Grammars and automata (1)

What grammars are for
- Constituency and structure
- Relations
- Compositionality, syntax-semantics mappings
- Constituent order
- Selectional restrictions
- Generalizations and abstraction

Grammars and automata (2)

Finite-state automata
- Appropriate for morphology, restricted sentence analysis and generation
- English noun morphotactics implemented as a finite-state recognizer
- English noun morphotactics implemented as a finite-state transducer

Grammars and automata (2)

Constituency (phrase structure, context free) grammars
- Unlike finite state automata, can make reference to phrasal categories
- Take the part-whole relationship as fundamental
- A sentence analysis consist of phrases, which may consist of phrases or words.
- A grammar consists of a set of context-free rewrite rules
```
S → NP VP PU
NP → JJ NN | JJ NNS | NP PP
VP → VBD NP
PP → IN PP
NN → news | effect
NNS → markets
JJ → economic | little | financial
VBD → had
IN → on
PU → .
```
- Variants
  - Probabilistic context-free grammars
  - Categories replaced with feature structures, for example, in Head-Driven Phrase Structure Grammar

Grammars and automata (3)

Dependency grammars
- Take the head-dependent relationship as fundamental.
- A sentence analysis consists of a set of labeled head-dependent relationships between words (there are no phrases).
- Some DG frameworks permit multiple levels (strata, dimensions), in which case an analysis is a multigraph
- A grammar takes the form of a lexicon with word-specific constraints about valency, order, and agreement
```
had:
   syn:
      out: sbj, obj
news:
   syn:
      in: (sbj), (obj)
      out: (nmod)
...
```

Working with grammars

Parsing
- Dynamic programming, chart parsing
- Constructive and eliminative parsing
- Deterministic parsing
- The fundamental problem: ambiguity (lexical, syntactic)
Generation
- Usually starts with semantic (and/or pragmatic) input
- Incremental and batch generation
- Lexically-driven and grammar-driven generation
- Fundamental problems
  - The mismatch between semantic/pragmatic and surface structure
  - Deciding what to mention
  - Referring expressions

Semantic/pragmatic representations

First-order predicate calculus
- A boy met a scary dog.
- `EE x,y. (boy(x) ^^ dog(y) ^^ scary(y) ^^ meet(x,y))`
Discourse Representation Structures
- A boy met a scary dog. He ran away from it.
Ontologies and thesauruses: explicit representations of lexical relationships and semantic/conceptual categories