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
1 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
2 The Where’s My Stuff Ontology Repair Plan Trigger: O t ⊢ stuff ( � c ) = v 1 , O s ⊢ stuff ( � c ) = v 2 , O t ⊢ v 1 � = v 2 Assume v 1 > v 2 . Other case dual. Split Stuff: ∀ � s : � τ. stuff σ invis ( � s ) ::= stuff ( � s ) − stuff σ vis ( � s ) Create New Axioms: Ax ( ν ( O t )) ::= {∀ � s : � τ. stuff σ invis ( � s ) ::= stuff ( � s ) − stuff σ vis ( � s ) } ∪ Ax ( O t ) Ax ( ν ( O s )) ::= { φ { stuff / stuff σ vis } | φ ∈ Ax ( O s ) } Invert definitions when v 1 < v 2 . Alan Bundy & Michael Chan Ontology Evolution in Physics STP Glasgow 28.3.08
3 Paradox of Latent Heat Alan Bundy & Michael Chan Ontology Evolution in Physics STP Glasgow 28.3.08
4 Application to the Latent-Heat Paradox Trigger: O t ⊢ Heat ( H 2 O, Start ( Freeze )) = Heat ( H 2 O, Start ( Freeze )) O s ⊢ Heat ( H 2 O, Start ( Freeze )) = Heat ( H 2 O, End ( Freeze )) O t ⊢ Heat ( H 2 O, Start ( Freeze )) � = Heat ( H 2 O, 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
5 Anomaly of Orbital Velocity Alan Bundy & Michael Chan Ontology Evolution in Physics STP Glasgow 28.3.08
6 Application to Dark Matter Trigger: O t ⊢ λs ∈ Spiral. � Rad ( s ) , Orb V el ( s ) � = Graph A O s ⊢ λs ∈ Spiral. � Rad ( s ) , Orb V el ( s ) � = Graph B O t ⊢ Graph A � = Graph B Splitting Spiral Galaxy: λs ∈ Spiral invis . � Rad ( s ) , Orb V el ( s ) � ::= λs ∈ Spiral. � Rad ( s ) , Orb V el ( s ) � − λs ∈ Spiral vis . � Rad ( s ) , Orb V el ( s ) � Alan Bundy & Michael Chan Ontology Evolution in Physics STP Glasgow 28.3.08
7 The Inconstancy Ontology Repair Plan Trigger: Ot ⊢ stuff ( � x ) ::= c ( � x ) s, � Os ( V ( � b 1) = v 1) ⊢ stuff ( � s ) = c 1( � s ) , . . . . . . s, � Os ( V ( � 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 )) } s, � { φ { stuff /ν ( stuff )( � s, � Ax ( ν ( Os ( V ( � bi ) = vi ))) ::= bi ) } | φ ∈ Ax ( Os ( V ( � bi ) = vi )) } Alan Bundy & Michael Chan Ontology Evolution in Physics STP Glasgow 28.3.08
8 MOdified Newtonian Dynamics ( mond ) • Provides alternative (Inconstancy-based) explanation of orbital 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
9 Application to MOND Trigger: G ::= 6 . 67 × 10 − 11 Ot ⊢ G = M 2 OV − 1( OV ( S 1) , Mass ( S 1) , λs ∈ Spiral \ { S 1 } . ( P osn ( s ) , Mass ( s ))) (= G 1) Os ( Acc ( S 1) = A 1) ⊢ . . . . . . G = M 2 OV − 1( OV ( Sn ) , Mass ( Sn ) , λs ∈ Spiral \ { Sn } . ( P osn ( s ) , Mass ( s ))) (= Gn ) Os ( Acc ( Sn ) = An ) ⊢ ∃ i � = j. Ot ⊢ Gi � = Gj Add Variad to Gravitational Constant: ν ( G ) ::= λs.F (6 . 67 × 10 − 11 , Acc ( s )) ν ( Ot ) ⊢ ν ( G )( S 1) = M 2 OV − 1( OV ( S 1) , Mass ( S 1) , λs ∈ Spiral \ { S 1 } . ( P osn ( s ) , Mass ( s ))) ν ( Os ( Acc ( S 1) = A 1)) ⊢ . . . . . . ν ( G )( Sn ) = M 2 OV − 1( OV ( Sn ) , Mass ( Sn ) , λs ∈ Spiral \ { Sn } . ( P osn ( s ) , Mass ( s ))) ν ( Os ( Acc ( Sn ) = An )) ⊢ Alan Bundy & Michael Chan Ontology Evolution in Physics STP Glasgow 28.3.08
10 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 ( O t ) and ν ( O s ) are conservative in this sense. Ax ( ν ( O t )) ::= {∀ � s : � τ. stuff σ invis ( � s ) ::= stuff ( � s ) − stuff σ vis ( � s ) } ∪ Ax ( O t ) Ax ( ν ( O s )) ::= { φ { stuff / stuff σ vis } | φ ∈ Ax ( O s ) } • The combined ontologies are not conservative. • Situation more complicated for Inconstancy. Alan Bundy & Michael Chan Ontology Evolution in Physics STP Glasgow 28.3.08
11 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
12 Implementation • Implemented both repair plans in galileo system in λ Prolog. – (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
13 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
14 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 λ Prolog galileo system. Alan Bundy & Michael Chan Ontology Evolution in Physics STP Glasgow 28.3.08
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