909

111991011199111

not1198862

(1199092 1199102 1199112) larr997888 not 119886

2(1199092 1199102 1199112)

1198862

([45 54] [10 12] perp) 1 DoC[30 60] [6 14] [2000 6000]⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

attributesrsquos domains for 119909211991021199112

dArr 1st interaction transition to continuous intervals

not1198861

(1199091 1199101 1199111) larr997888 not 119886

1(1199091 1199101 1199111)

1198861

([5 10] [10 20] 15) 1 DoC


111991011199111

not1198862

(1199092 1199102 1199112) larr997888 not 119886

2(1199092 1199102 1199112)

1198862

([45 54] [10 12] [2000 6000]) 1 DoC

[30 60] [6 14] [2000 6000]⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟attributesrsquos domains for 119909

211991021199112

dArr 2nd interaction normalization 119884 minus 119884min119884max minus 119884min

not1198861

(1199091 1199101 1199111) larr997888 not 119886

1(1199091 1199101 1199111)

1198861

([5 minus 5

10 minus 5

10 minus 5

10 minus 5] [

10 minus 5

30 minus 5

20 minus 5

30 minus 5]

[15 minus 10

20 minus 10

15 minus 10

20 minus 10])

equiv 1198861

([0 1] [02 06] [05 05]) 1 DoC

[0 1] [0 1] [0 1]⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟attributesrsquos domains for 119909

111991011199111

not1198862

(1199092 1199102 1199112) larr997888 not 119886

2(1199092 1199102 1199112)

1198862

([45 minus 30

60 minus 30

54 minus 30

60 minus 30] [

10 minus 6

14 minus 6

12 minus 6

14 minus 6]

[2000 minus 2000

6000 minus 2000

6000 minus 2000

6000 minus 2000])

equiv 1198862

([05 08] [05 075] [0 1]) 1 DoC


211991021199112

(9)

1

1

1

0

Interval length

Deg

ree o

f con

fiden

ce

Δl

Figure 1 Evaluation of the Degree of Confidence

The Degree of Confidence (DoC) is now evaluated usingDoC = radic1 minus Δ1198972 as it is illustrated in Figure 1 Here Δ119897 standsfor the length of the arguments intervals once normalized

As shown in Figure 1 one has the expected representationof the universe of discourse where all the predicatesrsquo argu-ments are nominal They speak for onersquos confidence that theunknown values of the arguments fit into the correspondentintervals referred to above

not1198861DoC

(1199091 1199101 1199111) larr997888 not 119886

1DoC(1199091 1199101 1199111)

1198861DoC

(0 0916 1) 05 DoC

[0 1] [02 06] [05 05]⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟attributesrsquos values range for 119909

111991011199111

[0 1] [0 1] [0 1]⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟attributesrsquos domain for 119909

111991011199111

not1198862DoC

(1199092 1199102 1199112) larr997888 not 119886

2DoC(1199092 1199102 1199112)

1198862DoC

(0954 0968 0) 06 0641

[05 08] [05 075] [0 1]⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟attributesrsquos values ranges for 119909

211991021199112


211991021199112

(10)

4 Onersquos Model

Therefore and in order to exemplify the applicability of ourapproach to default knowledge we will look at the relationaldatabase model since it provides a basic framework that fits


Lucidity

Drugs Alcohol Somnolence Level of consciousness

1 1 1 1 2

2 1 1 0 1

3 1 1 1 [0 1]

Differential

Neurological InfectiousToxic

metabolic

1 1 1 1

2 0 0 1

3 1 1 1

Alterations the way of thinking

Ideas of passivity Hallucinations Delusions

1 3 0 3 2

2 0 0 0 0

3 0 0 0 0

Delusional intuition

PerplexityEmotional

impoverishment

Depressive and euphoric

dysthymias

1 0 0 0 0

2 0 1 0 0

3 0 0 1 1

Schizophrenia

Agesexpredisposition

Genetic predisposition

Lucidity Differential

1 [012 018] 92 2 1 8 0

2 [005 006] 0 0 0 1

3 [012 018] 26 [0 1] 1 0 2

Agesex

predisposition

Age Sex

1 20 M

2 28 F

3 19 M

Kurt Schneider 1

Kurt Schneider 2

perp

Ks 1 Ks 2

Figure 2 An extension of the relational database model

into our expectations [50] and is understood as the genesis ofthe LP approach to knowledge representation and reasoning

Consider the scenario where a relational database is givenin terms of the extensions of the relations or predicatesdepicted in Figure 2 which stands for a situation whereone has to manage information about schizophrenia diseasedetection Under this scenario some incomplete data is alsoavailable For instance to patient ldquo2rdquo the genetic predispo-sition value is unknown while to patient ldquo3rdquo the lucidity(in both the extensions of the schizophrenia relation orpredicate) is in the interval [0 1] although the domain valuesto genetic predisposition range in the interval [09 915] andthe ones to lucidity are bound by the interval [0 2]

The psychiatrist fills the tables that link to the schizophre-nia table while heshe executes the psychopathologic examSome symptoms may be detected by the psychiatrist othersmay be perceived by additional exams (eg this happens withsome of the attributes of the DifferentialLucidity table) Atthis point the psychiatrist may fill some attributes with theunknown symbol (perp) and update the tables later

The agesex predisposition parameter which is evidencedin the schizophrenia table in Figure 2 is based on Table 1adapted from [1] These predisposition values are clusteredby age group and sex Thus the domain for this parameter

Table 1 Agesex predisposition adapted from [1]

Agesex predisposition(Annual rate per 1000)

Age group Male Female0ndash14 [0 018] [0 007]15ndash24 [012 018] [006 007]25ndash34 [006 012] [005 006]35ndash44 [003 006] [003 005]45ndash54 [002 003] [003 004]55ndash64 [001 002] [002 004]gt65 [0 001] [0 002]

is in the range [0 018] for males and for females is in therange [0 007] The genetic predisposition parameter whichis also evidenced in the schizophrenia table in Figure 2 isbased on Table 2 adapted from [51] its domain is in the range[09 915]

Lucidity is given in terms of the parameters or argumentsthat make a piece of Lucidity Table (Figure 2) The firstthree parameters are populated with a value between [0 1]wherein 0 (zero) denotes the presence of drugs and 1 (one)


Table 2 Genetic predisposition adapted from [51]

Genetic predisposition ()General population 09Foster brothers 18Spouses 21First cousins 26Nieces and nephews 39Grandchildren 43Stepbrothers 71Parents 92Brothers 142Dizygotic twin 145Dizygotic twin of the same sex 176Sons and daughters 164Children of father and mother schizophrenics 392Monozygotic twin living separately 776Monozygotic twin living together 915

the absence of drugs alcohol or somnolence The level ofconsciousness ranges in the interval [0 2] wherein zeromeans that the patient is in a torpor state one means thatthe patient presents obnubilation of the consciousness andtwo means he is in a waking state The differential diagnosesare represented in the differential table of the (Figure 2)Like the table lucidity it is populated with values between[0 1] meaning the presence or absence of neurologicalinfectious or toxicmetabolic diseases The lucidity and thedifferential diagnoses are important factors in the schizophre-nia diagnosis because if the patient is not lucid or heshehas one of the diseases previously mentioned the diagnosisis compromised In other words if one of the parametersof the lucidity and differential tables is zero the diagnosisis not settled properly Thus the lucidity and differentialvalues in the schizophrenia table are calculated through themultiplication of each parameter of table lucidity by the onesof the differential one In this way the domain of lucidityparameter in the schizophrenia table is in the range [0 2]while the domain to the differential value is in the range [0 1]

The tables Kurt Schneider 1 and Kurt Schneider 2 repre-sent the schizophrenia symptoms of first and second orderdelineated by Kurt Schneider [1 2] Relative to the tableKurt Schneider 1 (Ks 1) there are four clusters of symptomsThe former one alterations to the way of thinking rangesin the interval [0 3] with the meaning 0 (zero) absence ofalterations 1 (one) obsessive ideas 2 (two) escape of ideas 3(three) loudness theft broadcasting insertion interruptionand diffusion of the thinking The ideas of passivity arecategorized in the interval [0 2] with the connotation (0)zero absence of feelings impulses or somatic sensationsarising from outside that imposed on the patient 1 (one)feelings impulses or psychomotor activities with constantdoubt or uncertainty 2 (two) feelings impulses psychomo-tor activities or somatic sensations strange to himself andcontrolled by external agents to himself Hallucinations arerated in the interval [0 4] with the connotation 0 (zero)

absence of hallucinatory phenomena 1 (one) elementaryhallucinations 2 (two) visual hallucinations 3 (three) gus-tatory olfactory and kinesthetic hallucinations 4 (four)auditory hallucinations The latest delusions is grouped inthe interval [0 2] 0 (zero) absence of delusional ideas 1(one) delusional ideas assigning meanings of affective basis2 (two) delusional perception assigning a new meaningof autoreferential way In Kurt Schneider 2 (Ks 2) table allsymptoms showed in the (Figure 2) range in the interval[0 1] wherein 0 (zero) denotes the absence of the symptomand 1 (one) its presence Once these two tables are populatedthe values of Ks 1 and Ks 2 in the schizophrenia table are thesum of the values of respective symptoms In this way thesevalues range in the intervals [0 11] for Ks 1 and [0 4] forKs 2The higher these values are more evident is the diseaseIt is of great significance to note that first order symptomshave a much higher influence than the second order ones inschizophrenia detection

Let us now consider the extensions of the relations givenin (Figure 2) to populate the extension of the schizophreniapredicate

schizophrenia AgeSex PredispositionGenetic Predisposition

LucidityDifferentialKs 1Ks 2 997888rarr 0 1

(11)

where 0 (zero) and 1 (one) denote respectively the truth-values false and true It is now possible to give the extensionsof the predicate referred to above which may be set in theform

notsch(izophrenia) (AS(predisposition)G(predisposition) Luc(idity)

Dif(ferential)Ks 1Ks 2)

larr997888 not sch (ASG LucDifKs 1Ks 2)

sch ([012 018] 92 2 1 8 0) 1 DoC

[0 018] [09 915] [0 2] [0 1] [0 11] [0 4]⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟attributersquos values ranges

sch ([005 006] perp 0 0 0 1) 1 DoC


sch ([012 018] 26 [0 1] 1 0 2) 1 DoC


(12)

In this program the first clause denotes the closure ofpredicate schizophreniaThenext three clauses correspond tothe three cases presented in the extension of the schizophre-nia relation in (Figure 2) For example the second clausecorresponds to the patient 2 (two) a 28 (twenty eight)


years old woman Analyzing (Table 1) the psychiatrist fillsits agesex predisposition within the interval [005 006]face a domain that ranges between [0 007] Looking at itsgenetic predisposition the psychiatrist does not have anyinformation In this case the symbol ldquoperprdquo is used which standsfor an unknown value It subsumes that this variable maytake any value according to its domain that is in the range([09 915])

It is now possible to have the arguments of the predicatesextensions normalized to the interval [0 1] in order tocompute onersquos confidence that the nominal value of thearguments under considerations fit into the intervals depictedpreviously The normalization process presented below iswith respect to patient 2 (two)

Consider



dArr

sch ([005 006] perp 0 0 0 1) 1 DoC

[0 007] [09 915] [0 2] [0 1] [0 11] [0 4]⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟attributersquos domain


sch ([005 006] [09 915] [0 0] [0 0]

[0 0] [1 1]) 1 DoC



sch ([071 086] [0 1] [0 0] [0 0] [0 0]

[025 025]) 1 DoC

[0 1] [0 1] [0 1] [0 1] [0 1] [0 1]⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟attributersquos domains

dArr DoC calculation DoC = radic1 minus Δ1198972

schDoC (0989 0 1 1 1 1) 1 083

[071 086] [0 1] [0 0] [0 0] [0 0] [025 025]⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟attributersquos values range


(13)

Its terms make the training and test sets of the ArtificialNeural Network given below (Figure 3)

5 The Artificial Neural Network Topology

The previously presented diagnosis model works well todemonstrate how all the information comes together toform a diagnosis but it was built with the pure objectiveof demonstration In this section more reliable ways toassemble this information are considered Different ArtificialIntelligence (AI) and data mining tools can be used Neveset al [36 37] demonstrated how a Artificial Neural Network(ANN) can be successfully used to model data and capturecomplex relationships between inputs and outputs ANNssimulate the structure of the human brain being populatedby multiple layers of neurons The knowledge representationmodel defined in this work is appropriate for use with ANNs

Using a real case of 22-year-old male patient withno schizophrenic relatives an experienced psychiatristduring the diagnosis elaboration verified a full luciditystate of the patient (drugs 1 alcohol 1 somnolence 1level of consciousness 2) In the differential diagnosesthe symptoms verified were neurological 1 infectious1 toxicmetabolic perp (it was not possible to detect) Thepatient also presented theft broadcasting and diffusionof the thinking absence of feelings impulses or somaticsensations arising from outside that imposed on the patientabsence of hallucinatory phenomena delusional perceptionassigning a new meaning of autoreferential way Thereforethe values inserted in the Ks 1 table were alterations theway of thinking 3 ideas of passivity 0 Hallucinations 0Delusions 2 Regarding the Kurt Scheneider symptomsof second order the psychiatrist detected a weakpresence of emotional impoverishment symptoms andthe absence of the other three symptoms (delusionalintuition 0 perplexity 0 emotional impoverishment[025 075] depressive and euphoric dysthymias 0) Inthis way the schizophrenia clauses obtained are sch([012

018] 09 2 perp 5 [025 075]) 1 DoC and schDoC(0944

1 1 0 1 0992) 1 082 In (Figure 3) it is shown how thenormalized values of the interval extremes and theirs DoCvalues work as inputs to the ANN The output translates thechance of having schizophrenia and the DoC that one hason such a result In addition it was built a database of studycases that were used to train and test the ANNs As (Figure 3)demonstrates it was detected schizophrenia in the patientwith a DoC = 094

6 Conclusions

The diagnosis of schizophrenia is a hard and complex taskwhich needs to consider many different conditions withintricate relations among themThese characteristics put thisproblem into the area of problems that may be tackled by AItechniques Despite that little to no work has been done inthat direction

In this work the founding of a computational frameworkthat uses powerful knowledge representation techniques torepresent and structure the information is presented Thisrepresentation is above everything else very versatile andcapable of covering every possible instance representation byconsidering incomplete and unknown data This finding has


012

018

0944

1

09

09

1

1

025

075

0992

1

Bias

Disease

Bias

Yes

094


Geneticpredisposition

Kurt

Preprocessinglayer

Input layer

Hidden layer

Output layer

schDoC

Schneider 2

Figure 3 The ANN for the 22-year-old male

several reasons namely that data is not equal to informationthe translation of the raw measurements into interpretableand actionable read-outs is challenging and read-outs candeliver markers and targets candidates without preconcep-tion that is knowing how human conditions and risk factorsmay affect schizophrenia detection

7 Future Work

The knowledge representation and reasoning techniques pre-sented above are very versatile and capable of covering everypossible instance by considering incomplete contradictoryand even unknown data Indeed the new paradigm forknowledge representation and reasoning enables one to usethe normalized values of the interval boundaries and theirDoC values as inputs to different computational paradigmsThe output translates the problem solution and the systemsconfidence on such a happening Indeed the same problemmust be approached using other computational frameworkslike Case Based Reasoning [35] or Particle Swarm [38]among others

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This work is funded by National Funds through the FCTFundacao para a Ciencia e a Tecnologia (Portuguese Foun-dation for Science and Technology) within projects PEst-OEEEIUI07522014 and PEst-OEQUIUI06192012

References

[1] J A Liberman T S Stroup and D O Perkins Textbook ofSchizophrenia The American Psychiatric Publishing 1st edi-tion 2006

[2] S Frangou and R M Murray Schizophrenia Martin Dunitz2nd edition 2000

[3] R D Strous M Koppel J Fine S Nachliel G Shaked and AZ Zivotofsky ldquoAutomated characterization and identification ofschizophrenia in writingrdquo The Journal of Nervous and MentalDisease vol 197 no 8 pp 585ndash588 2009

[4] J Neves J Ribeiro P Pereira et al ldquoEvolutionary intelligencein asphalt pavement modeling and quality-of-informationrdquoProgress in Artificial Intelligence vol 1 no 1 pp 119ndash135 2012

[5] G J Hunter and K Beard ldquoUnderstanding error in spatialdatabasesrdquo Australian Surveyor vol 37 no 2 pp 108ndash119 1992

[6] G J Hunter ldquoManaging uncertainty in GISrdquo in GeographicInformation Science vol 2 pp 633ndash641 1999

[7] J Zhang and M F Goodchild Uncertainty in GeographicalInformation CRC Press New York NY USA 2002


[8] J Gottsegen D R Montello and M F Goodchild ldquoA compre-hensivemodel of uncertainty in spatial datardquo in Spatial AccuracyAssessment Land Information Uncertainty in Natural Resourcespp 175ndash181 1999

[9] LWang J Tao R Ranjan et al ldquoG-HadoopMapReduce acrossdistributed data centers for data-intensive computingrdquo FutureGeneration Computer Systems vol 29 no 3 pp 739ndash750 2013

[10] LWang Y Ma A Zomaya R Ranjan and D Chen ldquoA parallelfile system with application aware data layout policies in digitalearthrdquo IEEE Transactions on Parallel and Distributed Systems2014

[11] M Menzel R Ranjan L Wang S Khan and J Chen ldquoCloud-genius a hybrid decision supportmethod for automating themigration of webapplication clusters to public cloudsrdquo IEEETransactions on Computers no 99 p 1 2014

[12] Z Xu X Wei X Luo et al ldquoKnowle a semantic link networkbased system for organizing large scale online news eventsrdquoFuture Generation Computer Systems vol 43ndash44 pp 40ndash502015

[13] Y Liu L Chen X Luo L Mei C Hu and Z Xu ldquoSemantic linknetwork basedmodel for organizingmultimedia big datardquo IEEETransactions on Emerging Topics in Computing vol 2 no 3 pp376ndash387 2014

[14] A Pang ldquoVisualizing uncertainty in geo-spatial datardquo in Pro-ceedings of theWorkshop on the Intersections between GeospatialInformation and Information Technology 2001

[15] W Shi P Fisher and M F Goodchild Spatial Data QualityCRC Press New York NY USA 2003

[16] P Fisher A Comber and R Wadsworth ldquoApproaches touncertainty in spatial datardquo in Fundamentals of Spatial DataQuality pp 43ndash59 2006

[17] R Li B Bhanu C Ravishankar M Kurth and J Ni ldquoUncertainspatial data handling modeling indexing and queryrdquo Comput-ers and Geosciences vol 33 no 1 pp 42ndash61 2007

[18] T Hong K Hart L-K Soh and A Samal ldquoUsing spatial datasupport for reducing uncertainty in geospatial applicationsrdquoGeoInformatica vol 18 no 1 pp 63ndash92 2014

[19] X Luo Z Xu J Yu and X Chen ldquoBuilding association linknetwork for semantic link on web resourcesrdquo IEEE Transactionson Automation Science and Engineering vol 8 no 3 pp 482ndash494 2011

[20] Z Xu X Luo S Zhang X Wei L Mei and C Hu ldquoMin-ing temporal explicit and implicit semantic relations betweenentities using web search enginesrdquo Future Generation ComputerSystems vol 37 pp 468ndash477 2014

[21] Y Liu Q Zhang and L Ni ldquoOpportunity-based topologycontrol in wireless sensor networksrdquo IEEE Transactions onParallel andDistributed Systems vol 21 no 3 pp 405ndash416 2010

[22] F Hao G Min J Chen et al ldquoAn optimized computationalmodel for task-oriented multi-community-cloud social collab-orationrdquo IEEE Transactions on Services Computing vol 7 no 3pp 346ndash358 2014

[23] Y Liu L Ni and C Hu ldquoA generalized probabilistic topologycontrol for wireless sensor networksrdquo IEEE Journal on SelectedAreas in Communications vol 30 no 9 pp 1780ndash1788 2012

[24] P F Fisher ldquoModels of uncertainty in spatial datardquo inGeograph-ical Information Systems vol 1 pp 191ndash205 1999

[25] M Schneider ldquoUncertainty management for spatial dataindatabases Fuzzy spatial data typesrdquo in Advances in SpatialDatabases vol 1651 of Lecture Notes in Computer Science pp330ndash351 Springer Berlin Germany 1999

[26] L Freire A Roche and J-FMangin ldquoWhat is the best similaritymeasure for motion correction in fMRI time seriesrdquo IEEETransactions on Medical Imaging vol 21 no 5 pp 470ndash4842002

[27] T Warren Liao ldquoClustering of time series datamdasha surveyrdquoPattern Recognition vol 38 no 11 pp 1857ndash1874 2005

[28] A Kakas R Kowalski and F Toni ldquoThe role of abductionin logic programmingrdquo in Handbook of Logic in ArtificialIntelligence and Logic Programming vol 5 pp 235ndash324 OxfordUniversity Press Oxford UK 1998

[29] M Gelfond and V Lifschitz ldquoThe stable model semantics forlogic programmingrdquo in Logic Programming Proceedings of theIntrsquol Conference and Symposium R Kowalski and K BowenEds pp 1070ndash1080 1998

[30] L M Pereira and H T Anh ldquoEvolution prospectionrdquo inNew Advances in Intelligent Decision Technologies Results ofthe First KES International Symposium IDT Himeji Japan2009 K Nakamatsu Ed vol 199 of Studies in ComputationalIntelligence pp 51ndash63 Springer 2009

[31] J Neves J Machado C Analide A Abelha and L Brito ldquoThehalt condition in genetic programmingrdquo in Progress in ArtificialIntelligence vol 4874 of Lecture Notes in Computer Science pp160ndash169 Springer Berlin Germany 2007

[32] J Neves ldquoA logic interpreter to handle time and negation inlogic databasesrdquo in Proceedings of the Annual Conference of theACM on the Fifth Generation Challenge pp 50ndash54 ACM NewYork NY USA 1984

[33] J Kacprzyk F E Petry and A Yazici Uncertainty Approachesfor Spatial Data Modeling and Processing 2010

[34] D Klimesova and E Ocelıkova ldquoSpatial data uncertainty man-agementrdquo The International Archives of the PhotogrammetryRemote Sensing and Spatial Information Sciences vol 37 pp209ndash212 2008

[35] R Mendes J Kennedy and J Neves ldquoThe fully informedparticle swarm simpler maybe betterrdquo IEEE Transactions onEvolutionary Computation vol 8 no 3 pp 204ndash210 2004

[36] H Vicente J C Roseiro J M Arteiro J Neves and A TCaldeira ldquoPrediction of bioactive compound activity againstwood contaminant fungi using artificial neural networksrdquoCanadian Journal of Forest Research vol 43 no 11 pp 985ndash9922013

[37] A T Caldeira M R Martins M J Cabrita et al ldquoAromacompounds prevision using artificial neural networks influenceof newly indigenous Saccharomyces spp inwhitewine producedwith Vitis vinifera cv Siriardquo in Proceedings of the 6th Interna-tional Conference on Simulation and Modelling in the Food andBio-Industry (FOODSIM rsquo10) pp 33ndash40 June 2010

[38] D Carneiro P Novais F Andrade J Zeleznikow and J NevesldquoUsing case-based reasoning and principled negotiation toprovide decision support for dispute resolutionrdquoKnowledge andInformation Systems vol 36 no 3 pp 789ndash826 2013

[39] R Kowalski ldquoThe logical way to be artificially intelligentrdquoin Computational Logic in Multi-Agent Systems vol 3900 ofLecture Notes in Computer Science pp 1ndash22 Springer BerlinGermany 2006

[40] F K J Sheridan ldquoA survey of techniques for inference underuncertaintyrdquoArtificial Intelligence Review vol 5 no 1-2 pp 89ndash119 1991

[41] M Ginsberg Readings in Nonmonotonic Reasoning 1980[42] B Rodrigues S Gomes H Vicente et al ldquoSystematic coro-

nary risk evaluation through artificial neural networks based


systemsrdquo in Proceedings of the 27th International Conference onComputer Applications in Industry and Engineering (CAINE rsquo14)New Orleans La USA October 2014

[43] S Pereira S Gomes H Vicente et al ldquoAutomatic diagnosisof attention deficit hyperactivity disorder through an artificialneuronal networks based systemrdquo in Proceedings of the IEEEInternational Conference on Imaging Systems and Techniques(IST rsquo14) Santorini Greece October 2014

[44] V Abelha H Vicente J Machado and J Neves ldquoAn assess-ment on the length of hospital stay through artificial neuralnetworksrdquo in Proceedings of the 9th International Conference onKnowledge Information and Creativity Support Systems (KICSSrsquo14) Limassol Cyprus November 2014

[45] J Y Halpern ldquoReasoning about knowledge an overviewrdquo inProceedings of the Conference onTheoretical Aspects of Reasoningabout Knowledge pp 1ndash17 Morgan Kaufmann 1986

[46] B Kovalerchuk and G Resconi ldquoAgent-based uncertainty logicnetworkrdquo in Proceedings of the IEEE International Conference onFuzzy Systems (FUZZ rsquo10) pp 1ndash8 Barcelona Spain July 2010

[47] P Lucas ldquoQuality checking of medical guidelines throughlogical abductionrdquo in Research and Development in IntelligentSystems XX Proceedings of AI2003 the Twenty-third SGAI Inter-national Conference on Innovative Techniques and Applicationsof Artificial Intelligence pp 309ndash321 Springer London UK2004

[48] A Hommersom P J Lucas and P van Bommel ldquoChecking thequality of clinical guidelines using automated reasoning toolsrdquoTheory and Practice of Logic Programming vol 8 no 5-6 pp611ndash641 2008

[49] J Machado A Abelha P Novais and J Neves ldquoQuality ofservice in healthcare unitsrdquo International Journal of ComputerAided Engineering and Technology vol 2 no 4 pp 436ndash4492010

[50] Y Liu and M Sun ldquoFuzzy optimization BP neural networkmodel for pavement performance assessmentrdquo in Proceedingsof the IEEE International Conference on Grey Systems andIntelligent Services (GSIS rsquo07) pp 1031ndash1034 IEEE November2007

[51] W Mayer-Gross E Slater andM Roth Clinical Psychiatry vol1 Bailliere Tindal amp Cassel London UK 1954

Submit your manuscripts athttpwwwhindawicom

Computer Games Technology

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Distributed Sensor Networks


Advances in

FuzzySystems

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014


ReconfigurableComputing

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014


Applied Computational Intelligence and Soft Computing

thinspAdvancesthinspinthinsp

Artificial Intelligence

HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014

Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Electrical and Computer Engineering

Journal of

Journal of

Computer Networks and Communications


Hindawi Publishing Corporation

httpwwwhindawicom Volume 2014

Advances in

Multimedia


Biomedical Imaging


ArtificialNeural Systems

Advances in


RoboticsJournal of



Computational Intelligence and Neuroscience

Industrial EngineeringJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in



on the similarity between the signs and symptoms amongpsychic diseases and states Typically the earliest act forthe diagnosis of schizophrenia proceeds from the detectionof a specific outbreak ordinarily evinced by hallucinationsdelusions disorganized speech catatonic behavior abolitionand social separation or even additional personality disor-ders The psychiatric diagnosis is made through the clinicalinterview based on psychopathology but the problem isthat knowledge of psychopathology of anthology dependson the training and experience of the psychiatrist Theselimitations ldquoopen the doorrdquo to mistake and doubt From herethe practitioners may perform psychic exams intended todetect cognitive flaws delusional perception and abnormalchanges or thoughts among others [1 2]

Above any kind of dispute the main problem with thediagnosis of schizophrenia comes from the large numberof different mental diseases and states that may mimic itssigns such as epilepsy drug-induced psychosis affective psy-choses (eg bipolar major depressive disorders) Aspergersyndrome schizoaffective disorder and Wilsonrsquos disease Toface this situation the practitioner is forced to order extraexams namely toxicological tests electroencephalography(EEG) and brain computed tomography (CT)rsquos [1] Also thispinpointing is usually done over a large period of time (at least6months) therefore generating a huge amount of data whichhas to be treated and interpreted by the practitioner(s)

Facing such a large amount of facts even experiencedpsychiatrists have difficulties to make a precise diagnosisand distinguishing between this and other diseases Unfortu-nately there is not toomuchwork done in the area ofMedicalInformatics to help in this process although Strous et al [3]worked on a system that uses the differences on writing todiagnose schizophrenia

With this paper we make a start on the developmentof an unusual or original diagnosis assistance system forschizophrenia We will present a logic programming basedapproach in order to represent the knowledge and rea-soning with a focus on the Degree of Confidence (DoC)of the attributes set that makes a function or a predicate[4]

2 Related Work

Many studies presenting the concept of uncertainty andorldquoimperfect datardquo like [5ndash8] show that there is an emergentinterest in the problem of uncertainty as compared toaccuracy or error in data [9 10] The notion of uncer-tainty is broader than error or accuracy and includes thesemore restricted concepts While accuracy is the closenessof measurements or computations to their ldquotruerdquo value orsome value agreed to be the ldquotruthrdquo uncertainty can beconsidered any aspect of the data that results in less thanperfect knowledge about the phenomena being studied [11ndash13]

The consequences of the uncertainty in the data and inthe data quality to user exploring modelling visualizing and

querying have been also referred to in many studies [6 8 14ndash18] On the one hand it is consensual that when the dataare uncertain a different representation and uncertaintywhich can be reduced by ldquoacquiring additional informationor improving the quality of the information availablerdquo [6] isneeded that is in almost all decisions that one may take theinformation is not always exact but indeed imperfect in thesense thatwe handle estimated values probabilisticmeasuresor degrees of uncertainty [19 20] On the other handknowledge and belief are generally incomplete contradictoryor even error sensitive It is advisable the use of formaltools to deal with the problems that arise with the use ofpartial contradictory ambiguous imperfect nebulous ormissing information [13 21ndash23] Some general models havebeen presented [8 16 24] where uncertainty is associatedto the application of Probability Theory [16 17] Fuzzy SetTheory [25] Similarities [26 27] Other approaches forknowledge representation and reasoning have been proposedusing the Logic Programming (LP) paradigm namely inthe area of Model Theory [28ndash30] and Proof Theory [29 3132] Qualitative models and qualitative reasoning have beenaround in Artificial Intelligence research for some time [1433] in particular due to the growing need to offer support indecision-making processesThe evaluation of knowledge thatstems out from logic programs becomes a point of researchIn this sense the evaluation of knowledge that stems out fromlogic programs becomes a point of research Shi et al [15] andSchneider [25] work is a good example of quality evaluationusing logic They used abduction [14] and temporal logic forquality-checking of medical guidelines proposing a methodto diagnose potential problems in a guideline regarding thefulfillment of general medical quality criteria at a metalevelcharacterization They explored an approach which uses arelational translation to map the temporal logic formulas tofirst-order logic and a resolution-based theorem prover [25]In another research line the Quality-of-Information concept(QoI) [6 7 26 34] demonstrated their applicability in manydynamic environments and for decision making purposesThe objective is to build a quantification process of the QoIand an assessment of the argument values of a given predicatewith relation to their domains (here understood as Degree-of-Confidence (DoC)) which stems from a logic program ortheory during the evolutive process of searching solutions inorder to solve a problem in environments with default dataOur main contribution relies on the fact that at the end theinitial extensions of the predicates that make the universe ofdiscourse are given in terms of DoCs predicates that stand foronersquos confidence that the initial predicates arguments valuesof the predicates that make the universe of discourse fit intotheir respective domainsThis approach potentiates the use ofdiverse computational paradigms like Case Based Reasoning[35] Artificial Neural Networks (ANN) [36 37] and ParticleSwarm [38] just to name a few It also encapsulates initself a new vision of Multivalue Logics once a proof of atheorem in a conventional way is evaluated to the interval[0 1] Following these studies good results were achieved fordifferent purposes namely inHealthcare [27] Civil Law [39]





119902 larr997888 1199011

and 119901119899

and not1199021


(1199011


and not1199021


) (119899 119898 ge 0)

(1)




QoI119894


1

119873= 0 (119873 ≫ 0) (2)



QoI119894

=1

Card (3)


QoI119894

=1

(119862Card1


(4)



119896




sum1le119896le119899

119908119896

119894= 1 forall

119894 (5)



119894(119909) so that for a

value 119909 = (1199091 119909



119881119894

(119909) = sum1le119896le119899

119908119896


(119909)

119899 (6)


predicate119894

(1199091 119909

119899) QoI DoC (7)


119894(1199091 119909




1198861






not1198861

(1199091 1199101 1199111) larr997888 not 119886

1(1199091 1199101 1199111)

1198861

(perp [10 20] 15) 1 DoC


111991011199111

not1198862

(1199092 1199102 1199112) larr997888 not 119886

2(1199092 1199102 1199112)

1198862

([45 54] [10 12] perp) 1 DoC[30 60] [6 14] [2000 6000]⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟



not1198861

(1199091 1199101 1199111) larr997888 not 119886

1(1199091 1199101 1199111)

1198861

([5 10] [10 20] 15) 1 DoC


111991011199111

not1198862

(1199092 1199102 1199112) larr997888 not 119886

2(1199092 1199102 1199112)

1198862

([45 54] [10 12] [2000 6000]) 1 DoC


211991021199112


not1198861

(1199091 1199101 1199111) larr997888 not 119886

1(1199091 1199101 1199111)

1198861

([5 minus 5

10 minus 5

10 minus 5

10 minus 5] [

10 minus 5

30 minus 5

20 minus 5

30 minus 5]

[15 minus 10

20 minus 10

15 minus 10

20 minus 10])

equiv 1198861

([0 1] [02 06] [05 05]) 1 DoC


111991011199111

not1198862

(1199092 1199102 1199112) larr997888 not 119886

2(1199092 1199102 1199112)

1198862

([45 minus 30

60 minus 30

54 minus 30

60 minus 30] [

10 minus 6

14 minus 6

12 minus 6

14 minus 6]

[2000 minus 2000

6000 minus 2000

6000 minus 2000

6000 minus 2000])

equiv 1198862

([05 08] [05 075] [0 1]) 1 DoC


211991021199112

(9)

1

1

1

0

Interval length

Deg

ree o

f con

fiden

ce

Δl




not1198861DoC

(1199091 1199101 1199111) larr997888 not 119886

1DoC(1199091 1199101 1199111)

1198861DoC

(0 0916 1) 05 DoC


111991011199111


111991011199111

not1198862DoC

(1199092 1199102 1199112) larr997888 not 119886

2DoC(1199092 1199102 1199112)

1198862DoC

(0954 0968 0) 06 0641


211991021199112


211991021199112

(10)

4 Onersquos Model



Lucidity


1 1 1 1 2

2 1 1 0 1

3 1 1 1 [0 1]

Differential


metabolic

1 1 1 1

2 0 0 1

3 1 1 1



1 3 0 3 2

2 0 0 0 0

3 0 0 0 0


PerplexityEmotional

impoverishment


dysthymias

1 0 0 0 0

2 0 1 0 0

3 0 0 1 1

Schizophrenia




1 [012 018] 92 2 1 8 0

2 [005 006] 0 0 0 1

3 [012 018] 26 [0 1] 1 0 2

Agesex

predisposition

Age Sex

1 20 M

2 28 F

3 19 M

Kurt Schneider 1

Kurt Schneider 2

perp

Ks 1 Ks 2




















(11)





sch ([012 018] 92 2 1 8 0) 1 DoC


sch ([005 006] perp 0 0 0 1) 1 DoC


sch ([012 018] 26 [0 1] 1 0 2) 1 DoC


(12)





Consider



dArr

sch ([005 006] perp 0 0 0 1) 1 DoC



sch ([005 006] [09 915] [0 0] [0 0]

[0 0] [1 1]) 1 DoC



sch ([071 086] [0 1] [0 0] [0 0] [0 0]

[025 025]) 1 DoC



schDoC (0989 0 1 1 1 1) 1 083



(13)







6 Conclusions




012

018

0944

1

09

09

1

1

025

075

0992

1

Bias

Disease

Bias

Yes

094



Kurt

Preprocessinglayer

Input layer

Hidden layer

Output layer

schDoC

Schneider 2



7 Future Work




Acknowledgments


References






























































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in







119902 larr997888 1199011

and 119901119899

and not1199021


(1199011


and not1199021


) (119899 119898 ge 0)

(1)




QoI119894


1

119873= 0 (119873 ≫ 0) (2)



QoI119894

=1

Card (3)


QoI119894

=1

(119862Card1


(4)



119896




sum1le119896le119899

119908119896

119894= 1 forall

119894 (5)



119894(119909) so that for a

value 119909 = (1199091 119909



119881119894

(119909) = sum1le119896le119899

119908119896


(119909)

119899 (6)


predicate119894

(1199091 119909

119899) QoI DoC (7)


119894(1199091 119909




1198861






not1198861

(1199091 1199101 1199111) larr997888 not 119886

1(1199091 1199101 1199111)

1198861

(perp [10 20] 15) 1 DoC


111991011199111

not1198862

(1199092 1199102 1199112) larr997888 not 119886

2(1199092 1199102 1199112)

1198862

([45 54] [10 12] perp) 1 DoC[30 60] [6 14] [2000 6000]⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟



not1198861

(1199091 1199101 1199111) larr997888 not 119886

1(1199091 1199101 1199111)

1198861

([5 10] [10 20] 15) 1 DoC


111991011199111

not1198862

(1199092 1199102 1199112) larr997888 not 119886

2(1199092 1199102 1199112)

1198862

([45 54] [10 12] [2000 6000]) 1 DoC


211991021199112


not1198861

(1199091 1199101 1199111) larr997888 not 119886

1(1199091 1199101 1199111)

1198861

([5 minus 5

10 minus 5

10 minus 5

10 minus 5] [

10 minus 5

30 minus 5

20 minus 5

30 minus 5]

[15 minus 10

20 minus 10

15 minus 10

20 minus 10])

equiv 1198861

([0 1] [02 06] [05 05]) 1 DoC


111991011199111

not1198862

(1199092 1199102 1199112) larr997888 not 119886

2(1199092 1199102 1199112)

1198862

([45 minus 30

60 minus 30

54 minus 30

60 minus 30] [

10 minus 6

14 minus 6

12 minus 6

14 minus 6]

[2000 minus 2000

6000 minus 2000

6000 minus 2000

6000 minus 2000])

equiv 1198862

([05 08] [05 075] [0 1]) 1 DoC


211991021199112

(9)

1

1

1

0

Interval length

Deg

ree o

f con

fiden

ce

Δl




not1198861DoC

(1199091 1199101 1199111) larr997888 not 119886

1DoC(1199091 1199101 1199111)

1198861DoC

(0 0916 1) 05 DoC


111991011199111


111991011199111

not1198862DoC

(1199092 1199102 1199112) larr997888 not 119886

2DoC(1199092 1199102 1199112)

1198862DoC

(0954 0968 0) 06 0641


211991021199112


211991021199112

(10)

4 Onersquos Model



Lucidity


1 1 1 1 2

2 1 1 0 1

3 1 1 1 [0 1]

Differential


metabolic

1 1 1 1

2 0 0 1

3 1 1 1



1 3 0 3 2

2 0 0 0 0

3 0 0 0 0


PerplexityEmotional

impoverishment


dysthymias

1 0 0 0 0

2 0 1 0 0

3 0 0 1 1

Schizophrenia




1 [012 018] 92 2 1 8 0

2 [005 006] 0 0 0 1

3 [012 018] 26 [0 1] 1 0 2

Agesex

predisposition

Age Sex

1 20 M

2 28 F

3 19 M

Kurt Schneider 1

Kurt Schneider 2

perp

Ks 1 Ks 2




















(11)





sch ([012 018] 92 2 1 8 0) 1 DoC


sch ([005 006] perp 0 0 0 1) 1 DoC


sch ([012 018] 26 [0 1] 1 0 2) 1 DoC


(12)





Consider



dArr

sch ([005 006] perp 0 0 0 1) 1 DoC



sch ([005 006] [09 915] [0 0] [0 0]

[0 0] [1 1]) 1 DoC



sch ([071 086] [0 1] [0 0] [0 0] [0 0]

[025 025]) 1 DoC



schDoC (0989 0 1 1 1 1) 1 083



(13)







6 Conclusions




012

018

0944

1

09

09

1

1

025

075

0992

1

Bias

Disease

Bias

Yes

094



Kurt

Preprocessinglayer

Input layer

Hidden layer

Output layer

schDoC

Schneider 2



7 Future Work




Acknowledgments


References






























































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in





not1198861

(1199091 1199101 1199111) larr997888 not 119886

1(1199091 1199101 1199111)

1198861

(perp [10 20] 15) 1 DoC


111991011199111

not1198862

(1199092 1199102 1199112) larr997888 not 119886

2(1199092 1199102 1199112)

1198862

([45 54] [10 12] perp) 1 DoC[30 60] [6 14] [2000 6000]⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟



not1198861

(1199091 1199101 1199111) larr997888 not 119886

1(1199091 1199101 1199111)

1198861

([5 10] [10 20] 15) 1 DoC


111991011199111

not1198862

(1199092 1199102 1199112) larr997888 not 119886

2(1199092 1199102 1199112)

1198862

([45 54] [10 12] [2000 6000]) 1 DoC


211991021199112


not1198861

(1199091 1199101 1199111) larr997888 not 119886

1(1199091 1199101 1199111)

1198861

([5 minus 5

10 minus 5

10 minus 5

10 minus 5] [

10 minus 5

30 minus 5

20 minus 5

30 minus 5]

[15 minus 10

20 minus 10

15 minus 10

20 minus 10])

equiv 1198861

([0 1] [02 06] [05 05]) 1 DoC


111991011199111

not1198862

(1199092 1199102 1199112) larr997888 not 119886

2(1199092 1199102 1199112)

1198862

([45 minus 30

60 minus 30

54 minus 30

60 minus 30] [

10 minus 6

14 minus 6

12 minus 6

14 minus 6]

[2000 minus 2000

6000 minus 2000

6000 minus 2000

6000 minus 2000])

equiv 1198862

([05 08] [05 075] [0 1]) 1 DoC


211991021199112

(9)

1

1

1

0

Interval length

Deg

ree o

f con

fiden

ce

Δl




not1198861DoC

(1199091 1199101 1199111) larr997888 not 119886

1DoC(1199091 1199101 1199111)

1198861DoC

(0 0916 1) 05 DoC


111991011199111


111991011199111

not1198862DoC

(1199092 1199102 1199112) larr997888 not 119886

2DoC(1199092 1199102 1199112)

1198862DoC

(0954 0968 0) 06 0641


211991021199112


211991021199112

(10)

4 Onersquos Model



Lucidity


1 1 1 1 2

2 1 1 0 1

3 1 1 1 [0 1]

Differential


metabolic

1 1 1 1

2 0 0 1

3 1 1 1



1 3 0 3 2

2 0 0 0 0

3 0 0 0 0


PerplexityEmotional

impoverishment


dysthymias

1 0 0 0 0

2 0 1 0 0

3 0 0 1 1

Schizophrenia




1 [012 018] 92 2 1 8 0

2 [005 006] 0 0 0 1

3 [012 018] 26 [0 1] 1 0 2

Agesex

predisposition

Age Sex

1 20 M

2 28 F

3 19 M

Kurt Schneider 1

Kurt Schneider 2

perp

Ks 1 Ks 2




















(11)





sch ([012 018] 92 2 1 8 0) 1 DoC


sch ([005 006] perp 0 0 0 1) 1 DoC


sch ([012 018] 26 [0 1] 1 0 2) 1 DoC


(12)





Consider



dArr

sch ([005 006] perp 0 0 0 1) 1 DoC



sch ([005 006] [09 915] [0 0] [0 0]

[0 0] [1 1]) 1 DoC



sch ([071 086] [0 1] [0 0] [0 0] [0 0]

[025 025]) 1 DoC



schDoC (0989 0 1 1 1 1) 1 083



(13)







6 Conclusions




012

018

0944

1

09

09

1

1

025

075

0992

1

Bias

Disease

Bias

Yes

094



Kurt

Preprocessinglayer

Input layer

Hidden layer

Output layer

schDoC

Schneider 2



7 Future Work




Acknowledgments


References






























































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




Lucidity


1 1 1 1 2

2 1 1 0 1

3 1 1 1 [0 1]

Differential


metabolic

1 1 1 1

2 0 0 1

3 1 1 1



1 3 0 3 2

2 0 0 0 0

3 0 0 0 0


PerplexityEmotional

impoverishment


dysthymias

1 0 0 0 0

2 0 1 0 0

3 0 0 1 1

Schizophrenia




1 [012 018] 92 2 1 8 0

2 [005 006] 0 0 0 1

3 [012 018] 26 [0 1] 1 0 2

Agesex

predisposition

Age Sex

1 20 M

2 28 F

3 19 M

Kurt Schneider 1

Kurt Schneider 2

perp

Ks 1 Ks 2




















(11)





sch ([012 018] 92 2 1 8 0) 1 DoC


sch ([005 006] perp 0 0 0 1) 1 DoC


sch ([012 018] 26 [0 1] 1 0 2) 1 DoC


(12)





Consider



dArr

sch ([005 006] perp 0 0 0 1) 1 DoC



sch ([005 006] [09 915] [0 0] [0 0]

[0 0] [1 1]) 1 DoC



sch ([071 086] [0 1] [0 0] [0 0] [0 0]

[025 025]) 1 DoC



schDoC (0989 0 1 1 1 1) 1 083



(13)







6 Conclusions




012

018

0944

1

09

09

1

1

025

075

0992

1

Bias

Disease

Bias

Yes

094



Kurt

Preprocessinglayer

Input layer

Hidden layer

Output layer

schDoC

Schneider 2



7 Future Work




Acknowledgments


References






























































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in












(11)





sch ([012 018] 92 2 1 8 0) 1 DoC


sch ([005 006] perp 0 0 0 1) 1 DoC


sch ([012 018] 26 [0 1] 1 0 2) 1 DoC


(12)





Consider



dArr

sch ([005 006] perp 0 0 0 1) 1 DoC



sch ([005 006] [09 915] [0 0] [0 0]

[0 0] [1 1]) 1 DoC



sch ([071 086] [0 1] [0 0] [0 0] [0 0]

[025 025]) 1 DoC



schDoC (0989 0 1 1 1 1) 1 083



(13)







6 Conclusions




012

018

0944

1

09

09

1

1

025

075

0992

1

Bias

Disease

Bias

Yes

094



Kurt

Preprocessinglayer

Input layer

Hidden layer

Output layer

schDoC

Schneider 2



7 Future Work




Acknowledgments


References






























































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in






Consider



dArr

sch ([005 006] perp 0 0 0 1) 1 DoC



sch ([005 006] [09 915] [0 0] [0 0]

[0 0] [1 1]) 1 DoC



sch ([071 086] [0 1] [0 0] [0 0] [0 0]

[025 025]) 1 DoC



schDoC (0989 0 1 1 1 1) 1 083



(13)







6 Conclusions




012

018

0944

1

09

09

1

1

025

075

0992

1

Bias

Disease

Bias

Yes

094



Kurt

Preprocessinglayer

Input layer

Hidden layer

Output layer

schDoC

Schneider 2



7 Future Work




Acknowledgments


References






























































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




012

018

0944

1

09

09

1

1

025

075

0992

1

Bias

Disease

Bias

Yes

094



Kurt

Preprocessinglayer

Input layer

Hidden layer

Output layer

schDoC

Schneider 2



7 Future Work




Acknowledgments


References






























































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in

























































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in





















Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in










Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in



Documents

Research Article Abstract Computation in Schizophrenia