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LIN6932 Topics in Computational Linguistics: 

LIN6932 Topics in Computational Linguistics Lecture 6: Grammar and Parsing (I) February 15, 2007 Hana Filip

Outline for Grammar/Parsing: 

Outline for Grammar/Parsing Context-Free Grammars (CFG) and Constituency Some common CFG phenomena for English Sentence-level constructions NP, PP, VP Coordination Subcategorization Levels of complexity in grammars and automata: The Chomsky hierarchy Top-down and Bottom-up Parsing Earley Parsing Quick sketch of probabilistic parsing

Review: 

Review Parts of Speech Basic syntactic/morphological categories that words belong to Part of Speech tagging Assigning parts of speech to all the words in a sentence

Syntax: 

Syntax Syntax: from Greek syntaxis, “setting out together, arrangement’ Refers to the way words are arranged together, and their relationships Distinction: Prescriptive grammar: how people ought to talk Descriptive grammar: how they do talk Goal of syntax is to model the knowledge that people unconsciously have about the grammar of their native language

Syntax: 

Syntax Why should you care? Grammar checkers Question answering Information extraction Machine translation

4 key ideas of syntax: 

4 key ideas of syntax Constituency Grammatical relations Subcategorization Lexical dependencies Plus one part we won’t have time for: Movement/long-distance dependency

Context-Free Grammars: 

Context-Free Grammars Capture constituency and ordering Ordering: What are the rules that govern the ordering of words and bigger units in the language? Constituency: How words group into units and how the various kinds of units behave

Constituency: 

Constituency Noun phrases (NPs) Three parties from Brooklyn A high-class spot such as Mindy’s The Broadway coppers They Harry the Horse The reason he comes into the Hot Box How do we know these form a constituent? They can all appear before a verb: Three parties from Brooklyn arrive… A high-class spot such as Mindy’s attracts… The Broadway coppers love… They sit…

Constituency (II): 

Constituency (II) They can all appear before a verb: Three parties from Brooklyn arrive… A high-class spot such as Mindy’s attracts… The Broadway coppers love… They sit But individual words can’t always appear before verbs: *from arrive… *as attracts… *the is *spot is… Must be able to state generalizations like: Noun phrases occur before verbs

Constituency (III): 

Constituency (III) Preposing and postposing: On September 17th, I’d like to fly from Atlanta to Denver I’d like to fly on September 17th from Atlanta to Denver I’d like to fly from Atlanta to Denver on September 17th. But not: *On September, I’d like to fly 17th from Atlanta to Denver *On I’d like to fly September 17th from Atlanta to Denver

CFG Examples: 

CFG Examples S -> NP VP NP -> Det NOMINAL NOMINAL -> Noun VP -> Verb Det -> a Noun -> flight Verb -> left

CFGs: 

CFGs S -> NP VP This says that there are units called S, NP, and VP in this language That an S consists of an NP followed immediately by a VP Doesn’t say that that’s the only kind of S Nor does it say that this is the only place that NPs and VPs occur

Generativity: 

Generativity As with FSAs you can view these rules as either analysis or synthesis machines Generate strings in the language Reject strings not in the language Impose structures (trees) on strings in the language

Derivations: 

Derivations A derivation is a sequence of rules applied to a string that accounts for that string Covers all the elements in the string Covers only the elements in the string

Derivations as Trees: 

Derivations as Trees

CFGs more formally: 

CFGs more formally A context-free grammar has 4 parameters (“is a 4-tuple”) A set of non-terminal symbols (“variables”) N A set of terminal symbols  (disjoint from N) A set of productions P, each of the form A ->  Where A is a non-terminal and  is a string of symbols from the infinite set of strings (  N)* A designated start symbol S

Defining a CF language via derivation: 

Defining a CF language via derivation A string A derives a string B if A can be rewritten as B via some series of rule applications More formally: If A -> is a production of P  and  are any strings in the set (  N)* Then we say that A directly derives  Or A   Derivation is a generalization of direct derivation Let 1, 2, … m be strings in (  N)*, m>= 1, s.t. 1 2, 2 3… m-1 m We say that 1derives m or 1* m We then formally define language LG generated by grammar G As set of strings composed of terminal symbols derived from S LG = {w | w is in * and S * w}

Parsing: 

Parsing Parsing is the process of taking a string and a grammar and assigning correct trees to input strings Correct tree: a tree that covers all and only the elements of the input and has an S node at the top

Context?: 

Context? The notion of context in CFGs has nothing to do with the ordinary meaning of the word context in language. All it means is that the non-terminal on the left-hand side of a rule is out there all by itself (free of context) A -> B C Means that I can rewrite an A as a B followed by a C regardless of the context in which A is found

Key Constituents (English): 

Key Constituents (English) Sentences Noun phrases Verb phrases Prepositional phrases

Sentence-Types: 

Sentence-Types Declaratives: A plane left S -> NP VP Imperatives: Leave! S -> VP Yes-No Questions: Did the plane leave? S -> Aux NP VP WH Questions: When did the plane leave? S -> WH Aux NP VP

NPs: 

NPs NP -> Pronoun I came, you saw it, they conquered NP -> Proper-Noun Los Angeles is west of Texas NP -> Det Noun The president NP -> Nominal Nominal -> Noun Noun A morning flight to Denver

PPs: 

PPs PP -> Preposition NP From LA To Boston On Tuesday With lunch

Recursion: 

Recursion We’ll have to deal with rules such as the following where the non-terminal on the left also appears somewhere on the right (directly). NP -> NP PP [[The flight] [to Boston]] VP -> VP PP [[departed Miami] [at noon]]

Recursion: 

Recursion Of course, this is what makes syntax interesting 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 Etc.

Recursion: 

Recursion Of course, this is what makes syntax interesting [[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]] Etc.

Implications of recursion and context-freeness: 

Implications of recursion and context-freeness If you have a rule like VP -> V NP It only cares that the thing after the verb is an NP. It doesn’t have to know about the internal affairs of that NP

The Point: 

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

Bracketed Notation: 

Bracketed Notation [S [NP [PRO I] [VP [V prefer [NP [NP [Det a] [Nom [N morning] [N flight]]]]

Coordination Constructions: 

Coordination Constructions S -> S and S John went to NY and Mary followed him NP -> NP and NP VP -> VP and VP … In fact the right rule for English is X -> X and X

Other Syntactic stuff: 

Other Syntactic stuff Grammatical Relations Subject I booked a flight to New York The flight was booked by my agent. Object I booked a flight to New York Complement I said that I wanted to leave

Problems: 

Problems Agreement Subcategorization Movement (for want of a better term)

Agreement: 

Agreement This dog Those dogs This dog eats Those dogs eat *This dogs *Those dog *This dog eat *Those dogs eats

Possible CFG Solution: 

Possible CFG Solution S -> NP VP NP -> Det Nominal VP -> V NP … SgS -> SgNP SgVP PlS -> PlNp PlVP SgNP -> SgDet SgNom PlNP -> PlDet PlNom PlVP -> PlV NP SgVP ->SgV Np …

CFG Solution for Agreement: 

CFG Solution for Agreement It works and stays within the power of CFGs But its ugly (loss of generalization) And it doesn’t scale all that well

Subcategorization: 

Subcategorization Verbs have preferences for the number and syntactic kinds of constituents they co-occur with Sneeze: John sneezed intransitive verb Find: Please find [a flight to NY]NP transitive verb Give: Give [me]NP[a cheaper fare]NP ditransitive verb Help: Can you help [me]NP[with a flight]PP DO IO/Oblique Prefer: I prefer [to leave earlier]TO-VP VP complement Said: You said [United has a flight]S sentential complement …

Subcategorization: 

Subcategorization But not: *John sneezed the book *I prefer United has a flight *Give with a flight Subcategorization expresses the constraints that a lexical predicate places on the number and syntactic kinds of arguments it wants to take (occur with) So far we have only considerate one type of lexical predicate: verb Nouns, adjectives and prepositions also take arguments

So?: 

So? So the various CFG rules for VPs overgenerate. They permit the presence of strings containing verbs and arguments that don’t go together For example VP -> V NP predicts that Sneezed the book is a VP since “sneeze” is a verb and “the book” is a valid NP

Forward Pointer: 

Forward Pointer It turns out that verb subcategorization facts will provide a key element for semantic analysis (determining who did what to who in an event).

Possible CFG Solution: 

Possible CFG Solution VP -> V VP -> V NP VP -> V NP PP … VP -> IntransV VP -> TransV NP VP -> TransVwPP NP PP …

Movement: 

Movement Core example My travel agent booked the flight

Movement: 

Movement Core example [[My travel agent]NP [booked [the flight]NP]VP]S I.e. “book” is a straightforward transitive verb. It expects a single NP arg as the subject and a single NP arg within the VP

Movement - Long Distance Dependencies: 

Movement - Long Distance Dependencies What about? Which flight do you want me to have the travel agent book __? The direct object argument to “book” isn’t appearing in the right place. It is a long way from where it originally appeared And note that it is separated from its verb by 2 other verbs.

CFGs: a summary: 

CFGs: a summary CFGs appear to be just about what we need to account for a lot of basic syntactic structure in English But there are problems That can be dealt with adequately, although not elegantly, by staying within the CFG framework. There are simpler, more elegant, solutions that take us out of the CFG framework (beyond its formal power) Syntactic theories: HPSG, LFG, CCG, Minimalism, etc

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