1 IPSI 2003 © 2003 T. Abou-Assaleh, N. Cercone, & V. Keselj An Overview of the Theory of Relaxed...
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© 2003 T. Abou-Assaleh, N. Cercone, & V. Keselj 1 IPSI 2003 An Overview of the Theory of Relaxed Unification Tony Abou-Assaleh Nick Cercone & Vlado Keselj Faculty of Computer Science Dalhousie University
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Transcript of 1 IPSI 2003 © 2003 T. Abou-Assaleh, N. Cercone, & V. Keselj An Overview of the Theory of Relaxed...
© 2003 T. Abou-Assaleh, N. Cercone, & V. Keselj 1
IPSI 2003
An Overview of the Theory of Relaxed
UnificationTony Abou-Assaleh
Nick Cercone & Vlado Keselj
Faculty of Computer ScienceDalhousie University
© 2003 T. Abou-Assaleh, N. Cercone, & V. Keselj 2
IPSI 2003
Agenda• Introduction
• Classical Unification
• Relaxed Unification
• RU System
• Conclusion and Ongoing Work
© 2003 T. Abou-Assaleh, N. Cercone, & V. Keselj 3
IPSI 2003
Agenda• Introduction
• Classical Unification
• Relaxed Unification
• RU System
• Conclusion and Ongoing Work
© 2003 T. Abou-Assaleh, N. Cercone, & V. Keselj 4
IPSI 2003
Motivation• NLP using HPSG
• NLP: Natural Language Processing• HPSG: Head-driven Phrase Structure Grammar
• QA in TREC• QA: Question Answering• TREC: Text REtrieval Conference
• Can we do better?
© 2003 T. Abou-Assaleh, N. Cercone, & V. Keselj 5
IPSI 2003
History• Classical Unification
• Robinson, 1965
• Uncertainty in Logic:• Lee, 1972• Bacchus, 1990
• Relaxed Unification• Abou-Assaleh, 2002
© 2003 T. Abou-Assaleh, N. Cercone, & V. Keselj 6
IPSI 2003
Agenda• Introduction
• Classical Unification
• Relaxed Unification
• RU System
• Conclusion and Ongoing Work
© 2003 T. Abou-Assaleh, N. Cercone, & V. Keselj 7
IPSI 2003
ExampleA =
Car:
Model: Protégé
Make: Mazda
Year: 2000
VIN: 12345
Mileage: ?
B =
Car:
Model: Protégé
Make: Mazda
Year: 2000
VIN: ?
Mileage: 70,000
© 2003 T. Abou-Assaleh, N. Cercone, & V. Keselj 8
IPSI 2003
ExampleA U B =
Car:
Model: Protégé
Make: Mazda
Year: 2000
VIN: 12345
Mileage: 70,000
Substitution:
?VIN 12345
?Mileage 70,000
© 2003 T. Abou-Assaleh, N. Cercone, & V. Keselj 9
IPSI 2003
ExampleA = Car(Protégé, Mazda, 2000, 12345, X)
B = Car(Protégé, Mazda, 2000, Y, 70000)
A U B = Car(Protégé, Mazda, 2000, 12345, 70000)
= {X 7000, Y 12345}
© 2003 T. Abou-Assaleh, N. Cercone, & V. Keselj 10
IPSI 2003
Classical Unification• Substitution:
A set of mappings from variables to terms
• Unification:Two terms are unifiable if and only if there exists a unifying substitution
© 2003 T. Abou-Assaleh, N. Cercone, & V. Keselj 11
IPSI 2003
Visual Example
© 2003 T. Abou-Assaleh, N. Cercone, & V. Keselj 12
IPSI 2003
Agenda• Introduction
• Classical Unification
• Relaxed Unification
• RU System
• Conclusion and Ongoing Work
© 2003 T. Abou-Assaleh, N. Cercone, & V. Keselj 13
IPSI 2003
What’s wrong?• Classical Unification:
“Everything in the database is true and nothing else!” – Goerz
– Data can be incomplete– Data can be ambiguous– Data can be contradicting– Data can be erroneous
© 2003 T. Abou-Assaleh, N. Cercone, & V. Keselj 14
IPSI 2003
From Classical to Relaxed
Classical unification fails:
A = Car(12345, Protégé, Mazda, Details(Fuel(50)), 70000)
Q = Car(12345, Protégé, Mazda, Details(Fuel(45)), X)
A U Q = fail
© 2003 T. Abou-Assaleh, N. Cercone, & V. Keselj 15
IPSI 2003
From Classical to Relaxed
Relaxed unification succeeds:
A = Car(12345, Protégé, Mazda, Details(Fuel(50)), 70000)
Q = Car(12345, Protégé, Mazda, Details(Fuel(45)), X)
A U Q = Car(12345, Protégé, Mazda, Details(Fuel({50,45})), 70000)
= {X 70000}
© 2003 T. Abou-Assaleh, N. Cercone, & V. Keselj 16
IPSI 2003
Concepts• Encapsulate each function in a set• Allow structure sharing and recursion• Directed Graph:
– Set and function nodes– Edges to function nodes labelled with
function symbols– Edges to set nodes labelled with argument
index
© 2003 T. Abou-Assaleh, N. Cercone, & V. Keselj 17
IPSI 2003
Visual Representation
© 2003 T. Abou-Assaleh, N. Cercone, & V. Keselj 18
IPSI 2003
Example
© 2003 T. Abou-Assaleh, N. Cercone, & V. Keselj 19
IPSI 2003
Example: Variable
© 2003 T. Abou-Assaleh, N. Cercone, & V. Keselj 20
IPSI 2003
Example: Shared Set
© 2003 T. Abou-Assaleh, N. Cercone, & V. Keselj 21
IPSI 2003
Example: Recursive Set
© 2003 T. Abou-Assaleh, N. Cercone, & V. Keselj 22
IPSI 2003
Example: Recursive Function
© 2003 T. Abou-Assaleh, N. Cercone, & V. Keselj 23
IPSI 2003
Agenda• Introduction
• Classical Unification
• Relaxed Unification
• RU System
• Conclusion and Ongoing Work
© 2003 T. Abou-Assaleh, N. Cercone, & V. Keselj 24
IPSI 2003
RU System• RU Interpreter
• RU Engine– Generalized uniform representation of
terms and substitutions– Graph unification
© 2003 T. Abou-Assaleh, N. Cercone, & V. Keselj 25
IPSI 2003
RU System• Application
– Probabilistic Context Free Grammar (PCFG)
– PACLING’03
© 2003 T. Abou-Assaleh, N. Cercone, & V. Keselj 26
IPSI 2003
Agenda• Introduction
• Classical Unification
• Relaxed Unification
• RU System
• Conclusion and Ongoing Work
© 2003 T. Abou-Assaleh, N. Cercone, & V. Keselj 27
IPSI 2003
Conclusion• Novel theory
• Reasoning under uncertainty
• More general and higher efficacy
• Unification algorithm
• Accuracy measure
• RU System
© 2003 T. Abou-Assaleh, N. Cercone, & V. Keselj 28
IPSI 2003
Ongoing Work• Theory of Relaxed Unification
• Correctness and effectiveness of algorithms• Runtime and space complexities
• Stochastic Relaxed Unification• Probabilistic models for weights• Probabilistic correctness function
• RU System• Application to HPSG and QA
© 2003 T. Abou-Assaleh, N. Cercone, & V. Keselj 29
IPSI 2003
Thank you!
Questions or comments?
www.cs.dal.ca/~taa/
