Context Free Grammars Syntactic Grammaticality Syntax What Is

Doesn’t depend on Context Free Grammars • Having heard the sentence before • The sentence being true – I saw a unicorn yesterday • The sentence being meaningful – Colorless green ideas sleep furiously – *Furiously sleep ideas green colorless – I sperred a couple of gurpy fipps. October 2008 Grammatically is a formal property that we can investigate and describe

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Syntax What is Syntax?

By syntax, we mean various aspects of how words are strung together to form components of sentences and how those • Study of structure of language components are strung together to form sentences • Specifically, goal is to relate surface form (e.g., interface to • New Concept: Constituency phonological component) to semantics (e.g., interface to • Groups of words may behave as a single unit or constituent semantic component) • E.g., noun phrases • Morphology, phonology, semantics farmed out (mainly), issue is • Evidence word order and structure – Whole group appears in similar syntactic environment • Representational device is tree structure – E.g., before a verb – Preposed/postposed constructions – Note: notions of meaning play no role in syntax (sort-of)

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Structure in Strings Types of Linguistic Activity

• Descriptive: provide account of syntax of a language; often good enough for NLP engineering •Some words: the a small nice big very boy girl sees likes work • Some good sentences: • Explanatory: provide principles-and-parameters – the boy likes a girl – the small girl likes the big girl style account of syntax of (preferably) several – a very small nice boy sees a very nice boy languages • Some bad sentences: • Prescriptive: “prescriptive linguistics” is an oxymoron – *the boy the girl – *small boy likes nice girl • Can we find subsequences of words (constituents) which in some way behave alike?

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1 Structure in Strings More Structure in Strings Proposal Proposal -- ctd

•Some words: the a small nice big very boy girl sees likes •Some words: the a small nice big very boy girl sees likes • Some good sentences: • Some good sentences: – (the boy) likes (a girl) – ((the) boy) likes ((a) girl) – (the small girl) likes (the big girl) – ((the) (small) girl) likes ((the) (big) girl) – (a very small nice boy) sees (a very nice boy) – ((a) ((very) small) (nice) boy) sees ((a) ((very) nice) girl) • Some bad sentences: • Some bad sentences: –*(the boy) (the girl) –*((the) boy) ((the) girl) –*(small boy) likes (the nice girl) –*((small) boy) likes ((the) (nice) girl)

• This is a reasonable proposal: seems to capture some generality 7 8

From Substrings to Trees Node Labels?

•(((the) boy) likes ((a) girl)) •(((the) boy) likes ((a) girl) )

• Group words by distribution of constituents they head (part-of-speech, POS): – Noun (N), verb (V), adjective (Adj), adverb (Adv), determiner (Det)

• Category of constituent: XP, where X is POS likes – NP, S, AdjP, AdvP, DetP boy girl the a

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Node Labels Types of Nodes

•(((the/Det) boy/N) likes/V ((a/Det) girl/N)) •(((the/Det) boy/N) likes/V ((a/Det) girl/N))

S S nonterminal symbols Phrase-structure NPlikes NP = constituents NPlikes NP tree

DetP boy DetP girl DetP boy DetP girl

the a the a 11 terminal symbols = words 12

2 Context-Free Grammars CFG: Example

• Defined in formal language theory (comp sci) • Many possible CFGs for English, here is an example (fragment): –S → NP VP • Terminals, nonterminals, start symbol, rules –VP → V NP • String-rewriting system –NP → DetP N | DetP AdjP N • Start with start symbol, rewrite using rules, done –AdjP→ Adj | Adv AdjP → when only terminals left –N boy | girl –V → sees | likes • NOT A LINGUISTIC THEORY, just a formal device –Adj→ big | small –Adv → very –DetP→ a | the

13 the very small boy likes a girl 14

Derivations in a CFG Derivations in a CFG

S NP VP

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Derivations in a CFG Derivations in a CFG

DetP N VP the boy VP

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3 Derivations in a CFG Derivations in a CFG

the boy likes NP the boy likes a girl

19 a girl20

Derivations in a CFG; Key Constituents (English) Order of Derivation Irrelevant NP likes DetP girl • Sentences • Noun phrases • Verb phrases S → NP VP S VP → V NP • Prepositional phrases NP → DetP N | DetP AdjP N AdjP → Adj | Adv AdjP NP VP N → boy | girl V → sees | likes Adj → big | small V NP Adv → very DetP → a | the likes DetP N

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Recursion Recursion

• We’ll have to deal with rules such as the following • Can make things interesting. Consider the rule: where the non-terminal on the left also appears • NP -> NP PP somewhere on the right (directly). flights from Denver NP -> NP PP [[The flight] [to Boston]] flights from Denver to Miami flights from Denver to Miami in February VP -> VP PP [[departed Miami] [at noon]] flights from Denver to Miami in February on a Friday flights from Denver to Miami in February on a Friday under $300 flights from Denver to Miami in February on a Friday under $300 with lunch

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4 Recursion The Point

• If you have a rule like [[flights] [from Denver]] – VP -> V NP [[[flights] [from Denver]] [to Miami]] [[[[flights] [from Denver]] [to Miami]] [in February]] – It only cares that the thing after the verb is an NP. It doesn’t [[[[[flights] [from Denver]] [to Miami]] [in February]] [on a Friday]] have to know about the internal affairs of that NP Etc.

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The Point

• VP -> V NP • I hate flights from Denver flights from Denver to Miami flights from Denver to Miami in February flights from Denver to Miami in February on a Friday flights from Denver to Miami in February on a Friday under $300 flights from Denver to Miami in February on a Friday under $300 with lunch