Representational Change in Physics Theory Repair Plans Where’s My Stuff? Inconstancy Unite The Architecture of galileo C Theory Evolution in Physics Alan Bundy (Joint work with Jos Lehmann and Michael Chan) School of Informatics, University of Edinburgh University of St Andrews, 27 th November 2013
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Representational Change in Physics Theory Repair Plans Where’s My Stuff? Inconstancy Unite The Architecture of galileo Conclusion
Theory Evolution in Physics
Alan Bundy(Joint work with Jos Lehmann and Michael Chan)
School of Informatics,University of Edinburgh
University of St Andrews, 27th November 2013
Representational Change in Physics Theory Repair Plans Where’s My Stuff? Inconstancy Unite The Architecture of galileo Conclusion
Outline
1 Representational Change in Physics
2 Theory Repair Plans
3 Where’s My Stuff?
4 Inconstancy
5 Unite
6 The Architecture of galileo
7 Conclusion
Representational Change in Physics Theory Repair Plans Where’s My Stuff? Inconstancy Unite The Architecture of galileo Conclusion
Representational Change in Scientific Revolutions
Concepts Splitting: heat becomes energy and temperature.
one function becomes two.
Concepts Merging: morning star and evening star become Venus.
two constants become one.
Dependencies Increase: gravitational ‘constant’ depends on accel.
function gains an argument.
Dependencies Decrease: gravitational accel independent of mass.
function loses an argument.
Representational Change in Physics Theory Repair Plans Where’s My Stuff? Inconstancy Unite The Architecture of galileo Conclusion
Evolution in ‘Normal’ Science
“Essentially, all models are wrong, but some are useful” (Box& Draper 1987)
“But, it’s turtles all the way down.” (old lady quoted byHawking 1988)
Splitting a function: which new function replaces eachoccurrence of an old one?Adding an argument: what values should its occurrences take?Theory repair plans complete refinement definitions.Multiple small theories facilitate targeted repairs.
Representational Change in Physics Theory Repair Plans Where’s My Stuff? Inconstancy Unite The Architecture of galileo Conclusion
Theory Repair Plans
Aggregate atomic operations into theory repair plans.
Atomic operations: split/merge functions, add/removearguments, etc.
Trigger formula signals applicability and instantiates plan.
Repairs change language as well as beliefs.
Multiple theories used in both trigger and repair.
Representational Change in Physics Theory Repair Plans Where’s My Stuff? Inconstancy Unite The Architecture of galileo Conclusion
Example Theory Repair Plans
The Where’s My Stuff? theory repair plan.
Triggered by conflict between predicted and observed values ofstuff .Splits old stuff into visible, invisible and total stuff .
The Inconstancy theory repair plan.
Triggered by conflict between predicted independence andobserved dependence.Adds this dependency as new argument to stuff .
The Unite theory repair plan.
Triggered because two objects are the same on definingproperty.Equates these two objects.
Representational Change in Physics Theory Repair Plans Where’s My Stuff? Inconstancy Unite The Architecture of galileo Conclusion
Why Higher-Order Logic?
Many concepts in Physics are naturally higher-order,
e.g. orbit of planet: λt. Posn(Uranus, t).differential and integral calculus: Diff (Sin) = Cos.So, higher-order needed at object-level.
Polymorphic nature of theory repair plans.
e.g. stuff , =, < −.Need to quantify over types.So, higher-order needed at meta-level too.
Representational Change in Physics Theory Repair Plans Where’s My Stuff? Inconstancy Unite The Architecture of galileo Conclusion
The galileo System
Implementing trps in the galileo system using Isabelle andits locales.
galileo: Guided Analyses of Logical Inconsistencies Leadsto Evolved Theories.