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1、TDIS:anAlgebraicFormalizationJean-GabrielGANASCIALAFORIA-CNRS,InstitutBlaisePascal,EquipeACASAUniversitéPierreetMarieCurie,Tour46-0,4PlaceJussieu75252ParisCEDEX,FRANCEdistributivelatticeand,moregenerally,aproductofAbstracthierarchicalposets.InthelightofthesuccessofTop-DownInductionEvenifonlytop-down
2、inductionsystemsareconsidered,Systems(TDIS),theproblemstobeaddressedthereexistmanydifferentlearningstrategies.InthecaseofconcernthestructureofdescriptionsandthemostclassicalTDIS,itisadepthfirststrategy.Thismeansexplorationofstrategies.Thispaperintroducesathatonceanattributehasbeenchosenitistherootof
3、alltheformalmodeltodescribeTDIS,basedontheuseofgenerateddecisionsubtrees.Asshallbedemonstratedinthelatticetheoryand,moreprecisely,ontheuseofafollowing,thismayintroducesomeredundanciesintheGaloisconnection.Oneoftheadvantagesofthisresultingknowledgebase.Moreover,theclassicalTDISformalizationisthatitju
4、stifiestheextensiveuseofreliesonthehypothesisthatexampleshavetobeclassifiedattribute-valuerepresentationinthecaseofclassicalonlyoncebytheresultingknowledgebase.ButitappearsTDISandgeneralizesthisrepresentationtoproductsthatredundantclassificationscouldhavesomebeneficialofhierarchicalposets.Inaddition
5、,giventhatthereareeffects[Gams89].manydifferentlearningstrategiesforTDIS,thisInspiteofthesuccessful,extensiveuseofTDIS,theformalmodelshowsthelimitationsofclassicalfundamentalquestionsaboutthedescriptionspacehavenotstrategiesandoffersageneralframeworkinwhichyetbeensystematicallytackled.Forthisreasona
6、formalmanyotherstrategiescanbeexpressed.frameworktodescribeTDISisproposed.Thisframeworkis1-Introductionbasedontheuseoflatticetheoryand,moreprecisely,ontheDuringthelastdecade,manytop-downinductionsystems—useofaGaloisconnection.ItissimilartosomeworkinTDIS—havebeendeveloped—ID3[Quinlan83],ID5conceptual
7、dataanalysis[Wille89]butitgeneralizesthese[Utgoff88],CN2[Clark&Al.89],etc.Theyhavebeendifferentapproachestotakeintoaccountthenotionsofcomparedwithotherlearningtechniquessuchasbackbackgroundknowledgean
