OverviewGALILEOProject ACaseStudyinAtomicModeling OntologyRepairPlanbasedonCaseStudy Discussion Open Structure: Ontology Repair Plan based on Atomic Modeling Jos Lehmann joint work with Alan Bundy and Michael Chan SchoolofInformatics,UniversityofEdinburgh ARCOE 2009 OverviewGALILEOProject ACaseStudyinAtomicModeling OntologyRepairPlanbasedonCaseStudy Discussion Outline 1 Overview GALILEO Project Ontology Evolution in Physics 2 A Case Study in Atomic Modeling From Thomson’s to Rutherford’s atom 3 Ontology Repair Plan based on Case Study Open Structure 4 Discussion Future work OverviewGALILEOProject ACaseStudyinAtomicModeling OntologyRepairPlanbasedonCaseStudy Discussion GALILEO project and Ontology Evolution in Physics Aim: solving contradictions between multiple ontologies. Canonical case: contradictions in physics between theoretical expectations and experimental observations. Main results: Ontology Repair Plans (ORPs). Trigger: detects contradiction between ontologies. Repair: changes ontology axioms or signature. Create New Axioms: propagates changes as needed. Methodology: turn case studies in physics history into ORPs. Extract ORP’s conceptual backbone from case study. Represent ORP in higher-order logic. Implement ORP (λProlog and beyond). Some ORPs and their state of development. Developed and tested: Where’s My Stuff?, Inconstancy, Unite. Being tested: Open Structure, Close Structure. Under development: Unify. OverviewGALILEOProject ACaseStudyinAtomicModeling OntologyRepairPlanbasedonCaseStudy Discussion Thomson’s atom (1904) and Rutherford’s atom (1911) 11electronatomand15electronatom. Blackdotsandcircumferencesrepresentnegativechargesandtheirorbits/rings. Redcirclesrepresentpositivecharge(moreintensewheredarker). NotethatRutherford’satom’sstructureismonotonic:Thomson’satom’sconfigurationchangeswhen electronsareadded,Rutherford’satom’sconfigurationisstable. OverviewGALILEOProject ACaseStudyinAtomicModeling OntologyRepairPlanbasedonCaseStudy Discussion Rutherford’s scattering apparatus (1898-1911) R,fixedsourceofα-particles(doublepositivecharges). D,collimatingdiaphragm. F,fixedfoil. S,screen. M,microscope. ChamberisevacuatedandcanberotatedaroundF. Originalimagein(Geiger,1913),downloadedfrom.http://galileo.phys.virginia.edu OverviewGALILEOProject ACaseStudyinAtomicModeling OntologyRepairPlanbasedonCaseStudy Discussion Expected vs observed scattering Redspotsandlinesareα-particlesandtheirpaths. Half-dashedthinredlinesareidealundeflectedpaths. b’sand−b’sareimpactparameters(b=0forthirdparticle). r’saredistancesbetweenapointoftheatom’selectricfieldandtheatom’scenter. Ristheatom’sradius. th’sarescatteringangles. Expectedscatteringisminimal. Observedscatteringisminimal,largeoracompleterebound. OverviewGALILEOProject ACaseStudyinAtomicModeling OntologyRepairPlanbasedonCaseStudy Discussion The nucleus Thenucleusexplainsthedifferencebetweenexpectationsandobservations. Thenucleusentailsdifferentdeflectionfunctions: θ(b)Thomsonandθ(b)Rutherford calculatedifferentdeflectionanglesforsameb’s. Thenucleusalsoentailsdifferentscatteringpotentialfunctions: V(r)ThomsonandV(r)Rutherford calculatedifferentamountsofworkexcertedbypositiveelectricfields whendeflectingincidentparticlesatsamedistancer. OverviewGALILEOProject ACaseStudyinAtomicModeling OntologyRepairPlanbasedonCaseStudy Discussion Scattering potential functions for different structures 8>< Q4AπQ(cid:15)0B 1r R≤r V(r) = Thomson >: QAQB 1 (3R2−r2) 0≤r ≤R 4π(cid:15)0 2R3 Q Q 1 V(r) = A B Rutherford 4π(cid:15)0 r whereQAisthechargeofincidentparticle,QBisthechargeofthetargetatom,1/4π(cid:15)0istheCoulomb constant,risthedistancebetweentheincidentparticleandthecentreofthetargetatom,Ristheradius ofthetargetatom. V(r)Thomsonisbothnon-Coulombic(i.e.forvaluesofrlowerthantheatom’sradiusR,thepotentialis directlyproportionaltor)andCoulombic(i.e.forvaluesofrhigherthanR,thepotentialisinversely proportionaltor). V(r)Rutherford isonlyCoulombic(Rneedsnottobeconsidered). Formulaetakenfrom(Zoli,1998) OverviewGALILEOProject ACaseStudyinAtomicModeling OntologyRepairPlanbasedonCaseStudy Discussion Evolution of V(r) by existing ORPs 8>< Q4AπQ(cid:15)0B 1r R≤r V(r) = Thomson >: QAQB 1 (3R2−r2) 0≤r ≤R 4π(cid:15)0 2R3 Q Q 1 V(r) = A B Rutherford 4π(cid:15)0 r Whereismystuff?wouldsticktoThomson’satomicstructurebyincreasingQAandyieldingevolution V(r)::=V(r)vis+V(r)invis.Problem:howwouldtheadditionalchargebedistributedwrtR? Unite,theinverseofWhereismystuff?,wouldnotbeabletoletV(r)evolve. InconstoowouldsticktoThomson’satomicstructureandletV(r)evolveinsuchawaythattheCoulomb constant1/4π(cid:15)0woulddependondistancerfromthecenterofatom.Thiswouldyieldavery complicatedstructure. NeedforanORPthathandlesstructuralevolutionassuch,ratherthanbypivotingonquantities. Formulaetakenfrom(Zoli,1998) OverviewGALILEOProject ACaseStudyinAtomicModeling OntologyRepairPlanbasedonCaseStudy Discussion Open Structure ORP: Trigger Trigger:Ot ‘d4>d3≥cop≥d2>d1∧ ((stuff(d2)>stuff(d1)∧stuff(d3)>stuff(d4))∨ (stuff(d1)>stuff(d2)∧stuff(d4)>stuff(d3))). Os ‘∀d,d0:δ.d0>d →stuff(d)>stuff(d0). stuff representsfunctionsubjecttoevolution(V isstuff). stuff rangesoveratypeδofd’s(likeV rangesoverthetypedisofdistancesr’s). stuff’sdomaincontainsacut-offpointcop(likeV’sdomaincontainsR). Kisconstant(likeallotherquantitiesremainconstantthroughtoutV’sevolution). Twocasesofcontradiction: crested*vsopenstructureInOt,forallargumentsbelowcut-offpoint,valueofstuff isdirectly proportionaltoargument,inverselyproportionalotherwise.InOsvalueofstuff isalwaysinversely proportionaltoargument. trenched*vsopenstructureInOt,forallargumentsbelowcut-offpoint,valueofstuff isinversely proportionaltotheargumentwhile,directlyproportionalotherwiset.Osisthesameasinthefirstcase above. *tentativeterm