default inheritance in constraint-based frameworks
DESCRIPTION
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. Overview. motivation monotonic inheritance nonmonotonic unification nonmonotonic inheritance. - PowerPoint PPT PresentationTRANSCRIPT
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
24.06.2010 Default Inheritance 2
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
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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