Minds and Computers : An Introduction to the Philosophy of Artificial Intelligence
Download 1.05 Mb. Pdf ko'rish
|
document (2)
|
particular sentence before. Formal systems are prime candidates for the mechanisms which facilitate the productivity of language. We’ve seen how formal systems can recursively generate an infinite number of states from finite resources in a rule governed fashion. We’ve also seen how we can conduct a bottom-up search to determine whether or not a par- ticular state is generated in a given system. Now we’re going to see how we might use formal systems to specify the generative grammar of a language. The generative grammar for a language is a particular kind of formal system. It is a symbol system similar to the systems [STR] and [BIN] from Chapter 7. Some of its symbols – those which will appear at terminal nodes of its generation tree – can be interpreted as lexical items (words) of the language. The rest of its symbols can be inter- preted as grammatical categories, such as ‘sentence’, ‘noun phrase’, ‘adjective’ and so on. The rules of a generative grammar are rewrite rules, like those of [STR] and [BIN]. In the system [STR], the rewrite rules were context 149 dependent – whether or not we could apply a rule to a symbol depended on surrounding symbols in the state. The system [BIN], however, had context-free rewrite rules. A generative grammar has solely context-free rewrite rules which are such that there is only one symbol on the input side of any rule. A formal system which meets these criteria is called a phrase structure grammar. Given a phrase structure grammar, we can generate all and only the grammatical strings according to that grammar by constructing phrase structure trees. A phrase structure tree is just like the generation trees we have seen so far with one exception. Where in the past nodes have con- tained states, the nodes of a phrase structure tree each represent only a single symbol, with its descendant nodes representing the symbol(s) with which it is rewritten. The grammatical strings given by a grammar are read o ff across the terminal nodes of a phrase structure tree. Let’s construct an example phrase structure grammar to make all this clearer. 14.3 PHRASE STRUCTURE TREES We’re going to specify a phrase structure grammar for a fragment of English. The states of our phrase structure grammar will be finite strings of those symbols which feature in the rules. The initial state will be the symbol ‘S’. The rules of the system are as follows. S → S Con S / NP IVP / NP TVP NP Con → and / or / but NP → Det N Det → the / a N → Adj N N → man / woman / kitten / dog Adj → Adj Adj Adj → young / happy / cute / silly IVP → IVP Adv IVP → runs / eats / plays / smiles Adv → quickly / nicely / happily TVP → loves / disgusts / wants PP → P NP P → to We can use this phrase structure grammar to generate grammatical strings, as represented by the terminal nodes of the phrase structure trees shown in Figures 14.1, 14.2 and 14.3. 150 |
