Inverse Resolution

Inverse Resolution CMSC 671 - Principles of AI Mike Smith 2001/12/04

Inverse Resolution Why invert resolution? Wasn't resolution hard enough? • We can work resolution graphs backwards • We can learn theories from examples • We can use background knowledge to help • Inverse resolution can be "lifted" to FOL • We can capture knowledge beyond attributes • We can interpret the resulting theories

T = Theory B = Background Knowledge H = Hypothesis E = Examples Legend: Inverse Resolution – Learning Framework • Deductive framework: T entails E • Break T into B, H • Inductive framework: B ^ H entails E • Build set of resolution trees backwards from roots • New leaves not in prior knowledge are hypothesis

Inverting Resolution • Four Rules • Absorption • Identification • Intra-construction • Inter-construction

Absorption q <- A p <- A,B q <- A p <- q,B We can create a new clause p <- q,B by absorbing a conjunction of atoms (A) in the premise into a single atom (q) of the other clause q <- A p <- q,B p <- A,B

female(mary) daughter(X,Y) <- female(X), parent(Y,X) -1= {mary/X} Absorption #2 parent(ann, mary) daughter(mary,Y)<-parent(Y,mary) -1= {ann/Y} Absorption #1 Absorption– Example B parent(ann, mary) female(mary) father(henry,jane) <- parent(henry,jane) E daughter(mary,ann) grandfather(henry,john) <- parent(henry,jane), parent(jane,john) grandfather(henry,john) <- parent(henry,jane), male(henry) daughter(mary,ann)

Identification p <- A,B p <- A,q q <- B p <- A,q Because A,B and A,q have the same conclusion, B can be identified by q. p <- A,q q <- B p <- A,B

p <- A,B p <- A,C q <- B p <- A,q q <- C Intra-Construction Construct a clause that represents the similarity between the two clauses, (p <- A,q) and then q<-B and q<-C come from applying the identification rule. q <- B p <- A,q q <- C p <- A,B p <- A,C

q(henry,jane) <- parent(henry,jane) q(henry,jane) <- male(henry) grandfather(henry,john) <- parent(henry,jane), q(henry,jane) father(henry,jane) <- parent(henry,jane) father(henry,jane) <- male(henry) grandfather(henry,john) <- parent(henry,jane), father(henry,jane) grandfather(henry,john) <- parent(henry,jane), parent(jane,john) grandfather(henry,john) <- parent(henry,jane), male(henry) Intra-Construction Example B parent(ann, mary) female(mary) father(henry,jane) <- parent(henry,jane) E daughter(mary,ann) grandfather(henry,john) <- parent(henry,jane), parent(jane,john) grandfather(henry,john) <- parent(henry,jane), male(henry)

p <- A,B q <- A,C p <- r,B p <- r,B r <- A r <- A q <- r,C q <- r,C Inter-Construction Noting the common variable A, construct a clause r <- A (r is new atom). The remaining two conclusive clauses are the result of applying the absorption rule. p <- A,B p <- A,C

Using Inverse Resolution • Inductive Logic Programming (ILP) • ILP = Inductive Methods + Logic Programming • Two Major Induction Methods • Inverse Resolution • Top-Down Learning Methods

ILP Systems

Inductive Logic Programming Common Applications • Life Sciences / Molecular Biology • Predict 3D Protein Structures from Amino Acid Sequences • Predict Therapeutic Efficacy of Drugs • Predict Mutagenesis of Compounds • Natural Language • Learning Part of Speech Tagging • Learning Parsers

References • Camacho. (1994).The Use of Background Knowledge in Inductive Logic Programming. http://citeseer.nj.nec.com/camacho94use.html • Muggleton. (199?). Inductive Logic Programming. http://www.cs.york.ac.uk/mlg/ilp.html • Russell & Norvig. (1995). Artificial Intelligence: A Modern Approach. • van der Poel. (2000). Inductive Logic Programming - Theory. http://ww.kbs.twi.tudelft.nl/Education/Cyberles/Trondheim/ILP/html/ilp_th_01introd.html • Wang. (2000). Parallel Inductive Logic in Data Mining. http://citeseer.nj.nec.com/wang00parallel.html • Weber. (1996). ILP Systems on the ILPnet Systems Repository http://www-ai.ijs.si/ilpnet/irenefinal.ps

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Inverse Resolution