Inverse Resolution CMSC 671 Principles of AI Mike

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

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

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

Inverting Resolution A Four Rules A Absorption A Identification A Intra-construction A 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

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

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

Intra-Construction p <- A, B q <- B p <- A, C p <- A, q q <- C 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 p <- A, B q <- C p <- A, C

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) q(henry, jane) <- <father(henry, jane) parent(henry, jane) q(henry, jane) <- <father(henry, jane) male(henry) grandfather(henry, john) <<grandfather(henry, john) parent(henry, jane), q(henry, jane) father(henry, jane) grandfather(henry, john) <parent(henry, jane), parent(jane, john) grandfather(henry, john) <parent(henry, jane), male(henry)

Inter-Construction p <- A, B p <- r, B q <- A, C r <- A q <- r, C 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 <- r, B r <- A p <- A, B q <- r, C p <- A, C

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

ILP Systems

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

References A Camacho. (1994). The Use of Background Knowledge in Inductive Logic Programming. http: //citeseer. nj. nec. com/camacho 94 use. html A Muggleton. (199? ). Inductive Logic Programming. http: //www. cs. york. ac. uk/mlg/ilp. html A Russell & Norvig. (1995). Artificial Intelligence: A Modern A van der Poel. (2000). Inductive Logic Programming - Theory. Approach. http: //ww. kbs. twi. tudelft. nl/Education/Cyberles/Trondheim/ILP/html/ilp_th_01 introd. html A Wang. (2000). Parallel Inductive Logic in Data Mining. http: //citeseer. nj. nec. com/wang 00 parallel. html A Weber. (1996). ILP Systems on the ILPnet Systems Repository http: //www-ai. ijs. si/ilpnet/irenefinal. ps

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