Semantic construction withgraph grammars

Grammars for Trees and Graphs

Leonie Harter & Katharina Stein

1

Koller (2015)

Content

• Motivation

• Recap IRTGs

• Definition of s-graphs

• S-graph algebra

• S-graph grammar

• Formal aspects

• Conclusion

2

Motivation

• Task: construction of semantic representations derived from naturallanguage strings

• The data-based turnaround in semantic parsing resulted in a large number of semantically annotated corpora

3

Motivation

• A large proportion of these sembanks use graphs like this for semantic representation:

• The graphs in this paper arealso AMR (abstractmeaning representation) graphs like this one

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Motivation

• Previous works about semantic parsing- are complicated- don't use grammars but statistics or have top-down perspective

→ differ strongly from traditional/linguistic approaches to semantic→ construction

• This grammar formalism- builds graphs bottom up with 3 combiningoperations

- is grammar based

→ doesn't want to give up previous linguistic research insights

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Recap IRTGs

Figure 1: example of an IRTG

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V

Definition of s-graphs

• Directed graph

• Labeled nodes

• Labeled edges

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Definition of s-graphs

• Each node can be marked with a set of source names s ∈ S

• S: fixed finite set containing the source names

• Source names: represent the possible semantic argument positions

• Each source name s can only be label for one node

• s-source of G: node marked with source s

• Nodes marked with at least one source: sources of G

• Every graph has a root source

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Example algebra for s-graphs

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Values Operations

• The rename operationG[a → b] every a-source of G becomes a b-source of GG[b] is a shortcut for G[root → b]

• The forget operationfa1,…,an(G) every node, that was an ai-source is noai-source anymore

• The merge operationG1 ‖ G2 evaluates to a Graph G‘, that consists ofall nodes and edges of G1 and G2. If G1 has an a-source u and G2 has an a-source v, then u and v are mapped to the same node in G‘

The rename operation

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The merge operation

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The forget operation

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Example: the boy wants to sleep

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Example: the boy wants to sleep

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Example: the boy wants to sleep

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Example: the boy wants to sleep

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Example: the boy wants to sleep

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Example: the boy wants to sleep

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Example: the boy wants to sleep

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Example: the boy wants to sleep

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Example: the boy wants to sleep

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S-graph grammar

IRTG grammar formalism

Consits of :

• RTG rules

• Homomorphisms

−hs: for strings

−hg: for graphs

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S-graph grammar for complements

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Example: the boy wants to sleep

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derivation tree t

comb_subj

boy

sleep

want1

Example: the boy wants to sleep

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term hs(t)

•

the boy •

wants to sleep

fsubj(∙)

‖

fvcomp(∙) ∙[subj]

‖

G1 ∙[vcomp]

G3

G2

term hg(t)

Example: the boy wants to sleep

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derivation tree tterm hs(t) term hg(t) s-graph [[hg(t)]]String [[hs(t)]]

The boy wants to sleep

S-graph grammar for adjuncts

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Structural Ambiguities

The boy sometimes sleeps and snores

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Structural Ambuiguities

The boy sometimes sleeps and snores

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comb_subj

boy

snore

sleep

sometimes

coord

comb_subj

boy

snore

sometimes

sleep

coord

1. 2.

<root>

Lexicon graphs

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Gsometimes

Gboy

Gsnore Gsleep

Gand

The boy sometimes sleeps and snores (1)

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fsubj(∙)

Gboy

f1,2(∙) ∙[subj]

‖

‖

∙[2]

Gcoord

‖

Gsnore∙[1]

‖

GsleepGsometimes

f1,2(∙)

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comb_subj

boy

snore

sleep

sometimes

coord

1.

33

Gsleep

Gsometimes Gsleep

1.

34

Gsleep

Gsometimes Gsleep

1.

G1

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comb_subj

boy

snore

sleep

sometimes

coord

1.

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1.

G1[1] ‖ Gsnore[2])

G1

G1[1]

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1.

G1[1] ‖ Gsnore[2])

G1

G1[1]

G1[1]

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1.

G1[1] ‖ Gsnore[2])

Gand

G1[1]

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1.

G1[1] ‖ Gsnore[2])

G1[1] Gand

G1[1]

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1.

G1[1] ‖ Gsnore[2])

Gsnore

Gsnore[2]

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1.

G1[1] ‖ Gsnore[2])

Gsnore

Gsnore[2]

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1.

G1[1] ‖ Gsnore[2])

G1[1] ‖ Gsnore[2]

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1.

G1[1] ‖ Gsnore[2])

G1[1] ‖ Gsnore[2]

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1.

G1[1] ‖ Gsnore[2])

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1.

G1[1] ‖ Gsnore[2])

G2

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comb_subj

boy

snore

sleep

sometimes

coord

1.

<root>

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Gboy[subj]

fsubj(G2 ‖ Gboy[subj])

1.

Gboy

<root>

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Gboy[subj]

fsubj(G2 ‖ Gboy[subj])

1.

Gboy

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Gboy[subj]

G2 ‖ Gboy[subj]

fsubj(G2 ‖ Gboy[subj])

G2

1.

G2

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Gboy[subj]

G2 ‖ Gboy[subj]

fsubj(G2 ‖ Gboy[subj])

G2

1.

G2

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fsubj(G2 ‖ Gboy[subj])

1.

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fsubj(G2 ‖ Gboy[subj])

1.

53

comb_subj

boy

snore

sleep

sometimes

coord

1.

The boy sometimes sleeps and snores (1)

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fsubj(∙)

Gboy

f1,2(∙) ∙[subj]

‖

‖

∙[2]

Gcoord

‖

Gsnore∙[1]

‖

GsleepGsometimes

f1,2(∙)

The boy sometimes sleeps and snores (2)

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fsubj(∙)

Gboy

∙[subj]

‖

‖

f1,2(∙)

Gcoord Gsnore∙[1]

Gsleep

Gsometimes

∙[2]‖

The boy sometimes sleeps and snores

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fsubj(∙)

Gboy

∙[subj]

‖

‖

f1,2(∙)

Gcoord Gsnore∙[1]

Gsleep

Gsometimes

∙[2]‖

fsubj(∙)

Gboy

f1,2(∙) ∙[subj]

‖

‖

∙[2]

Gcoord

‖

Gsnore∙[1]

‖

GsleepGsometimes

f1,2(∙)

1. 2.

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2.

comb_subj

boy

snore

sometimes

sleep

coord

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Gsleep[1]

2.

Gsleep

Gsleep[1] ‖ Gsnore[2])

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Gsleep[1]

2.

Gsleep

Gsleep[1] ‖ Gsnore[2])

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2.Gsleep[1] ‖ Gsnore[2])

Gand

Gsleep[1]

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2.Gsleep[1] ‖ Gsnore[2])

Gand

Gsleep[1]

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2.Gsleep[1] ‖ Gsnore[2])

Gsnore

Gsnore[2]

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2.Gsleep[1] ‖ Gsnore[2])

Gsnore

Gsnore[2]

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2.Gsleep[1] ‖ Gsnore[2])

Gsleep[1] ‖ Gsnore[2]

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2.Gsleep[1] ‖ Gsnore[2])

Gsleep[1] ‖ Gsnore[2]

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2.

Gsleep[1] ‖ Gsnore[2])

G1

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2.

comb_subj

boy

snore

sometimes

sleep

coord

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G1

G1Gsometimes

2.

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G1

G1Gsometimes

2.

G2

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2.

comb_subj

boy

snore

sometimes

sleep

coord

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Gboy

fsubj(G2 ‖ Gboy[subj])

2.

Gboy

<root>

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Gboy

fsubj(G2 ‖ Gboy[subj])

2.

Gboy

<root>

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fsubj(G2 ‖ Gboy[subj])

2.

G2

G2 ‖ Gboy[subj]

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fsubj(G2 ‖ Gboy[subj])

2.

G2

G2 ‖ Gboy[subj]

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fsubj(G2 ‖ Gboy[subj])

2.

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2.

comb_subj

boy

snore

sometimes

sleep

coord

The boy sometimes sleeps and snores (2)

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fsubj(∙)

Gboy

∙[subj]

‖

‖

f1,2(∙)

Gcoord Gsnore∙[1]

Gsleep

Gsometimes

∙[2]‖

Complement vs Adjunct

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Combining complement with head Combining adjunct with head

Rename root of the complement with theargument position

Forget argument names because slot forcomplement is filled

S-graph for adjunct has a root source wherethe modifiee should be added

Merge s-graph for the adjunct with thes-graph for the head being modified

Relative clauses

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Relative clauses

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Formal aspects

• S-graph grammars: map strings to graphs

• Algorithmically:

• Compute parse chart from the string

• Pick best derivation tree t

• Compute the value of t in the graph interpretation

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Conclusion

• Linguistically natural grammar formalism

• Possible to construct semantic graph representations with IRTGs

• Graph-based compositional semantic construction based on linguisticprinciples

• Source names of s-graphs are linguistically meaningful

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Thank you for your attention

Questions?

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