Download Inverse Resolution

Inverse Resolution
CMSC 671 - Principles of AI
Mike Smith
2001/12/04
Inverse Resolution
Why invert resolution?
Wasn't resolution hard enough?
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We can work resolution graphs backwards
We can learn theories from examples
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We can use background knowledge to help
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Inverse resolution can be "lifted" to FOL
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We can capture knowledge beyond attributes
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We can interpret the resulting theories
Inverse Resolution –
Learning Framework
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Deductive framework: T entails E
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Break T into B, H
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Inductive framework: B ^ H entails E
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Build set of resolution trees backwards from roots
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New leaves not in prior knowledge are hypothesis
Legend: T = Theory
B = Background Knowledge
H = Hypothesis
E = Examples
Inverting Resolution
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Four Rules
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Absorption
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Identification
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Intra-construction
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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)
parent(henry,jane)
q(henry,jane) <- <father(henry,jane)
male(henry)
male(henry)
grandfather(henry,john) <<grandfather(henry,john)
parent(henry,jane),
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

Inductive Logic Programming (ILP)
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ILP = Inductive Methods + Logic Programming
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Two Major Induction Methods
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Inverse Resolution
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Top-Down Learning Methods
ILP Systems
SYSTEM
RESEARCHERS
GOLEM
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
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Muggleton. (199?). Inductive Logic Programming.
http://www.cs.york.ac.uk/mlg/ilp.html

Russell & Norvig. (1995). Artificial Intelligence: A Modern

van der Poel. (2000). Inductive Logic Programming - Theory.
Approach.
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?