Add the following context-free grammar rules to the dog's world grammar of Section 15.2.1. Map the resulting grammar into transition networks. sentence ↔ noun_phrase verb_phrase prepositional_phrase prepositional_phrase ↔ preposition noun_phrase preposition ↔ with preposition ↔ to preposition ↔ on

Data from section 15.2.1

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Chapter 3 introduced the use of rewrite rules to specify a grammar. The rules listed below define a grammar for simple transitive sentences such as "The man likes the dog." The rules are numbered for reference. 1. 2. sentence noun_phrase verb_phrase noun phrase noun 3. 4. verb_phrase verb noun_phrase article noun 8. 9. 10. 11. 5. verb_phrase verb noun_phrase 6. article a 7. article the noun man noun dog verb likes verb bites Rules 6 through 11 have English words on the right-hand side; these rules form a dic- tionary of words that may appear in sentences. These words are the terminals of the gram- mar and define a lexicon of the language. Terms that describe higher-level linguistic concepts (sentence, noun_phrase, etc.) are called nonterminals. Nonterminals appear in this typeface. Note that terminals do not appear in the left-hand side of any rule. A legal sentence is any string of terminals that can be derived using these rules. A der- ivation begins with the nonterminal symbol sentence and produces a string of terminals through a series of substitutions defined by the rules of the grammar. A legal substitution replaces a symbol that matches the left-hand side of a rule with the symbols on the right- hand side of that rule. At intermediate stages of the derivation, the string may contain both terminals and nonterminals and is called a sentential form.