jurafsky&martin_3rdEd_17 (1).pdf

# N a set of non terminal symbols or variables s a set

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N a set of non-terminal symbols (or variables ) S a set of terminal symbols (disjoint from N ) R a set of rules or productions, each of the form A ! b , where A is a non-terminal, b is a string of symbols from the infinite set of strings ( S [ N ) S a designated start symbol and a member of N For the remainder of the book we adhere to the following conventions when dis- cussing the formal properties of context-free grammars (as opposed to explaining particular facts about English or other languages). Capital letters like A , B , and S Non-terminals S The start symbol Lower-case Greek letters like a , b , and g Strings drawn from ( S [ N ) Lower-case Roman letters like u , v , and w Strings of terminals A language is defined through the concept of derivation. One string derives an- other one if it can be rewritten as the second one by some series of rule applications. More formally, following Hopcroft and Ullman (1979) , if A ! b is a production of R and a and g are any strings in the set ( S [ N ) , then we say that a A g directly derives abg , or a A g ) abg . Directly derives Derivation is then a generalization of direct derivation: Let a 1 , a 2 , ..., a m be strings in ( S [ N ) , m 1, such that a 1 ) a 2 , a 2 ) a 3 ,..., a m - 1 ) a m We say that a 1 derives a m , or a 1 ) a m . Derives We can then formally define the language L G generated by a grammar G as the set of strings composed of terminal symbols that can be derived from the designated

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174 C HAPTER 11 F ORMAL G RAMMARS OF E NGLISH start symbol S . L G = { w | w is in S and S ) w } The problem of mapping from a string of words to its parse tree is called syn- tactic parsing ; we define algorithms for parsing in Chapter 12. Syntactic parsing 11.3 Some Grammar Rules for English In this section, we introduce a few more aspects of the phrase structure of English; for consistency we will continue to focus on sentences from the ATIS domain. Be- cause of space limitations, our discussion is necessarily limited to highlights. Read- ers are strongly advised to consult a good reference grammar of English, such as Huddleston and Pullum (2002) . 11.3.1 Sentence-Level Constructions In the small grammar L 0 , we provided only one sentence-level construction for declarative sentences like I prefer a morning flight . Among the large number of constructions for English sentences, four are particularly common and important: declaratives, imperatives, yes-no questions, and wh-questions. Sentences with declarative structure have a subject noun phrase followed by Declarative a verb phrase, like “I prefer a morning flight”. Sentences with this structure have a great number of different uses that we follow up on in Chapter 29. Here are a number of examples from the ATIS domain: I want a flight from Ontario to Chicago The flight should be eleven a.m. tomorrow The return flight should leave at around seven p.m.
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