The Hamming Seminars Alan Bundy University of Edinburgh

Richard Hamming's Talk “If you want to do great work, you must work on important problems, and you should have an idea” “When I went to lunch Friday afternoon, I would only discuss great thoughts …”

What are the Important Problems? Why are these problems important? Why are they timely? What form will solutions take? What approaches look promising? What are the time-frames? How does your research relate?

Automated Ontology Evolution Alan Bundy University of Edinburgh

What is Automated Ontology Evolution? Ontology = logical theory = knowledge base = … In theory of computing, maths, AI, semantic web, etc. Ontologies usually static: manually constructed. Fixed during inference. Ontology evolution is how they change: To meet changing environment, goals, etc. Usually manual, possibly with machine assistance. Can we automate this and interleave it with inference? 15/10/09

Example: Coin-in-the-slot Parking meter requires £ 5. Must be in coins. Not including new 50 p. Or bent or underweight coins. But some foreign coins will work. 15/10/09

Why is it important? Humans construct and evolve ontologies. But Many we have failed to automate it. applications require it. Agents whose environment/goals change. Agents that communicate. Representational change can make inference more efficient. 15/10/09

Representation Key to Inference John Mc. Carthy’s Mutilated Checkerboard: Can we tile board with dominos? Colouring of domino removes search from solution. 15/10/09

Why is it timely? Increased understanding of representational space, e. g. , expressivity/tractability tradeoffs. Build on ontology matching work. Build on belief revision work. Build on analogy work, esp. for creating representation. Increased understanding of fault diagnosis and repair. 15/10/09

Relevant Books 15/10/09

What form will solutions take? Changes both to beliefs and language. Triggered by inference failures: Contradictory ontologies. Mismatch with world modelled. Inefficient inference. Analysis/diagnosis of failure. Suggest/implement repair. 15/10/09

Example: Evolution of ‘Motherhood’ • Motherhood: Mother(person) • Maternal. Grand. Mother(p) = Mother(p)) • Types: natural, step, adopted, foster, surrogate, egg donor, . . • Split Relations: Step. Mother(mum, child) • Add Argument: Mother(mum, child, kind) • Mother(gm, m, k ) Æ Mother(m, gc, k ) ! 1 2 Maternal. Grand. Mother(gm, gc, Combine(k 1, k 2)) 15/10/09

What approaches look promising? Ontology repair plans: combine atomic steps into common patterns; address huge combinatorial explosion; address partiality of refinement. Lakatos is source of inspiration: “Proofs and Refutations” book; common patterns of ‘proof’ repair; applies outwith maths. Category Theory: modularise big theories; isolate contradiction. 15/10/09

Lakatos Book “Monster-barring” “Monster-adjustment” “Exception-barring” “Lemma-incorporation” 15/10/09

What are the time-frames? Currently, have manual change, possibly with machine assistance. Expect incremental progress over several decades. Full automation in limited domains in next decade, perhaps. Sometimes, 15/10/09 must have human in loop.

Ontology evolution to reduce search • Saul Amarel study of Missionaries and cannibals. • How change of representation affects search space size. • Successive representations significantly reduce search. • Paper in “Machine Intelligence 3” 1968! 15/10/09

How does our research relate? Cynthia: evolves functional programs. TM: repairs faulty or open maths conjectures. ORS: repairs multi-agent plans whose execution fails. Galileo: repairs physical theories refuted by experimental evidence. Wheelbarrow: cognitive model of mathematical invention. 15/10/09

Ontology Evolution in Programs • Cynthia: analogical editor for ML programs. • Edit old ML program into new one. • Ph. D project of Jon Whittle. • Powerful commands to change names, arguments, types, recursion, etc. • Commands edit synthesis proof, from which program is rederived. • Ensures well-formedness, coverage and termination of synthesised program. 15/10/09

Example: Length to Size • Initial Program: length of list. • Change to count size of tree. • Change data-type to trees. • Automatically changes recursion. • Flags up now faulty code. • Correct flagged code. • Checks termination. • Change name of program to count length([])=0 length([H|T])=length(T)+1 count(leaf(S))=1 15/10/09 count(node(L, R))=count(L)+count(R)

Ontology Evolution in Maths • HR Program creates new concepts and conjectures from examples. • Ph. D project of Simon Colton. • TM Program uses HR, Otter and Mace to repair faulty mathematical ontologies. • Project of Alison Pease and Simon Colton. • TM methods based on Lakatos “Proofs and Refutations”. 15/10/09

Example: Near-Miss Conjectures • TM/HR system repairs faulty conjectures. • Example: 8 x, y. x £ y = y £ x. • TPTP doctored theorem in Group Theory. • Mace finds 8 examples and 2 counterexamples. • HR invents new concept: 8 z. z =z. • TM applies Lakatos’s Strategic Withdrawal. • Otter proves conjecture for all groups with above -1 property. • Cooperation between 4 reasoning processes. 15/10/09

Ontology Evolution for Agents • ORS Program: repairs faulty ontologies by analysing failed multi-agent plans. • Ph. D of Fiona Mc. Neill • Changes include abstraction and refinement of signatures, • e. g. adding arguments, changing predicates. • Allows agents with slightly different ontologies to communicate. • Technology essential for Semantic Web 15/10/09

Example: Hotel Bill • Planning agent (PA) forms plan, • but it fails. • Failing action: Pay(PA, Hotel, $200). • Hotel agent refuses to accept money. • Surprising question precedes failure. • Money(PA, $200, credit_card) • Where PA expected Money(PA, $200) • Change binary Money to ternary. 15/10/09

Ontology Evolution in Physics • GALILEO: evolves physical theories. • Project with Michael Chan & Jos Lehmann. • Experimental evidence may contradict known theory. • Using ontology repair plans to capture common patterns. • Where’s my stuff? • Inconstancy. • Unite. • Case studies include: dark matter, latent heat, Boyle’s Law, etc. 15/10/09

Example: Dark Matter • Mismatch between prediction and observation: • orbital velocities of stars in spiral galaxies. • Use WMS to split galaxy into: • visible stars; • invisible dark matter halo; • and their total. • Alternative solution: r a d i u s • Uses Inconstancy (MOND) • gravity depends on relative acceleration. 15/10/09 actual predicted orbital velocity

Ontology Evolution in Mathematics • Wheelbarrow project: • Project of Alan Smaill, Alison Pease & Markus Guhe. • Adapts Lakatos ideas on evolution of mathematical theories. • And Lakoff and Núñez on role of metaphor in mathematical invention. • Applied to conjecture making, problem solving, etc. 15/10/09

Example: Polygons to Polyhedra 5=5 • V=E for 2 D polygons. • Is there an analogous theorem for 3 D polyhedra? • What do V & E map to? • Edges, faces, angles, vertices? • Euler conjectured: V-E+F=2. • Topic of Lakatos’ book. 15/10/09 20 -30+12=2

Conclusion • Automated ontology evolution: • Required for many important applications; • Raises difficult research challenges. • The time is ripe: • We have novel approaches; • And promising initial progress. • Several Edinburgh projects in this area. 15/10/09