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1、RealizationProblemforFormalConceptAnalysis?N.V.ShilovLavren'evav.,6,Novosibirsk630090,Russiashilov@iis.nsk.suAbstract.FormalConceptAnalysis(FCA)isanapproachtoknowledgeengineering,representation,andanalysis.A`standard'FCA-work
owstartswithsome`experimen
2、tal'data,classi esobjects"andtheirat-tributes"inthedata,representsrelationsbetweenobjectsandattributesbyanumberofcross-tables(matrices),couplescompatiblesetsofobjectsandattributesintoconcepts,andbuildsanumberofconceptlattices.Incontrast,FCArealizatio
3、nproblemstartswith`fragments'ofsomecross-tablesandconceptlatticesandtrytogeneratedatathatmatchthesefragmentsofcross-tablesandconceptlatticessimultaneously.Thepa-perde nesformallytheFCArealizationproblemandprovesthatitisdecidable.Itisdonebyreductionofth
4、eproblemtotheconsistencyprob-lemfordescriptionlogicALBO.ButitisstillanopenquestionwhetherFCA-realizationproblemhavebettercomplexityboundthanALBOhas.1IntroductionFormalConceptAnalysis(FCA)byR.WilleandB.Ganter[2]isanalgebraicframeworkforknowledgeengineer
5、ing,representation,andanalysis.Ittakessome`experimental'data,classi esobjects"andtheirattributes"inthedata.ThenmathematicalpartofFCAtakesmatricesthatspecifyrelationbetweenobjectsandattributesasaninputand ndscorresponding`naturalclusters'(sets)ofattri
6、butesand`naturalclusters'(sets)ofobjects.Everypairofcorresponding`natural'setsofobjectsandattributesformsaformalconcept1.Thesetoffor-malconceptsobeysthemathematicalaxiomsde ningalattice,andiscalledaconceptlattice.LetusillustratebasicFCAnotionsbythefoll
7、owingexample.AssumethatsomeComputerScienceDepartmenthas1FullProfessor(F),1AssociateProfes-sor(A),1Lecture(L),2Tutors(T1andT2),and1ResearchProgrammer(R).CoursesprovidedbythedepartmentareProgrammingLanguages(PL),Oper-atingSystems(OS),DataBases(DB),andFor
8、malMethods(FM).Researchrangethesametopics.Sampledataaboutsta teachingandresearchpro learepresentedinthetables1.?Thisresearchissupportedinpartsby(a)byjointgrantRFBR05-01-04003-a-DFGprojectCOMO,GZ:436RUS113/829/0-1,(b)byIntegrationGrantn.
