Lecture: Context-Free Grammars
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The document discusses context-free grammars (CFGs) and their application in modeling the syntax of languages, emphasizing their role in capturing constituency and addressing issues of agreement and subcategorization. It outlines key components of CFGs, including rules, terminals, and non-terminals, and presents examples relevant to English grammar. Practical activities are included to reinforce understanding and application of CFG concepts.
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Subcategorization
Sneeze: John sneezed
Find: Please find [a flight to NY]NP
Give: Give [me]NP[a cheaper fare]NP
Help: Can you help [me]NP[with a
flight]PP
Prefer: I prefer [to leave earlier]TO-VP
Told: I was told [United has a flight]S
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Lecture: Context-Free Grammars
- 1. Context-Free Grammars Slideshare: http://www.slideshare.net/marinasantini1/lecture-contextfree-grammars Mathematics for Language Technology http://stp.lingfil.uu.se/~matsd/uv/uv15/mfst/ Last Updated: 6 March 2015 Marina Santini [email protected] Department of Linguistics and Philology Uppsala University, Uppsala, Sweden Spring 2015 1
- 2. Acknowledgements Several slides borrowed from Jurafsky and Mar6n (2009). Prac6cal ac6vi6es by Mats Dahllöf and J&M (2009). 2
- 3. Reading Required Reading: Compendium (3): 8 Mats Dahllöf: Kontext-fria grammatiker (CFG) • http://stp.lingfil.uu.se/~matsd/uv/uv14/mfst/dok/oh7.pdf Further Reading: Chapter 12.1-‐12.3 and Chapter 16.1-‐16.2.1 in Jurafsky D. & Mar6n J. (2009) Speech and Language Processing: An introduc,on to natural language processing, computa,onal linguis,cs, and speech recogni,on. Online draM version: hOp://stp.lingfil.uu.se/~san6nim/ml/2014/ JurafskyMar6nSpeechAndLanguageProcessing2ed_draM%202007.pdf 3
- 4. Outline Context-Free Grammars (CFGs) A grammar for English: Examples Practical Activities 4
- 6. 6 The Chomsky Hierachy Regular (DFA) Context- free (PDA) Context- sensitive (LBA) Recursively- enumerable (TM) • A containment hierarchy of classes of formal languages
- 7. 7 Informal Comments A context-free grammar is a notation for describing languages. It is more powerful than finite automata or REs, but still cannot define all possible languages. Useful for nested structures.
- 8. 8 Constituency The basic idea here is that groups of words within utterances can be shown to act as single units. And in a given language, these units form coherent classes that can be shown to behave in similar ways With respect to their internal structure And with respect to other units in the language
- 9. 9 Constituency Internal structure We can describe an internal structure to the class (might have to use disjunctions of somewhat unlike sub-classes to do this). External behavior For example, we can say that noun phrases can come before verbs
- 10. 10 Constituency For example, it makes sense to the say that the following are all noun phrases in English... Why? One piece of evidence is that they can all precede verbs. This is external evidence
- 11. 11 Grammars and Constituency Of course, there’s nothing easy or obvious about how we come up with right set of constituents and the rules that govern how they combine... That’s why there are so many different theories of grammar and competing analyses of the same data.
- 12. 12 Context-Free Grammars Context-free grammars (CFGs) Also known as • Phrase structure grammars • Backus-Naur form Consist of Rules Terminals Non-terminals
- 13. 13 Context-Free Grammars Terminals We’ll take these to be words (for now) Non-Terminals The constituents in a language • Like noun phrase, verb phrase and sentence Rules Rules are equations that consist of a single non-terminal on the left and any number of terminals and non-terminals on the right.
- 14. 14 Some NP Rules Here are some rules for our noun phrases Together, these describe two kinds of NPs. One that consists of a determiner followed by a nominal And another that says that proper names are NPs. The third rule illustrates two things • An explicit disjunction – Two kinds of nominals • A recursive definition – Same non-terminal on the right and left-side of the rule
- 15. 15 L0 Grammar
- 16. 16 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
- 17. 17 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
- 18. 18 Definition - Repetition More formally, a CFG consists of
- 19. 19 Parsing Parsing is the process of taking a string and a grammar and returning a (multiple?) parse tree(s) for that string CFG is just more powerful language than FSA • Remember this means that there are languages we can capture with CFGs that we can’t capture with finite-state methods
- 20. A grammar for English: Examples 20
- 21. 21 An English Grammar Fragment Sentences Noun phrases Verb phrases
- 22. 22 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-NP Aux NP VP
- 23. 23 Noun Phrases Let’s consider the following rule in more detail... NP → Det Nominal Most of the complexity of English noun phrases is hidden in this rule. Consider the derivation for the following example All the morning flights from Denver to Tampa leaving before 10
- 24. 24 Noun Phrases
- 25. 25 NP Structure Clearly this NP is really about flights. That’s the central criticial noun in this NP. Let’s call that the head. We can dissect this kind of NP into the stuff that can come before the head, and the stuff that can come after it.
- 26. 26 Determiners Noun phrases can start with determiners... Determiners can be Simple lexical items: the, this, a, an, etc. • A car Or simple possessives • John’s car Or complex recursive versions of that • John’s sister’s husband’s son’s car
- 27. 27 Nominals Contains the head and any pre- and post- modifiers of the head. Pre- • Quantifiers, cardinals, ordinals... – Three cars • Adjectives and Aps – large cars • Ordering constraints – Three large cars – ?large three cars
- 28. 28 Postmodifiers Three kinds Prepositional phrases • From Seattle Non-finite clauses • Arriving before noon Relative clauses • That serve breakfast Same general (recursive) rule to handle these Nominal → Nominal PP Nominal → Nominal GerundVP Nominal → Nominal RelClause
- 29. 29 Agreement By agreement, we have in mind constraints that hold among various constituents that take part in a rule or set of rules For example, in English, determiners and the head nouns in NPs have to agree in their number. This flight Those flights *This flights *Those flight
- 30. 30 Problem Our earlier NP rules are clearly deficient since they don’t capture this constraint NP → Det Nominal • Accepts, and assigns correct structures, to grammatical examples (this flight) • But its also happy with incorrect examples (*these flight) Such a rule is said to overgenerate. We’ll come back to this in a bit
- 31. 31 Verb Phrases English VPs consist of a head verb along with 0 or more following constituents which we’ll call arguments.
- 32. 32 Subcategorization But, even though there are many valid VP rules in English, not all verbs are allowed to participate in all those VP rules. We can subcategorize the verbs in a language according to the sets of VP rules that they participate in. This is a modern take on the traditional notion of transitive/intransitive. Modern grammars may have 100s or such classes.
- 33. 33 Subcategorization Sneeze: John sneezed Find: Please find [a flight to NY]NP Give: Give [me]NP[a cheaper fare]NP Help: Can you help [me]NP[with a flight]PP Prefer: I prefer [to leave earlier]TO-VP Told: I was told [United has a flight]S …
- 34. 34 Subcategorization *John sneezed the book *I prefer United has a flight *Give with a flight As with agreement phenomena, we need a way to formally express the constraints
- 35. 35 Why? Right now, the various rules for VPs overgenerate. They permit the presence of strings containing verbs and arguments that don’t go together For example VP -> V NP therefore Sneezed the book is a VP since “sneeze” is a verb and “the book” is a valid NP
- 36. 36 Possible CFG Solution Possible solution for agreement. Can use the same trick for all the verb/ VP classes. SgS -> SgNP SgVP PlS -> PlNp PlVP SgNP -> SgDet SgNom PlNP -> PlDet PlNom PlVP -> PlV NP SgVP ->SgV Np …
- 37. 37 CFG Solution for Agreement It works and stays within the power of CFGs But its ugly And it does not scale all that well because of the interaction among the various constraints explodes the number of rules in our grammar
- 38. 38 The Point 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) Ex: LFG (Lexical Functional Grammar), HPSG (Head- Driven Phrase Structure Grammar), etc.
- 39. 39 Summary Context-free grammars can be used to model various facts about the syntax of a language. When paired with parsers, such grammars consititute a critical component in many applications. Constituency is a key phenomena easily captured with CFG rules. But agreement and subcategorization do pose significant problems
- 40. Prac6cal Ac6vity 1 The language L contains all strings over the alphabet {a,b} that begin with a and end with b, ie: Write context-free grammar rules that generate the language L. 40
- 41. Practical Activity 1: Possible Solution 41
- 42. Practical Activity 2 Look at the following CFG rules: Draw a parse tree for the string aba. 42
- 43. Practical Activity 2: Possible Solution 43
- 44. Practical Activity 3 Draw tree structures for the following phrases and sentences: 1. Dallas 2. I would like to fly on American airlines. 3. after five p.m. 4. Does American 487 have a first class section? 5. early flights 6. any delays in Denver 44
- 45. Practical Activity 3: Possible Solutions 45
- 46. The End 46