Context Free Grammars
Syntax = rules describing how words can connect to each other Goal of syntax is to model the knowledge people unconsciously have about the grammar of their native language
Syntax Why should you care? Grammar checkers Question answering Information extraction Machine translation
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 Constituency How words group into units and how the various kinds of units behave
Constituency Ordering: What are the rules that govern the ordering of words and bigger units in the language?
Constituency E. g. , Noun phrases (NPs) • • • Three parties from Brooklyn A high-class SUV 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: � But individual words can’t always appear before verbs: � Three parties from Brooklyn arrive… A high-class SUV such as Mindy’s attracts… The Broadway coppers love… They sit *from arrive… *as attracts… *the is *spot is… Must be able to state generalizations like: Noun phrases occur before verbs
Preposing and postposing: � On September 17 th, I’d like to fly from Atlanta to Denver � I’d like to fly on September 17 th from Atlanta to Denver � I’d like to fly from Atlanta to Denver on September 17 th. But not: � *On September, I’d like to fly 17 th from Atlanta to Denver
Context-Free Grammars Context-free grammars (CFGs) � Also known as Phrase structure grammars Backus-Naur form Consist of � Rules � Terminals � Non-terminals
Context-Free Grammars Terminals � We’ll take these to be words Non-Terminals � The constituents in a language Like noun phrase, verb phrase and sentence Rules � Rules are equations that consist of a single nonterminal on the left and any number of terminals and non-terminals on the right.
CFG Example S -> NP VP NP -> Det NOMINAL -> Noun VP -> Verb Det -> a Noun -> flight Verb -> left these rules are defined independent of the context where they might occur -> CFG
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 Generativity � As • • • with FSAs we 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
Parsing is the process of taking a string and a grammar and returning a (many? ) parse tree(s) for that string
Context? The non-terminal on the left-hand side of a rule is out there all by itself �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) • • Sentences Noun phrases Verb phrases Prepositional phrases
Some NP Rules Here are some rules for the 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
CFGs more formally A context-free grammar has 4 parameters (“is a 4 -tuple”) 1) A set of non-terminal symbols (“variables”) N 2) A set of terminal symbols (disjoint from N) 3) A set of productions P, each of the form 4) 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
Derivations A derivation is a sequence of rules expansion Common to represent derivation by a parse tree
Bracketed Notation [S [NP [PRO I]] [VP [V prefer] [NP [Det a] [Nom [N morning] [N flight] ] ]
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 10/2/2020 21
NPs NP -> Pronoun � NP -> Proper-Noun � � I came, you saw it, they conquered Los Angeles is west of Texas John Hennessy is the president of Stanford NP -> Det Noun � The president NP -> Nominal -> Noun Nominal l Noun � A morning flight to Denver
PPs PP -> Preposition NP � From LA � To the store � On Tuesday morning � With lunch
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 Example � flights from Denver � 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
Determiners Noun phrases can start with determiners. . . Determiners can be � Simple A � Or lexical items: the, this, a, an, etc. car simple possessives John’s � Or complex recursive versions of that John’s 10/2/2020 car sister’s husband’s son’s car 26
Pre-determiners Word classes that appear in the NP before the determiner are called predeterminers Eg: all the flights Word classes that appear in the NP between the determiner and the head noun are called post determiners ( they include cardinal numbers, ordinal numbers and quantifiers, adjective phrase) Eg: one stop The first one The nonstop flight the least expensive fare
Nominals Contains the head any pre- and postmodifiers of the head. � Pre Quantifiers, cardinals, ordinals. . . Three cars Adjectives large cars Ordering 10/2/2020 constraints Three large cars ? large three cars 28
NP->(det) (card) (ord) (quant) (AP) Nominal After the head noun there can be post modifiers
Postmodifiers Three kinds � Prepositional phrases � Non-finite clauses � Any flights arriving before noon Relative clauses All flights from Seattle a flight that serves breakfast Same general (recursive) rule to handle these � � Nominal PP Nominal Gerund. VP Nominal Rel. Clause Gerund. VP-> Gerund. V NP Gerund. V PP Gerund. V (being, preferring, arriving…) Gerund. V NP PP � � 10/2/2020 Rel. Clause -> (who, that) VP 30
Coordination Constructions Noun phrases and other units can be conjoined with conjunctions like and, or and but S -> S and S � John went to NY and Mary followed him NP -> NP and NP ( the flights and the costs) VP -> VP and VP (leaving Denver and arriving in Sanfrancisco) …
Practice: Another Recursion Example 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 Example flights from Denver 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
Potential Problems in CFG Agreement Subcategorization Movement
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
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
NP Structure Clearly this NP is really about flights. That’s the central criticial noun in this NP. It is 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.
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
Nominals Contains the head any pre- and postmodifiers of the head. Pre- Quantifiers, cardinals, ordinals. . . Three cars Adjectives large cars Ordering constraints Three large cars ? large three cars
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 PP Nominal Gerund. VP Nominal Rel. Clause
Agreement This dog *This dogs Those dogs *Those dog This dog eats *This dog eat Those dogs eat *Those dogs eats
Verb Phrases English VPs consist of a head verb along with 0 or more following constituents which we’ll call arguments.
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 … *John sneezed the book *I prefer United has a flight *Give with a flight Subcat expresses the constraints that a predicate places on the number and type of the argument it wants to take
Overgeneration 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 In lecture: go over the grammar for assignment 3
Possible CFG Solution Possible solution for agreement. Sg. S -> Sg. NP Sg. VP Can use the same trick for all the verb/VP classes. Pl. S -> Pl. Np Pl. VP Sg. NP -> Sg. Det Sg. Nom Pl. NP -> Pl. Det Pl. Nom Pl. VP -> Pl. V NP Sg. VP ->Sg. V Np …
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 within the VP as an argument, and a single NP arg as the subject.
Movement 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 in fact a long way from where its supposed to appear. And note that it’s separated from its verb by 2 other verbs.
Formally… To put all previous discussions/examples in a formal definition for CFG: A context free grammar has four parameters: 1. 2. 3. 4. A set of non-terminal symbols N A set of terminal symbols T A set of production rules P, each of the form A a, where A is a non-terminal, and a is a string of symbols from the infinite set of strings (T N)* A designated start symbol S
Grammar equivalence and normal form Strong equivalence: two grammars are strongly equivalent if: they generate/accept the same set of strings they assign the same phrase structure to each sentence two grammars are weakly equivalent if: they generate/accept the same set of strings they do not assign the same phrase structure to each sentence Normal form Restrict the form of productions Chomsky Normal Form (CNF) Right hand side of the productions has either one or two terminals or non-terminals e. g. A -> BC A -> a Any grammar can be translated into a weakly equivalent CNF A -> B C D <=> A-> B X X -> C D
Treebanks are corpora in which each sentence has been paired with a parse tree (presumably the right one). These are generally created By first parsing the collection with an automatic parser And then having human annotators correct each parse as necessary. This generally requires detailed annotation guidelines that provide a POS tagset, a grammar and instructions for how to deal with particular grammatical constructions.
Penn Treebank Penn Tree. Bank is a widely used treebank. §Most well known is the Wall Street Journal section of the Penn Tree. Bank. § 1 M words from the 1987 -1989 Wall Street Journal.
Treebank Grammars Treebanks implicitly define a grammar for the language covered in the treebank. Simply take the local rules that make up the subtrees in all the trees in the collection and you have a grammar. Not complete, but if you have decent size corpus, you’ll have a grammar with decent coverage.
Treebank Grammars Such grammars tend to be very flat due to the fact that they tend to avoid recursion. For example, the Penn Treebank has 4500 different rules for VPs. Among them. . .
Heads in Trees Finding heads in treebank trees is a task that arises frequently in many applications. Particularly important in statistical parsing We can visualize this task by annotating the nodes of a parse tree with the heads of each corresponding node.
Lexically Decorated Tree
Head Finding The standard way to do head finding is to use a simple set of tree traversal rules specific to each non-terminal in the grammar.
Treebank Uses Treebanks (and headfinding) are particularly critical to the development of statistical parsers Chapter 14 Also valuable to Corpus Linguistics Investigating the empirical details of various constructions in a given language
Dependency Grammars In CFG-style phrase-structure grammars the main focus is on constituents. But it turns out you can get a lot done with just binary relations among the words in an utterance. In a dependency grammar framework, a parse is a tree where the nodes stand for the words in an utterance The links between the words represent dependency relations between pairs of words. Relations may be typed (labeled), or not.
Dependency Parse They hid the letter on the shelf
Dependency Parsing The dependency approach has a number of advantages over full phrase-structure parsing. Deals well with free word order languages where the constituent structure is quite fluid Parsing is much faster than CFG-bases parsers Dependency structure often captures the syntactic relations needed by later applications CFG-based approaches often extract this same information from trees anyway.
Dependency Parsing There are two modern approaches to dependency parsing Optimization-based approaches that search a space of trees for the tree that best matches some criteria Shift-reduce approaches that greedily take actions based on the current word and state.
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 Treebanks pair sentences in corpus with their corresponding trees.