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1、TechReportOSU-CISRC-3/95-TR22,Comp.&Info.Sci.,OhioStateU.,19951SpatialAggregate:TheoryandApplicationtoQualitativePhysicsyKennethYipFengZhaoMay8,1995AbstractEectivereasoningaboutaphysicalsystemrequiresanappropriatemappingfromthesystemcharacteristicstoabstractionsthatmatchtheimpedanceofthetask

2、athand.InQualitativePhysics,threeontologicalabstractionsarewidelyused:device,process,andconstraint.Wepresentaframeworkandanewontologicalabstraction,theeldontology,tounifymanyreasoningtasksinvolvingimage-likeanaloguerepresentationssuchasthevelocityeldforuidmotion,phasespacefordynamicalsystems,

3、andcongurationspaceformechanismanalysis.mAeldisdenedasamappingfromonecontinuum(sayR)toanothern(sayR).Aeldistypicallyinformation-rich.Totransformtheinformation-richrepresentationintosymbolicdescriptionswellsuitedforexplainingthestructureandbehaviorofthesystem,weproposeatheoryofmulti-layerspati

4、alabstractions.Abstractionineachlayerisrepresentedbyaneighborhoodgraphwhosenodesareobjectsandedgesareadjacencyrelations.Themulti-layertheoryhastwoadvantages:(1)Anonlocalpropertyofalowerlayercanberedescribedasalocalpropertyofahigherlayer,and(2)Oneachlayertheneighborhoodgraphprovidesacommoninte

5、rfacetosupportidenticalmodularcomputations.Toillustrateourtheory,weexaminethecomputationalstructureofthreeimplementedprograms{KAM,MAPS,andJ&S{thatintegratesymbolic,numerical,andvisualreasoning.Weshowasmallsetofgenericoperatorsthatconstruct,transform,lter,classify,andsearchneighborhoodgraphsca

6、pturethecommonalitiesoftheseprograms.Wedevelopalanguage,awayoforganiz-ingprogramsaroundneighborhoodgraphs,tomakeprogramswritteninthisstyleclear.DepartmentofComputerScience,YaleUniversity,NewHaven,CT06520.yCorrespondingauthor:FengZhao,DepartmentofComputerandInformationScience,TheOhioStateUniv

7、ersity,2015NeilAve.,Columbus,OH43210.E-mail:fz@cis.ohio-state.edu,Phone:614-292-1553,Fax:614-292-29111IntroductionItiscommonlybelievedthattherearetwostylesofscienticthinking:analytical,alogicalchainofsymbolicreasoningfrompremisestoconclusions