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

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Overview

• motivation

• monotonic inheritance

• nonmonotonic unification

• nonmonotonic inheritance

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Motivation

• for inheritance– compact representations (elimin.

redundancies)– modelling of relations and generalizations

• for default inheritance– systematic modelling of regularities,

subregularities, and irregularities

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Tweety

bird

eagle penguincan fly can not fly

bird

eagle penguin

can fly

can not fly

monotonic

nonmonotonic

no information at all

conflict resolution necessary

arbitraryalternants

Monotonic Inheritance in Constraint-based Frameworks

PATR, ALE, CUF, QType, ...

GPSG, HPSG, LFG, UCG, ...

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Levels for Inheritance Mechanisms

• static type signature

• macros

• relational constraints

• type constraints

• lexical rules

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Typical Static Type Signatures

• two sets: – types T– features F

• two relations: – immediate subtype

T 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)

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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.

top:ftop

x :gtop:f

a

c

f:x

zg:

h:top

y:gx:f

b

subtype

appropriateness

multipleinheritance

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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 2FSs

Descr FSs

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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)

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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.

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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)

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Persistent Local Coindexation

a < f:x, g:x.

a constr f:Var & g:Var.

x:gx:f

a

1:g

x1:f

a

token identity

type identity

subtype

type constraint

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Nonlocal Coindexation

a constr f:Var & @true(b & h:Var). type constraint

true(top) ::= top. relational constraint

a

f: 1

g:y

b

h: 1 x

g:z

x y z

top

like a nonpersistent copying operation

orthogonal?

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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 Unification

Bouma, Carpenter, Lascarides, Copestake, Briscoe, ...

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Credulous Default Unification

F: 1 b F: 1 aF:a F:a,

G: G:bG: 1 G: 1

ó• c

<

nondefault default nondeterministic result

Lascarides/Copestake 1999

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Sceptical Default Unification

s

s

F: F:F:aG: G:b G:H: H:c H:c

F: bF:a F:aG: G: G:H: H:c H

1 1

1 1

1

1:c

ò

ò

<

<

nondefault default deterministic result

Erjavec1998

b?

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Nonassoziative Operation

Lascarides/Copestake1999

a b ó

a c óc

c b ó

F:c F:a F: F: c

G:c G

1

:b G: G

1

1 1:

ó ó< <

F:c F:a F: F:c

G:c G:b G:cG

1

1:

ó ó< <

nd d

nd d

nd d

nd d

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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

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YetAnotherDefaultUnification

(Lascarides/Copestake 1999)

: : 1 : 1/ , , ,

: 2 : 1 : 1

: 2

verb

PAST PAST PASTverb verb

PASTP PASTP PASSP

PASSP

•

/ : ,:

regverbPAST ed regverb

PAST

•

/ : ,:

pst t verbPAST t pst t verb

PAST

•

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YADU Inheritance

(Lascarides/Copestake 1999)

: : 1 : 1/ , , ,

: 2 : 1 : 1

: 2

verb

PAST PAST PASTverb verb

PASTP PASTP PASSP

PASSP

•

: 1 : 1: , , , ,

/ : 1 : 1: 2

: ,: 2

regverbPAST PAST

PAST verb verbPASTP PASSP

PASTPPAST ed regverb

PASSP

•

: 1 : 1: , , , ,

/ : 1 : 1: 2

: , , : ,: 2

pst t verbPAST PAST

PAST verb verbPASTP PASSP

PASTPPAST ed regverb PAST t pst t verb

PASSP

•

: 1

: 1

: 1

verb

PAST

PASTP

PASSP

: 1

: 1

: 1

regverb

PAST ed

PASTP

PASSP

: 1

: 1

: 1

pst t verb

PAST t

PASTP

PASSP

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

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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

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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

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Transformation of Nonmonotonic to Monotonic Signatures

1:

1:

1:

PASSP

PASTP

edPAST

verb

tPASTverbtpst

:

1:

1:

1:

/

PASSP

PASTP

PAST

verbtpstverb

edPASTverb

:

tPASTverbtpst

:

nonmonotonic monotonic

generalization of verb and pst-t-verb