8.1.Learning and Logic - Acknowledgement Material derived...

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11s1: COMP9417 Machine Learning and Data Mining Learning and Logic April 19, 2010 Acknowledgement: Material derived from slides for the book Machine Learning, Tom M. Mitchell, McGraw-Hill, 1997 http://www-2.cs.cmu.edu/~tom/mlbook.html and the book Inductive Logic Programming: Techniques and Applications by N. Lavrac and S. Dzeroski, Ellis Horwood, New York, 1994 (available at http://www-ai.ijs.si/SasoDzeroski/ILPBook/ ) and the paper by A. Cootes, S.H. Muggleton, and M.J.E. Sternberg “The automatic discovery of structural principles describing protein fold space”. Journal of Molecular Biology, 2003. (available at http://www.doc.ic.ac.uk/~shm/jnl.html) and the book Data Mining (2e), Ian H. Witten and Eibe Frank, Morgan Kaufmann, 2005. http://www.cs.waikato.ac.nz/ml/weka Aims This lecture will introduce you to theoretical and applied aspects of representing hypotheses for machine learning in first-order logic. Following it you should be able to: outline the key di ff erences between propositional and first-order learning describe the problem of learning relations and some applications reproduce the basic FOIL algorithm and its use of information gain outline the problem of induction in terms of inverse deduction describe inverse resolution and least general generalisation define the θ -subsumption generality ordering for clauses [Recommended reading: Mitchell, Chapter 10] [Recommended exercises: 10.5 – 10.7 (10.8)] COMP9417: April 19, 2010 Learning and Logic: Slide 1 Relevant programs Progol http://www.doc.ic.ac.uk/~shm/progol.html Aleph http://web.comlab.ox.ac.uk/oucl/research/areas/machlearn/Aleph FOIL http://www.rulequest.com/Personal/ iProlog http://www.cse.unsw.edu.au/~claude/research/software/ Golem http://www.doc.ic.ac.uk/~shm/golem.html See also: http://www-ai.ijs.si/~ilpnet2/systems/ COMP9417: April 19, 2010 Learning and Logic: Slide 2
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Representation in Propositional Logic Propositional variables: P, Q, R, . . . Negation: ¬ S, ¬ T, . . . Logical connectives: , , , Well-formed formulae: P Q , ( ¬ R S ) T , etc. Inference rules: modus ponens Given B and A B infer A modus tollens Given ¬ A and A B infer ¬ B Enable sound or valid inference. COMP9417: April 19, 2010 Learning and Logic: Slide 3 Meaning in Propositional Logic Propositional variables stand for declarative sentences (properties): P the paper is red Q the solution is acid Potentially useful inferences: P Q If the paper is red then the solution is acid Meaning of such formulae can be understood with a truth table : P Q P Q T T T T F F F T T F F T COMP9417: April 19, 2010 Learning and Logic: Slide 4 Representation in First-Order Predicate Logic We have a richer language for developing formulae: constant symbols: Fred, Jane, Copper, Manganese, . . . function symbols: Cons, Succ, . . . variable symbols: x, y, z, . . . predicate symbols: Parent, Likes, Binds, . . .
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