Ontology Evolution in Physics Alan Bundy & Michael Chan STP - - PowerPoint PPT Presentation

Ontology Evolution in Physics

Alan Bundy & Michael Chan STP Glasgow 28.3.08

Alan Bundy & Michael Chan Ontology Evolution in Physics STP Glasgow 28.3.08

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Introduction

• Ontology repair needed for changing world and changing goals.

– Changes to signature as well as beliefs, – e.g., splitting of functions and addition of arguments.

• Physics has good historical records of triggers and repairs.

– Needs higher-order ontology.

• Aggregate atomic repairs into ontology repair plans.

– To address problems of search and ambiguity.

• Apply to historical case studies in physics.

Alan Bundy & Michael Chan Ontology Evolution in Physics STP Glasgow 28.3.08

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The Where’s My Stuff Ontology Repair Plan

Trigger: Ot ⊢ stuff ( c) = v1, Os ⊢ stuff ( c) = v2, Ot ⊢ v1 = v2 Assume v1 > v2. Other case dual. Split Stuff: ∀ s : τ. stuff σinvis( s) ::= stuff ( s) − stuff σvis( s) Create New Axioms: Ax(ν(Ot)) ::= {∀ s : τ. stuff σinvis( s) ::= stuff ( s) − stuff σvis( s)} ∪ Ax(Ot) Ax(ν(Os)) ::= {φ{stuff /stuff σvis} | φ ∈ Ax(Os)} Invert definitions when v1 < v2.

Alan Bundy & Michael Chan Ontology Evolution in Physics STP Glasgow 28.3.08

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Paradox of Latent Heat

Alan Bundy & Michael Chan Ontology Evolution in Physics STP Glasgow 28.3.08

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Application to the Latent-Heat Paradox

Trigger: Ot ⊢ Heat(H2O, Start(Freeze)) = Heat(H2O, Start(Freeze)) Os ⊢ Heat(H2O, Start(Freeze)) = Heat(H2O, End(Freeze)) Ot ⊢ Heat(H2O, Start(Freeze)) = Heat(H2O, End(Freeze)) Splitting Heat: ∀o:obj, t:mom. LHF(o, t) ::= Heat(o, t) − Temp(o, t)

Alan Bundy & Michael Chan Ontology Evolution in Physics STP Glasgow 28.3.08

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Anomaly of Orbital Velocity

Alan Bundy & Michael Chan Ontology Evolution in Physics STP Glasgow 28.3.08

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Application to Dark Matter

Trigger: Ot ⊢ λs ∈ Spiral. Rad(s), Orb V el(s) = GraphA Os ⊢ λs ∈ Spiral. Rad(s), Orb V el(s) = GraphB Ot ⊢ GraphA = GraphB Splitting Spiral Galaxy: λs ∈ Spiralinvis. Rad(s), Orb V el(s) ::= λs ∈ Spiral. Rad(s), Orb V el(s) − λs ∈ Spiralvis. Rad(s), Orb V el(s)

Alan Bundy & Michael Chan Ontology Evolution in Physics STP Glasgow 28.3.08

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The Inconstancy Ontology Repair Plan

Trigger: Ot ⊢ stuff ( x) ::= c( x) Os(V ( s, b1) = v1) ⊢ stuff ( s) = c1( s), . . . . . . Os(V ( s, bn) = vn) ⊢ stuff ( s) = cn( s), ∃i = j. Ot ⊢ ci( s) = cj( s) Add Variad: ν(stuff ) ::= λ y,

• x. F (c(

x), V ( x, y)) Create New Axioms: Ax(ν(Ot)) ::= {φ{stuff /ν(stuff )( y)} | φ ∈ Ax(Ot) \{stuff ( x) ::= c( x)}} ∪ {ν(stuff ) ::= λ y,

• x. F (c(

x), V ( x, y))} Ax(ν(Os(V ( s, bi) = vi))) ::= {φ{stuff /ν(stuff )( bi)} | φ ∈ Ax(Os(V ( s, bi) = vi))}

Alan Bundy & Michael Chan Ontology Evolution in Physics STP Glasgow 28.3.08

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MOdified Newtonian Dynamics (mond)

• Provides

alternative (Inconstancy-based) explanation

• f
• rbital

velocity anomaly.

• mond - The gravitational force is different at low accelerations.
• Acceleration provides variad to Gravitational ’Constant’.

Alan Bundy & Michael Chan Ontology Evolution in Physics STP Glasgow 28.3.08

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Application to MOND

Trigger: Ot ⊢ G ::= 6.67 × 10−11 Os(Acc(S1) = A1) ⊢ G = M2OV −1(OV (S1), Mass(S1), λs ∈ Spiral \ {S1}. (P osn(s), Mass(s))) (= G1) . . . . . . Os(Acc(Sn) = An) ⊢ G = M2OV −1(OV (Sn), Mass(Sn), λs ∈ Spiral \ {Sn}. (P osn(s), Mass(s))) (= Gn) ∃i = j. Ot ⊢ Gi = Gj Add Variad to Gravitational Constant: ν(Ot) ⊢ ν(G) ::= λs.F (6.67 × 10−11, Acc(s)) ν(Os(Acc(S1) = A1)) ⊢ ν(G)(S1) = M2OV −1(OV (S1), Mass(S1), λs ∈ Spiral \ {S1}. (P osn(s), Mass(s))) . . . . . . ν(Os(Acc(Sn) = An)) ⊢ ν(G)(Sn) = M2OV −1(OV (Sn), Mass(Sn), λs ∈ Spiral \ {Sn}. (P osn(s), Mass(s)))

Alan Bundy & Michael Chan Ontology Evolution in Physics STP Glasgow 28.3.08

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Conservative Extensions and Minimal Repairs

• Want repairs to be minimal.
• Adapt conservative extension.

φ ∈ Sig(O) = ⇒ (ν(O) ⊢ ν(φ) ⇐ ⇒ O ⊢ φ)

• In wms, both ν(Ot) and ν(Os) are conservative in this sense.

Ax(ν(Ot)) ::= {∀ s: τ. stuff σinvis( s) ::= stuff ( s) − stuff σvis( s)} ∪ Ax(Ot) Ax(ν(Os)) ::= {φ{stuff /stuff σvis} | φ ∈ Ax(Os)}

• The combined ontologies are not conservative.
• Situation more complicated for Inconstancy.

Alan Bundy & Michael Chan Ontology Evolution in Physics STP Glasgow 28.3.08

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Use of Contexts in Repair Plans

Why have separate theoretical and sensory ontologies?

• Enables control over contradiction.
• Focuses effect of repair operations.
• Allows use of conservative extension to show minimality.

Alan Bundy & Michael Chan Ontology Evolution in Physics STP Glasgow 28.3.08

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Implementation

• Implemented both repair plans in galileo system in λProlog.

– (Guided Analyses of Logical Inconsistencies Leads to Evolved Ontologies)

• Higher-order logic needed at both object- and meta-level.
• Polymorphism required for stuff , =, <, −, etc.
• Successfully tested on 6 development examples.

– wms tested on dark matter, latent heat, elastic energy and missing planet. – Inconstancy tested on mond and Boyle’s Law.

• Plan to build larger test set for evaluation.

Alan Bundy & Michael Chan Ontology Evolution in Physics STP Glasgow 28.3.08

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Research Programme

• Discovery, analysis and formalisation of physics case studies:

both development and test sets.

• Development of physics ontologies: before and after repair.
• Development of a theory of ontology evolution.
• Development of a few, generic ontology repair plans.
• Implementation and evaluation of these repair plans.

Alan Bundy & Michael Chan Ontology Evolution in Physics STP Glasgow 28.3.08

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Conclusion

• Ontology evolution is a key technology for adaptive, interactive agents.
• Physics is good development domain because of historical record.
• Higher-order logic needed at object- and meta-levels.
• Repair plans address problems of search and ambiguity.
• Developed and tested two repair plans so far.
• Implemented in λProlog galileo system.

Alan Bundy & Michael Chan Ontology Evolution in Physics STP Glasgow 28.3.08