LDG-basic-slides

Logical Description Grammarfor sentence and discourse interpretation

Introduction to the grammar system

Noor van Leusen

Radboud University

2012

Noor van Leusen (Radboud University) Logical Description Grammar for sentence and discourse interpretation 2012 1 / 42

Content

Content

Logical Description Grammar as a method for the description ofsentence syntax and semantics.Muskens 1996, 2001. /cf. ‘Saarbruecken school’.

Underspecified representations. Syntactic and semantic properties oflinguistic trees. Parsing by deduction. CDRT and local contexts in thesemantic dimension.vLeusen&Muskens 2003

Discourse processing and the computation of coherence in LDG.Anaphora and Presupposition.vLeusen 2007 /cf. Gardent&Webber 1998, Egg&Redeker 2006.

Implicit discourse relations. Inferring discourse meaning.


LDG framework for Sentence Analysis Introducing Logical Description Grammar

Description Grammar for sentence analysis

LDG combines description theory (Vijay-Shanker c.s.) lexicalised TAG(Joshi, Webber c.s.) and compositional DRT (Kamp, Muskens).

With a view to ambiguity and implicitness of meaning it generates‘underspecified representations’.

It describes syntactic, semantic and pragmatic constraints in parallel,and is specifically tuned to model the interaction of these constraints.

The semantics integrates a context parameter , employed in thetreatment of anaphora, presupposition and accommodation.



Discourse contexts and discourse descriptions

Discourse contexts are represented by discourse descriptions.

Discourse descriptions are built up incrementally from sentence descriptions.

r

k ′

+

relation

k

Sentence representations are linked to their discourse context by explicit

connectives or implicit discourse relations.



Underspecified representations

There are two levels of linguistic analysis:

sentence description (underspecified representation)

?

set of verifying trees (fully specified linguistic repr.)

Sentence descriptions are statements in classical type logic.

They partially describe properties of linguistic trees, constrainingsyntactic, semantic and pragmatic features in parallel.

In case of ambiguity, more than one tree class verifies a description.


LDG framework for Sentence Analysis Linguistic Representations

Linguistic Tree Representations

Sentence and discourse representations are tree structures, decorated withlexemes, syntactic labels, semantic values, and local contexts.



Example tree, showing just syntax and lexemes:

S

S

DP

D

Max

VP

V

opened

DP

D

a

NP

N

can

In situ analysis of quantifiers (’a can’): lexeme in surface position,

quantification potential is scoped out (at top S).



Fine-grained compositional DRT

[..|...] is a DRS, to the left of the | sign is the universe, to the rightthe conditions.

uk ,wk , ok , . . . are discourse markers;

uk , ok store individuals.uk represent new referents (generated in the discourse);ok represent given referents; they are globally available and interpretedreferentially rather than existentially;wk store worlds.wr is the marker for the actual world.

⊕ merges DRSs, ⊑ denotes inclusion, |≍ entailment.

‘proper(K )’ defines K as a DRS in which no free discourse markersoccur.



Context Parameter

Each node in a tree structure carries a DRS which is its local context.(cf. Karttunen 1974)

The compositional semantics refers to this context parameter in theresolution of anaphora, presupposition satisfaction and projection, andaccommodation in general.



Local contexts and context-sensitivity

Local contexts ‘collect’ information on the semantic tier of thediscourse context.

They are constructed going top-down and from left to right through adiscourse or sentence tree.

The local context of the root node is B , the implicit background .

Anaphora and projective elements such as presupposition triggersintroduce conditions on local contexts.

Accommodation/projection results from satisfying these conditions inpartially underspecified local backgrounds.


LDG framework for Sentence Analysis Description Grammar as a reasoning system

Description Grammar, a constraint-based reasoning system

A description grammar G consists of lexical descriptions and somegeneral axioms.

It generates a sentence description ∆u per processed utterance u.

The grammar is itself a description, a set of statements in type logic.

Given the theory G + ∆u, a language user may reason about andobtain the possible verifying trees of the sentence descriptionM(∆u).


LDG framework for Sentence Analysis Description Grammar as a reasoning system

While G represents a language user’s general linguistic knowledge, asentence description ∆u represents his specific linguistic knowledge ofthe sentence.

Linguistic knowledge means knowledge in any of the relevantdomains, such as phonology, syntax, semantic and pragmatics.

Sentence interpretation is a reasoning process.

Since descriptions can be partial, G + ∆u can have more than a singleverifying tree, and the syntax or semantics of the sentence can remainunderspecified.

Each verifying tree comes with a possible reading of the sentence.


LDG framework for Sentence Analysis Lexicon and General Axioms

G consists of lexical descriptions and general axioms

General axioms constrain the general configurational and semanticproperties of linguistic representations.

∀k ¬[k ≺ k] No node precedes itself∀k [Γk 6|≍⊥ ∧ Γr ⊕ σr 6|≍⊥] Local contexts are consistent


LDG framework for Sentence Analysis Lexicon and General Axioms

Lexical descriptions

characterise the syntactic, semantic, and pragmatic properties oflexemes. They describe ‘little trees’ similar to elementary structures inTAG.

Lexical description of the noun can:

∀k [can(k)→ (cn(k) ∧ σ(k) = λv [ |wr : can v ]) ]

∀k [cn(k)→ ∃k2(ℓ(k) = n ∧ ℓ(k2) = np ∧ k2 � k∧

σ(k2) = σ(k) ∧ k+

← {k2} ∧ k−

← ∅)]

Graphic representation:NP

+k2

λv [ | wr : can v ]

Nk

can


LDG framework for Sentence Analysis Example description

Sentence description of ‘Max opened a can’

Sentence descriptions consist of the lexical descriptions of the lexemesoccurring in them, taking into account their surface order.

Graphic representation:

S−r

Γr = B

DP+10

o0

[o0 | wr : Max o0] ⊑ B

D0

Max

S+11

σ13(σ12)

DP−12 VP

−13

VP+14

λv [ | wr : v opened σ15]

V1

opened

DP−15

S+16

[u2 | ] ⊕ σ19(u2) ⊕ σ17

S−17

Γ17 = Γ16 ⊕ [u2 | ] ⊕ σ19(u2)

DP+18

u2

D2

a

NP−19

NP+20


N3

can



Syntactic properties

Each lexeme enters its own lexical description.

S, VP, DP, NP, D, V are syntactic labels.

Dashed lines stand for underspecified dominance relations, straight

lines for immediate dominance.

The general axioms enforce that the described structures are tree

structures.

+ and - represent anchoring relations. Each node must be bothpositively and negatively anchored to some lexical element. Thegeneral axioms enforce that + and - marked nodes are paired offone-to-one and the pairs identified.

Parsing comes down to reasoning about node identifications.



Semantic properties

σ associates semantic values with nodes.σα

k indicates a semantic value of type α.

Semantic values are in ‘finegrained compositional DRT’.

Γ associates Karttunen-style local contexts with nodes.

B , the local context of the root node, represents the implicit, general

background to the discourse.

Indefinite descriptions introduce fresh discourse referents.

Names are presuppositional elements. They introduce a condition onB which has the effect of resolving or accommodating them in themain DRS of the resulting discourse meaning.


LDG framework for Sentence Analysis Reasoning about the description

Parsing as deduction I

S−r

Γr = B

DP+10

o0

[o0 | wr : Max o0] ⊑ B

D0

Max

S+11

σ13(σ12)

DP−12 VP

−13

VP+14


V1

opened

DP−15

S+16

[u2 | ] ⊕ σ19(u2) ⊕ σ17

S−17

Γ17 = Γ16 ⊕ [u2 | ] ⊕ σ19(u2)

DP+18

u2

D2

a

NP−19

NP+20


N3

can

What tree structures fit this description?



Parsing as deduction II

On the assumption that there are currently no other lexemes than the onesprocessed, the language user may reason about verifying trees of thedescription.

Parsing The only way to pair of + and - marked nodes that is inaccordance with the grammar is

r = 16 ∧ 11 = 17 ∧ 10 = 12 ∧ 13 = 14 ∧ 15 = 18 ∧ 19 = 20



Parsing as deduction III

S−r

Γr = B

DP+10

o0

[o0 | wr : Max o0] ⊑ B

D0

Max

S+11

σ13(σ12)

DP−12 VP

−13

VP+14


V1

opened

DP−15

S+16

[u2 | ] ⊕ σ19(u2) ⊕ σ17

S−17

Γ17 = Γ16 ⊕ [u2 | ] ⊕ σ19(u2)

DP+18

u2

D2

a

NP−19

NP+20


N3

can

r = 16 ∧ 11 = 17 ∧ 10 = 12 ∧ 13 = 14 ∧ 15 = 18 ∧ 19 = 20



If the language user adds this inferred information to the discoursedescription, we get

S16

[u2 | wr : o0 opened u2, wr : can u2]B

[o0 | wr : Max o0] ⊑ B

S11

DP10

D0

Max

VP14

V1

opened

DP18

D2

a

NP20

N3

can

The linguistic tree we saw before is the single verifying tree of thisdescription; there is no ambiguity.



Inferring Discourse Meaning

The meaning of a discourse given a general background B isidentified with B ⊕ σr

what was ‘taken for granted’ updated with ‘what was said’, while atthe same time all constraints collected in the description are satisfied.

The discourse meaning of ‘Max opened a can’ is

B ⊕ [u2 | wr : o0 opened u2, wr : can u2],

where [wr | ] ⊑ B and [o0 | wr : Max o0] ⊑ B hold.



Sentence meaning

Sentences figure as minimal discourses.

Sentence meaning cannot be computed independently of computingdiscourse meaning, unless an out of the blue context is assumed.

Given a discourse description and a sentence whose root node is k,the sentence meaning ‘in context’ corresponds to Γk ⊕ σk , where allconstraints contributed by elements dominated by k must be satisfied.


Discourse Processing An example Discourse

Discourse processing: an incrementation step

‘Max opened a can. It contained the money.’

S−

rB

S+16

[u2 | wr : o0 opened u2, wr : can u2 ]

[o0 | wr : Max o0 ] ⊑ B

Max opened a can

DP+24

σ5

[σk | ] ⊑ Γ24

σ5 ∈ Tms24

D5it

S+25

σ26(σ27)

DP−

26VP

−

27

VP+28

λv[ | wr : v contained σ29]

V6contained

DP−

29

DP+30

σ7[σ7 | ] ⊑ Γ30

Γ30 |≍ [ | wr : money σ7]

D7the

NP9money

‘it’ and ‘the money’ are context dependent items.


Discourse Processing An example Discourse

Anaphora resolution and presupposition

is the topic of another slide-show.

In the example, the hearer will infer σ5 = u2,

and accommodate/project

[ u7′ | wr : money u7′] ⊑ B and [o0 | wr : Max o0] ⊑ B


Discourse Processing Further reasoning about the discourse description

Further reasoning about node identifications...

(1) S−

rB

S+16


[o0 | wr : Max o0] ⊑ B

Max opened a can

S+25

[ | wr : σ5 contained σ7 ]

[σ5 | ] ⊑ Γ24, [σ7 | ] ⊑ Γ30

Γ30 |≍ [ | wr : money σ7]

σ5 ∈ Tmostsalient24

It contained the money

Heuristics must guide the reasoning process: ‘safe’ conclusions drawnearlier must not be lost through the incrementation step.


Discourse Processing Selecting an appropriate discourse relation

.. and implicit discourse relations

(2) S−

rB

S+16


[o0 | wr : Max o0] ⊑ B

Max opened a can

S+25


[σ5 | ] ⊑ Γ24, [σ7 | ] ⊑ Γ30

Γ30 |≍ [ | wr : money σ7]



The grammar enforces coherence by requiring that every discoursedescription describes a discourse parse tree.

So the sentence structure must be attached to the discourse contextstructure.



There must be an implicit anchor

Additional structure can only be contributed by a lexical anchor (dueto lexicalisation).

Since no overt lexeme is available, the anchor must be implicit.

The only implicit elements in the grammar that can contribute thelink are discourse relations.

It must be one of the discourse relations in the lexicon.



Lexical description for discourse relation Elaboration

S+k1

σk2 ⊕ σk4 ⊕ [ | wr :εk4 ⊆ εk2 ]

topicsubord(k2, k4)

S−k2

Γk2 = Γk1

Sk3

Rel⋄k

elaboration

S−k4

Γk4 = Γk2 ⊕ σk2

Elaboration expresses that there is a part-whole relation linking the maineventualities introduced by the two arguments.

There is an additional constraint topicsubord(k2, k4) on the informationstructural tier.



Discourse topical constraints

This presupposes a discourse topical hierarchy can be constructed onthe basis of the information structure of input clauses andcharacteristic constraints contributed by individual discourse relations.Cf. Asher & Lascarides (2003), Buring, Roberts, van Kuppevelt.

topicsubord(k, k ′) means the discourse unit headed by node k ‘topicsubordinates’ the discourse unit headed by node k ′.

c .commontopic(k, k ′) conveys that the discourse units share a‘contingent common topic’.



Lexical description for discourse relation Narration

S+k1

σk2 ⊕ σk3 ⊕ [ | wr :εk2 < εk3 ]

c.commontopic(k2, k3)

S−k2

Γk2 = Γk1

Rel⋄k

narration

S−k3


Narration expresses a temporal sequence: the main eventuality of thecontextual argument temporally precedes the main eventuality of the rightargument.



Lexical description for discourse relation Background

S+k1

σk2 ⊕ σk4 ⊕ [ | wr :εk2 © εk4 ]

topicsubord(k1, k4)

S−k2

Γk2 = Γk1

Sk3

Rel⋄k

background

S−k4


Background expresses that the main eventualities introduced by the twoarguments are overlapping.

There is a subordinating topic relation (very unclear! Cf. A&L 2003).



There must be a discourse relation (underspecified as yet)

Sr

σ26(σ16)(σ25)

B

S16


B

[o0 | wr : Max o0 ] ⊑ B

Max opened a can

S

Rel26S25


Γ25

[σ5 | ], [σ7 | ] ⊑ Γ25

Γ25 |≍ [ | wr : money σ7]





The hearer selects a discourse relation from his lexicon, on the basis of his

linguistic knowledge of this discourse, world knowledge, and common sense

expectations, e.g. Background :

Sr

[u2 | wr : o0 opened u2, wr : can u2] ⊕ [ | wr : σ5 contained σ7] ⊕ [ | wr :εk2© εk4

]

B

S16


B

[o0 | wr : Max o0] ⊑ B

Max opened a can

S

Rel4background

topicsubord (k1, k4)

S25


B ⊕ [u2 | wr : o0 opened u2, wr : can u2]

[σ5 | ], [σ7 | ] ⊑ B ⊕ [u2 | wr : o0 opened u2, wr : can u2 ]

B ⊕ [u2 | wr : o0 opened u2, wr : can u2 ] |≍ [ | wr : money σ7]





Multidimensionality/interacting grammatical levels

The selection of a suitable discourse relation and the resolution ofcontext dependent elements in the new sentence is interdependent.

This is modelled direcly in that the choice of a suitable relation is theoutcome of constraint satisfaction in all grammatical levels (syntax,semantics, pragmatics) in parallel .



Preferences

A full-fledged discourse grammar must contain means to computepreferences over interpretations, some form of soft constraints, toobtain full disambiguation at any stage in an ongoing discourse. cf.

Asher and Lasc. 2003, vLeusen 2007

Given the choice of a specific discourse relation the exampledescription describes a single verifying tree structure.

Underspecification/ambiguity of interpretation is the case when ahearer derives two or more equally preferred discourse relations.


Discourse Processing Computing a Discourse Meaning

Computing a Discourse Meaning

The discourse meaning that can be inferred from the description is anunderspecified DRS:

B ⊕ [ u2 |wr : o0 opened u2, wr : can u2, wr : σ5 contained σ7]⊕ [ | wr :εk2 © εk4 ],

where, among others, the following conditions must be satisfied:

(3) a. [o0 | wr : Max o0] ⊑ B

b. [σ5 | ] ⊑ B ⊕ [u2 | wr : o0 opened u2, wr : can u2]

c. σ5 ∈ Tmostsalient24

d. B ⊕ [u2 | wr : o0 opened u2, wr : can u2] |≍ [ | wr : moneyσ7]

e. [σ7 | ] ⊑ B ⊕ [u2 | wr : o0 opened u2, wr : can u2]


Wrapping up Wrapping up

Some issues w.r.t. current LDG formalism

Processing units are sentences or clauses. What changes if weimplement incrementation per lexeme?

Decidability issue.

Lexical descriptions can contain feature structures, but how dofeatures interact with semantic composition and local contexts?

Do discourse tree structures represent update history, d-topicstructure, speech acts, or RST-like coherence relations?

How to put a preference system in place?

Can goals, beliefs, intentions, commitments, attitudes of thediscussion participants, dynamics of the utterance situation bemodelled?


Wrapping up Wrapping up

Pointer to further topics

Another slide-show explains in more detail

The integration of the context parameter (local contexts) in thecompositional semantics of the grammar.

The specifics of anaphora resolution and presupposition ’by constraintsatisfaction’.

and of accommodation and projection by abduction of underspecifiedcontent or global contextual information.


Wrapping up References

References

Asher & Lascarides 2003. Logics of Conversation.

Buering 2003. On D-Trees, Beans, and B-Accents.

Gardent & Webber 1998. Describing Discourse Semantics.

Gazdar 1979. Pragmatics. Implicature, presupposition and logical form.

Heim 1982. The Semantics of Definite and Indefinite Noun Phrases.

Karttunen 1974. Presupposition and Linguistic Context.

van Kuppevelt 1995 Discourse Structure, Topicality and Questioning

van Leusen 2007. Description Grammar for Discourse.

van Leusen & Muskens 2003.Construction by Description in Discourse Representation.

Lewis 1979. Score-keeping in a language game.

Muskens 1996. Combining Montague Semantics and Discourse Representation.

Muskens 2001. Talking about Trees and Truth-conditions.

van der Sandt 1992. Presupposition Projection as Anaphora Resolution.

Vijay-Shanker 1992. Using descriptions of trees in a tree-adjoining grammar.

Webber & Joshi 1998. Anchoring a lexicalised tree-adjoining grammar for discourse.


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