### Artificial IntelligenceAIMA Exercises

Consider the sentence “Someone walked slowly to the supermarket” and a lexicon consisting of the following words:
$Pronoun \rightarrow \textbf{someone} \quad Verb \rightarrow \textbf{walked}$
$Adv \rightarrow \textbf{slowly} \quad Prep \rightarrow \textbf{to}$
$Article \rightarrow \textbf{the} \quad Noun \rightarrow \textbf{supermarket}$
Which of the following three grammars, combined with the lexicon, generates the given sentence? Show the corresponding parse tree(s).
$$\quad\quad\quad\quad (A):\quad\quad\quad\quad \quad\quad\quad\quad(B):\quad\quad\quad\quad \quad\quad\quad\quad(C):\\ \quad\quad\quad\quad S \rightarrow NP \space VP \quad\quad\quad\quad \quad\quad\quad\quad S\rightarrow NP\space VP \quad\quad\quad\quad S\rightarrow NP\space VP\\ \quad\quad\quad\quad NP\rightarrow Pronoun \quad\quad\quad\quad NP\rightarrow Pronoun \quad\quad\quad\quad NP\rightarrow Pronoun\\ \quad\quad\quad\quad NP\rightarrow Article\space Noun \quad\quad\quad\quad NP\rightarrow Noun \quad\quad\quad\quad NP\rightarrow Article\space NP\\ \quad\quad\quad\quad VP\rightarrow VP\space PP \quad\quad\quad\quad NP\rightarrow Article\space NP \quad\quad\quad\quad VP\rightarrow Verb\space Adv\\ \quad\quad\quad\quad VP\rightarrow VP\space Adv\space Adv \quad\quad\quad\quad VP\rightarrow Verb\space Vmod \quad\quad\quad\quad Adv\rightarrow Adv\space Adv\\ \quad\quad\quad\quad VP\rightarrow Verb \quad\quad\quad\quad Vmod\rightarrow Adv\space Vmod \quad\quad\quad\quad Adv\rightarrow PP\\ \quad\quad\quad\quad PP\rightarrow Prep\space NP \quad\quad\quad\quad Vmod\rightarrow Adv \quad\quad\quad\quad PP\rightarrow Prep\space NP\\ \quad\quad\quad\quad NP\rightarrow Noun \quad\quad\quad\quad Adv\rightarrow PP \quad\quad\quad\quad NP\rightarrow Noun\\ \quad\quad\quad\quad\quad \quad\quad\quad\quad PP\rightarrow Prep\space NP \quad\quad\quad\quad \quad\quad\quad\quad$$ For each of the preceding three grammars, write down three sentences of English and three sentences of non-English generated by the grammar. Each sentence should be significantly different, should be at least six words long, and should include some new lexical entries (which you should define). Suggest ways to improve each grammar to avoid generating the non-English sentences.

Consider the sentence “Someone walked slowly to the supermarket” and a lexicon consisting of the following words:
$Pronoun \rightarrow \textbf{someone} \quad Verb \rightarrow \textbf{walked}$
$Adv \rightarrow \textbf{slowly} \quad Prep \rightarrow \textbf{to}$
$Article \rightarrow \textbf{the} \quad Noun \rightarrow \textbf{supermarket}$
Which of the following three grammars, combined with the lexicon, generates the given sentence? Show the corresponding parse tree(s).
$$\quad\quad\quad\quad (A):\quad\quad\quad\quad \quad\quad\quad\quad(B):\quad\quad\quad\quad \quad\quad\quad\quad(C):\\ \quad\quad\quad\quad S \rightarrow NP \space VP \quad\quad\quad\quad \quad\quad\quad\quad S\rightarrow NP\space VP \quad\quad\quad\quad S\rightarrow NP\space VP\\ \quad\quad\quad\quad NP\rightarrow Pronoun \quad\quad\quad\quad NP\rightarrow Pronoun \quad\quad\quad\quad NP\rightarrow Pronoun\\ \quad\quad\quad\quad NP\rightarrow Article\space Noun \quad\quad\quad\quad NP\rightarrow Noun \quad\quad\quad\quad NP\rightarrow Article\space NP\\ \quad\quad\quad\quad VP\rightarrow VP\space PP \quad\quad\quad\quad NP\rightarrow Article\space NP \quad\quad\quad\quad VP\rightarrow Verb\space Adv\\ \quad\quad\quad\quad VP\rightarrow VP\space Adv\space Adv \quad\quad\quad\quad VP\rightarrow Verb\space Vmod \quad\quad\quad\quad Adv\rightarrow Adv\space Adv\\ \quad\quad\quad\quad VP\rightarrow Verb \quad\quad\quad\quad Vmod\rightarrow Adv\space Vmod \quad\quad\quad\quad Adv\rightarrow PP\\ \quad\quad\quad\quad PP\rightarrow Prep\space NP \quad\quad\quad\quad Vmod\rightarrow Adv \quad\quad\quad\quad PP\rightarrow Prep\space NP\\ \quad\quad\quad\quad NP\rightarrow Noun \quad\quad\quad\quad Adv\rightarrow PP \quad\quad\quad\quad NP\rightarrow Noun\\ \quad\quad\quad\quad\quad \quad\quad\quad\quad PP\rightarrow Prep\space NP \quad\quad\quad\quad \quad\quad\quad\quad$$ For each of the preceding three grammars, write down three sentences of English and three sentences of non-English generated by the grammar. Each sentence should be significantly different, should be at least six words long, and should include some new lexical entries (which you should define). Suggest ways to improve each grammar to avoid generating the non-English sentences.

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