Syntax, semantics, and grammars (1)

What is syntax for?

Constituency and structure

He took a rake out of the closet.
He took [ a rake ] [ out of the closet ].
He took [ a rake [ out of the closet ] ].
He took a rake out of the closet.

What goes with what?
What modifies or "complements" what?
How do languages indicate this?
- Order: things that go together are close together.
- Morphology: things that go together are marked as such.
  Guugu Yimithirr
```
	Yarraga-aga-mu-n  gudaa    gunda-y   biiba-ngun
	boy-GEN-mu-ERG    dog-ABS  hit-PAST  father-ERG
	'The boy's father hit the dog.'
	
```

Relations

The pile of leaves that Toad had raked for Frog blew everywhere.
The pile of leaves that Toad had raked [0] for Frog blew everywhere.
He will never guess who raked his leaves.
She sent herself an email.

How are words tied together through relations?
- Coreference
- Grammatical relations: SUBJECT, DIRECT OBJECT, INDIRECT OBJECT
How do languages indicate this?
- Word order
- Morphology on the word on one end or the other or both
- Syntactic and lexical conventions

Compositionality, syntax-semantics mappings

messy leaves
Toad ran through the grass so that Frog would not see him.

How do the constituents of a phrase or sentence map onto the constituents of the associated meaning?
How are novel combinations of words and phrases interpreted? (Here is an extreme example involving "colorless, green ideas".)

Constituent order

Rana llegó a la casa de Sapo.
'Frog got to Toad's house.'

Llegó Rana a la casa de Sapo.

Llegó a la casa de Sapo Rana.

A la casa de Sapo llegó Rana.

What constraints are there are on the order in which constituents can appear?

Selectional restrictions

messy room, messy hair, messy leaves, messy thoughts, messy star
devote your time, devote yourself, devote your blood, devote your name

What constraints are there on the kinds of modifiers or complements that can be associated with particular words?

Grammaticality and obligatoriness

He took a rake out of the closet.

What does a particular language require in order for a sentence to be "grammatical"?
Why does this matter?

Generalizations and abstraction

I left the keys in the car.
What did I leave in the car?
Where did I leave the keys?
The keys I left in the car.
the keys (that) I left in the car

Al broke the iPod.
The iPod broke.
The iPod was broken by Al

How can abstraction reveal how surface sentences are related to one another?

Constituency grammars

Sentences consist of constituents (phrases), which consist of constituents or words

Context-free grammars (pushdown automata, recursive transition networks)

A grammar for a fragment of English

S    → NP VP 	             VP   → TV NP      
NP   → (Det) AdjP* N PP*    VP   → LV AdjP      
NP   → NP CoordConj NP      VP   → LV PP      	      
NP   → Pro                  VP   → CV that S  
VP   → Aux VP               AdjP → Adv* Adj   
VP   → IV                   PP   → P NP       
	 		      
N → tomatoes                TV → can
Pro → this                  LV → seemed
CoordConj → and             Adj → pretty
Aux → can                   Adv → pretty
IV → died                   P → under
CV → said

Problems with simple context-free grammars

Agreement

(in Swahili)

   Wavulana watatu wadogo walianguka.
   boys     three  small  fell
   'Three small boys fell.'

   Viti   vitatu vidogo vilianguka.
   chairs three  small  fell
   'Three small chairs fell.'

   Nyumba   tatu  ndogo zilianguka.
   house(s) three small fell
   'Three small houses fell.'

   Meno  matatu madogo yalianguka.
   teeth three  small  fell
   'Three small teeth fell.'

In a CFG for Swahili, we seem to need separate NP rules and separate S rules for each class of nouns. For English Ss (which are much simpler), we would have
S → NP_sing VP_sing
S → NP_plur VP_plur

Long-distance dependencies
- What did you say you thought Bill wanted to wear?
- The ordinary rules fail to apply here because wear, a transitive verb, does not have an immediately following direct object.
- We seem to need separate rules for each way in which a clause like Bill wanted to wear (something) can be embedded in a question which asks about the "something", rules like the following
  ("TVP-NP" means "transitive VP without its normal NP", "S-NP" means "sentence without an expected NP", and "SCV" means "verb taking a sentence complement" like say)
  S → NP VP
  S → WH+N Aux NP TVP-NP
  S → WH+N Aux NP SCV S-NP
- There would need to be many of these, they would not permit embedding at an arbitrary level, and they would not show how questions are related to the corresponding statements.

Context-free grammars with complex categories (feature structures) [HPSG, LFG]

Handling agreement
[cat=S] → [cat=NP, num=?n] [cat=VP, num=?n]
[cat=NP, num=?n] → [cat=N, num=?n]
[cat=VP, num=?n] → [cat=V, arg1=0, num=?n]

Willard: [cat=N, num=sing, lex=willard]
people: [cat=N, num=plur, lex=person]
dances: [cat=V, arg1=0, num=sing, lex=dance]
Handling long-distance dependencies
- A set of rules using the slash feature
  [cat=S] → [+WH, cat=?c] [cat=Aux, num=?n] [cat=S, slash=?c, num=?n]
  [cat=S, slash=?s, num=?n] → [cat=NP, num=?n] [cat=VP, slash=?s]
  [cat=VP, slash=?s] → [cat=V, arg1=[cat=NP]] [cat=NP, slash=?s]
  [cat=?c, slash=?c] → 0
- Representation of the who does Max love? (dtrs is a feature that takes the set of daughter constituents as its value)
  [cat=S, dtrs={[+WH, cat=NP, form='who'], [cat=Aux, num=sing, form='does'], [cat=S, slash=NP, num=sing, dtrs={[cat=NP, form='Max', num=sing], [cat=VP, slash=NP, dtrs={[cat=V, arg1=[cat=NP], form='love'], [cat=NP, slash=NP, form='0']}]}]}]
How syntax and semantics are related (in an old version of HPSG)
Order may be represented separately from constituency relations (for example, in HPSG).
In HPSG, words and phrases are typed feature structures organized in a type hierarchy.

Probabilistic context-free grammars

Simple CFGs, with or without categories replaced by feature structures, can't help us prefer one analysis of a sentence over another
Probabilistic (or stochastic) CFGs have a probability associated with each rule: the probability of the right-hand side, given the left-hand side of the rule. Thus the sum of the probabilities for the rules with a given LHS must be 1.
The probability of a given analysis of a sentence is the product of the probabilities of all of the rules used in the analysis (assuming statistical independence of all of the rules).
For disambiguation, select the parse for a sentence that has the highest probability.

Dependency grammars

The structure of a sentence can be represented as a set of relations (dependencies) between words; there are no phrasal nodes.
Each dependency is a directed arc between a head and a dependent word.
Each sentence has one root word which has no head. Each word in a sentence can have at most one head.
Examples and advantages of dependency over constituency grammars (Nivre)
A dependency grammar
- A set of arc labels
- Constraints on arcs into and out of particular words or word classes
  - A verb can be the root of a sentence or the head of a relative clause
    verb: [in: {} | {relcl?}]
  - A transitive verb must have a subject and a direct object
    tv: [out: {subj!, obj!}]
- (Sometimes) constraints on the structure of an analysis, for example, the projectivity constraint: every word occurring between a word dand its head his either dominated by d or by h.

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