Open Structure: Ontology Repair Plan based on Atomic - arcoe

13 Pages·2009·0.4 MB·English

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