An Extended GHKM Algorithm forInducing λ-SCFG

Peng Lipengli09@gmail.comTsinghua University

Semantic Parsing

• Mapping natural language (NL) sentence to its computable meaning representation (MR)

NL: Every boy likes a star

MR:

variablepredicate

Motivation

• Common way: inducing probabilistic grammarPCFG: Probabilistic Context Free Grammar

Motivation

• Common way: inducing probabilistic grammarCCG: Combinatory Categorial Grammar

Motivation

• Common way: inducing probabilistic grammarSCFG: Synchronous Context Free Grammar

Motivation

• State of the art: SCFG + λ-calculus (λ-SCFG)• Major challenge: grammar induction– It is much harder to find the correspondence between

NL sentence and MR than between NL sentences• SCFG rule extraction is well-studied in MT• GHKM is the most widely used algorithm• We want to adapt GHKM to semantic parsing• Experimental results show that we get the state-

of-the-art performance

Background

• State of the art: SCFG + λ-calculus (λ-SCFG)

• λ-calculus– λ-expression: – β-conversion: bound variable substitution

– α-conversion: bound variable renaming

λ-SCFG Rule Extraction

• Outline1. Building training examples

1. Transforming logical forms to trees2. Aligning trees with sentences

2. Identifying frontier nodes3. Extracting minimal rules4. Extracting composed rules

Building Training Examples

NL: Every boy likes a star

MR:

Building Training Examples

Building Training Examples

Building Training Examples

boy human pop like

Building Training Examplesboy human pop like

Every boy likes a star

Identifying Frontier Nodes

Identifying Frontier Nodes

Identifying Frontier Nodes

Identifying Minimal Frontier Tree

Identifying Minimal Frontier Tree

Identifying Minimal Frontier Tree

Identifying Minimal Frontier Tree

Minimal Rule Extraction

X

X

Minimal Rule Extraction

X

X

Minimal Rule Extraction

X

X

Composed Rule Extraction

λ-SCFG Rule Extraction

• Outline1. Building training examples

1. Transforming logical forms to trees2. Aligning trees with sentences

2. Identifying frontier nodes3. Extracting minimal rules4. Extracting composed rules

Modeling

• Log-linear model + MERT training

• Target

Experiments

• Dataset: GEOQUERY– 880 English questions with corresponding Prolog

logical form–

• Metric

Experiments

SCFG

PCFG

CCG

Experiments

• F-measure for different languages

* en - English, ge - German, el - Greek, th - Thai

Experiments

Experiments