1. Default Inheritance in Constraint-based Frameworks Christof Rumpf Heinrich-Heine-Universität Düsseldorf January 17, 2003 http://www.phil-fak.uni-duesseldorf.de/~rumpf/talks/DefaultInheritance.pdf

2. 17.01.03Default Inheritance2 Overview motivation monotonic inheritance nonmonotonic unification nonmonotonic inheritance

3. 17.01.03Default Inheritance3 Motivation for inheritance –compact representations (elimin. redundancies) –modelling of relations and generalizations for default inheritance –systematic modelling of regularities, subregularities, and irregularities

4. 17.01.03Default Inheritance4 Tweety bird eaglepenguin can flycan not fly bird eaglepenguin can fly can not fly monotonic nonmonotonic no information at all conflict resolution necessary arbitrary alternants

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

6. 17.01.03Default Inheritance6 Levels for Inheritance Mechanisms static type signature type constraints macros relational constrains lexical rules

7. 17.01.03Default Inheritance7 Typical Static Type Signatures two sets: –types T –features F two relations: –immediate subtype T  T, azyclic –appropriateness, without polyfeatures a partial function F  T  T multiple inheritance of feature/value-pairs via subtype relation and unification type clashes possible no coindexation, since there are no variables in the description language

8. 17.01.03Default Inheritance8 Inheritance in a Type Signature top > a, b, x, y < f:top. a > c < g:x. b > c < g:y, f:x. x > z. y > z. z < h:top. subtype appropriateness multiple inheritance weak relation to DATR: N1:<> == N2 modulo othogonal inheritance

9. 17.01.03Default Inheritance9 Type Constraints they add information to the types in a static type signature their description language can be a feature logic with –variables  coindexation –disjunction  nondeterminism –negation  nondeterminism –recursion  disables offline computability Descr   (FSs)

10. 17.01.03Default Inheritance10 Persistent Local Coindexation a < f:x, g:x. a constr f:Var & g:Var. token identity type identity subtype type constraint weak relation to DATR: N1:P1 == P2 (only monotonic)

11. 17.01.03Default Inheritance11 Nonlocal Coindexation a constr f:Var & @true(b & h:Var). type constraint true(top) ::= top. relational constraint x y z top like a nonpersistent copying operation weak relation to DATR: N1:P1 == N2:P2 (only monotonic) orthogonal?

12. 17.01.03Default Inheritance12 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 –can introduce a kind of ‚orthogonal‘ inheritance

13. 17.01.03Default Inheritance13 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)

14. 17.01.03Default Inheritance14 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.

15. 17.01.03Default Inheritance15 Lexical Rules build binary relations in the lexicon –Input –Output help to avoid redundancies and express systematic relationships between lexical entries desire nonmonotonic unification –copying of compatible input information into the output (no commutativity required) feature logic expressions that match/define lexical entries

16. 17.01.03Default Inheritance16 Inheritance with Lexical Rules Lexical rules establish two kinds of inheritance –Immediate inheritance between lexical entries that match the input/output specifications of a specific lexical rule (normally nonmonotonic inheritance). –Lexial rules define another implicit inheritance hierarchy: the output of one rule might unify with the input of another rule (normally monotonic inheritance). Lexical rules can be replaced by relational constraints (Krieger 94, Bouma 96).

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

18. 17.01.03Default Inheritance18 Notation there is no homogeneous notation –top, bottom –subsumption –unification –default-Unification nonkommutative

19. 17.01.03Default Inheritance19 Credulous Default Unification nondefault default nondeterministic result Lascarides/Copestake 1999

20. 17.01.03Default Inheritance20 Sceptical Default Unification nondefault default deterministic result Erjavec 1998 b?

21. 17.01.03Default Inheritance21 Nonassoziative Operation Lascarides/Copestake 1999 nd d

22. 17.01.03Default Inheritance22 Criteria for Default Unification 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. Lascarides et al. 1996

23. 17.01.03Default Inheritance23 Y et A nother D efault U nification (Lascarides/Copestake 1999)

24. 17.01.03Default Inheritance24 YADU Inheritance (Lascarides/Copestake 1999)

25. Nonmonotonic Type Signatures Subrelex: Modelling Subregularities in the Lexikon (SFB 282 Project) QType: A Grammar Developement Environment with Nonmonotonic Inheritance in the Type Signature

26. 17.01.03Default Inheritance26 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 reconstruct relevant NL phenomena treated by the nonmonotonicity community

27. 17.01.03Default Inheritance27 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

28. 17.01.03Default Inheritance28 Subrelex Inheritance regular variant 1 variant 2 variant n subregular 1 subregular 2..... subregular i irregular 1 irregular 2 transformation in monotonic inheritance network through insertion of additional types some ad hoc type signature leaves monotoni c inheritanc e nonmonotoni c inheritance

29. 17.01.03Default Inheritance29 Transformation of Nonmonotonic to Monotonic Signatures nonmonotonicmonotonic generalization of verb and pst-t-verb

30. 17.01.03Default Inheritance30 Consequences Nonmonotonicity in the type signature only leads to different considerations concerning grammar development: –Almost all information of relevance would be placed in the type signature. –Other levels of representation (syntax rules, lexical entries, lexical rules) loose some of their importance.