Inverse Resolution

CMSC 671 - Principles of AI

Mike Smith

2001/12/04

Inverse Resolution

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

Why invert resolution? Wasn't resolution hard enough?

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

T = TheoryB = Background KnowledgeH = HypothesisE = Examples

Legend:

Inverting Resolution

Four Rules Absorption Identification Intra-construction Inter-construction

Absorption

q <- A p <- q,B

p <- A,B

p <- A,Bq <- A

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

Absorption – ExampleBparent(ann, mary)female(mary)father(henry,jane) <-

parent(henry,jane)

Edaughter(mary,ann)grandfather(henry,john) <- parent(henry,jane), parent(jane,john)grandfather(henry,john) <- parent(henry,jane), male(henry)

daughter(mary,ann)

daughter(mary,Y)<-parent(Y,mary)

-1= {ann/Y} Absorption #1

parent(ann, mary)

female(mary) daughter(X,Y) <- female(X), parent(Y,X)

-1= {mary/X} Absorption #2

Identification

p <- A,q q <- B

p <- A,B

p <- A,qp <- A,B

q <- B p <- A,q

Because A,B and A,q have the same conclusion, B can be identified by q.

Intra-Construction

p <- A,B p <- A,C

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

p <- A,B

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

p <- A,C

Construct a clause that represents the similarity between thetwo clauses, (p <- A,q) and then q<-B and q<-C come fromapplying the identification rule.

Intra-Construction ExampleBparent(ann, mary)female(mary)father(henry,jane) <- parent(henry,jane)

Edaughter(mary,ann)grandfather(henry,john) <- parent(henry,jane), parent(jane,john)grandfather(henry,john) <- parent(henry,jane), male(henry)

grandfather(henry,john) <- parent(henry,jane), parent(jane,john)

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

q(henry,jane) <- parent(henry,jane)

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

q(henry,jane) <- male(henry)

father(henry,jane) <- parent(henry,jane)

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

father(henry,jane) <- male(henry)

Inter-Construction

p <- A,B p <- A,C

p <- A,B

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

q <- A,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 q <- r,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

SYSTEM RESEARCHERSGOLEM Muggleton and Cao

LINUS Lavrac and Dzeroski

Progol Muggleton

CLINT De Raedt

FOIL Quinlan

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

Questions?