Default Inheritance in Constraint-based Frameworks

1. Default Inheritance in Constraint-based Frameworks Christof Rumpf Heinrich-Heine-Universität Düsseldorf June 24, 2010 http://www.phil-fak.uni-duesseldorf.de/~rumpf/talks/DefaultInheritance2.pdf

2. Overview • motivation • monotonic inheritance • nonmonotonic unification • nonmonotonic inheritance Default Inheritance

3. Motivation • for inheritance • compact representations (elimin. redundancies) • modelling of relations and generalizations • for default inheritance • systematic modelling of regularities, subregularities, and irregularities Default Inheritance

4. Tweety bird no information at all monotonic eagle penguin arbitraryalternants can fly can not fly bird can fly nonmonotonic conflict resolution necessary eagle penguin can not fly Default Inheritance

5. Monotonic Inheritance in Constraint-based Frameworks PATR, ALE, CUF, QType, ... GPSG, HPSG, LFG, UCG, ...

6. Levels for Inheritance Mechanisms • static type signature • macros • relational constraints • type constraints • lexical rules Default Inheritance

7. two sets: types T features F two relations: immediate subtypeT  T, azyclic appropriateness, without polyfeatures a partial functionF  T  T multiple inheritance of feature/value-pairs via subtype relation and unification no coindexation, since there are no variables in the description language finite description for infinite sets of objects (i.e. lists) Typical Static Type Signatures Default Inheritance

8. top > a, b, x, y < f:top. a > c < g:x. b > c < g:y, f:x. x > z. y > z. z < h:top. Inheritance in a Type Signature subtype multipleinheritance appropriateness Default Inheritance

9. Feature Logic • a feature logic is used to describe instances of the classes of objects defined in the type signature • it usually includes • variables  coindexation • conjunction  unification • disjunction nondeterminism • negation nondeterminism Descr FSs Descr 2FSs Default Inheritance

10. Macros • are abbreviations for feature logic expressions • can be named and create independent inheritance hierarchies • do not add anything new to the signature • can be used to refine and extend the classes of objects defined in the signature beyond the signature (creating new instances) Default Inheritance

11. Relational Constraints • define a general CLP language over feature logic expressions (definite clauses). • are an extension of macros with recursion and, perhaps control operators like cut or negation by failure. • might be used within type constraints. • can not be computed offline in general. Default Inheritance

12. Type Constraints • they add information to the types in a static type signature • their description language can be a feature logic incl. relational constraints • offline computability of the static type signature not guaranteed (append and other recursive operations) Default Inheritance

13. a < f:x, g:x. a constr f:Var & g:Var. Persistent Local Coindexation subtype type identity type constraint token identity Default Inheritance

14. a constr f:Var & @true(b & h:Var). type constraint true(top) ::= top. relational constraint Nonlocal Coindexation top x y z like a nonpersistent copying operation orthogonal? Default Inheritance

15. Inheritance with Type Constraints • type constraints • rely on the type hierarchy - they can not be named and therefore not build an additional hierarchy (like macros) • add information to the signature that is inherited top down with unification • can introduce a kind of ‚orthogonal‘ inheritance Default Inheritance

16. Default Unification Bouma, Carpenter, Lascarides, Copestake, Briscoe, ...

17. Credulous Default Unification nondefault default nondeterministic result Lascarides/Copestake 1999 Default Inheritance

18. Sceptical Default Unification Erjavec 1998 b? nondefault default deterministic result Default Inheritance

19. Nonassoziative Operation nd d nd d nd d nd d Lascarides/Copestake1999 Default Inheritance

20. Criteria for Default Unification Lascarides et al. 1996 • Nondefault information is marked. • DU can not fail. • DU behaves like MU if there is no conflicting information. • DU is deterministic. • DU is commutative und associative. • Defaults are ordered by specificity. Default Inheritance

21. YetAnotherDefaultUnification (Lascarides/Copestake 1999) Default Inheritance

22. YADU Inheritance (Lascarides/Copestake 1999) Default Inheritance

23. Nonmonotonic Type Signatures Subrelex: Modelling Subregularitiesin the Lexikon (SFB 282 Project, 2000-2002) QType: A Grammar Developement Environment with Nonmonotonic Inheritance in the Type Signature

24. Subrelex Goals • nonmonotonic, but declarative representations for regularities, subregularities und irregularities in a constraint-based framework • tractable implementation • formalize and implement empirical linguistic results of other SFB 282 projects (i.e. CB-LDG, Rumpf & Stiebels 1998) • reconstruct relevant NL phenomena treated by the nonmonotonicity community Default Inheritance

25. Subrelex Methods • use of nonmonotonic inheritance in the type signature • allow type constraints to enrich the expressive power of signatures • transform nonmonotonic signatures to monotonic ones offline • use monotonic signatures and monotonic unification at parsetime Default Inheritance

26. Transformation of Nonmonotonic to Monotonic Signatures generalization of verb and pst-t-verb nonmonotonic monotonic Default Inheritance