1 IPSI 2003 © 2003 T. Abou-Assaleh, N. Cercone, & V. Keselj An Overview of the Theory of Relaxed Unification Tony Abou-Assaleh Nick Cercone & Vlado Keselj Faculty of Computer Science Dalhousie University

2 IPSI 2003 © 2003 T. Abou-Assaleh, N. Cercone, & V. Keselj Agenda Introduction Classical Unification Relaxed Unification RU System Conclusion and Ongoing Work

3 IPSI 2003 © 2003 T. Abou-Assaleh, N. Cercone, & V. Keselj Agenda Introduction Classical Unification Relaxed Unification RU System Conclusion and Ongoing Work

4 IPSI 2003 © 2003 T. Abou-Assaleh, N. Cercone, & V. Keselj 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?

5 IPSI 2003 © 2003 T. Abou-Assaleh, N. Cercone, & V. Keselj History Classical Unification Robinson, 1965 Uncertainty in Logic: Lee, 1972 Bacchus, 1990 Relaxed Unification Abou-Assaleh, 2002

6 IPSI 2003 © 2003 T. Abou-Assaleh, N. Cercone, & V. Keselj Agenda Introduction Classical Unification Relaxed Unification RU System Conclusion and Ongoing Work

7 IPSI 2003 © 2003 T. Abou-Assaleh, N. Cercone, & V. Keselj Example A = Car: Model:Protégé Make:Mazda Year:2000 VIN:12345 Mileage:? B = Car: Model:Protégé Make:Mazda Year:2000 VIN:? Mileage:70,000

8 IPSI 2003 © 2003 T. Abou-Assaleh, N. Cercone, & V. Keselj Example A U B = Car: Model:Protégé Make:Mazda Year:2000 VIN:12345 Mileage:70,000 Substitution: ? VIN  ? Mileage  70,000

9 IPSI 2003 © 2003 T. Abou-Assaleh, N. Cercone, & V. Keselj Example A = 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}

10 IPSI 2003 © 2003 T. Abou-Assaleh, N. Cercone, & V. Keselj 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

11 IPSI 2003 © 2003 T. Abou-Assaleh, N. Cercone, & V. Keselj Visual Example

12 IPSI 2003 © 2003 T. Abou-Assaleh, N. Cercone, & V. Keselj Agenda Introduction Classical Unification Relaxed Unification RU System Conclusion and Ongoing Work

13 IPSI 2003 © 2003 T. Abou-Assaleh, N. Cercone, & V. Keselj 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

14 IPSI 2003 © 2003 T. Abou-Assaleh, N. Cercone, & V. Keselj 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

15 IPSI 2003 © 2003 T. Abou-Assaleh, N. Cercone, & V. Keselj 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}

16 IPSI 2003 © 2003 T. Abou-Assaleh, N. Cercone, & V. Keselj 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

17 IPSI 2003 © 2003 T. Abou-Assaleh, N. Cercone, & V. Keselj Visual Representation

18 IPSI 2003 © 2003 T. Abou-Assaleh, N. Cercone, & V. Keselj Example

19 IPSI 2003 © 2003 T. Abou-Assaleh, N. Cercone, & V. Keselj Example: Variable

20 IPSI 2003 © 2003 T. Abou-Assaleh, N. Cercone, & V. Keselj Example: Shared Set

21 IPSI 2003 © 2003 T. Abou-Assaleh, N. Cercone, & V. Keselj Example: Recursive Set

22 IPSI 2003 © 2003 T. Abou-Assaleh, N. Cercone, & V. Keselj Example: Recursive Function

23 IPSI 2003 © 2003 T. Abou-Assaleh, N. Cercone, & V. Keselj Agenda Introduction Classical Unification Relaxed Unification RU System Conclusion and Ongoing Work

24 IPSI 2003 © 2003 T. Abou-Assaleh, N. Cercone, & V. Keselj RU System RU Interpreter RU Engine –Generalized uniform representation of terms and substitutions –Graph unification

25 IPSI 2003 © 2003 T. Abou-Assaleh, N. Cercone, & V. Keselj RU System Application –Probabilistic Context Free Grammar (PCFG) –PACLING’03

26 IPSI 2003 © 2003 T. Abou-Assaleh, N. Cercone, & V. Keselj Agenda Introduction Classical Unification Relaxed Unification RU System Conclusion and Ongoing Work

27 IPSI 2003 © 2003 T. Abou-Assaleh, N. Cercone, & V. Keselj Conclusion Novel theory Reasoning under uncertainty More general and higher efficacy Unification algorithm Accuracy measure RU System

28 IPSI 2003 © 2003 T. Abou-Assaleh, N. Cercone, & V. Keselj 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

29 IPSI 2003 © 2003 T. Abou-Assaleh, N. Cercone, & V. Keselj Thank you! Questions or comments?