Artificial Intelligence Problem Set 2: Solutions A. There are two different parse trees for "John met a man and a dog in the park:" (Here and below I will abbreviate "SIMPLE-NP" as "SNP" S ---> NP ---> SNP ---> ---> John | |-> VP ---> ---> met | |-> NP ---> SNP ---> ---> a | | | | | |-> ---> man | | | |-> and | | | |-> SNP ---> ---> a | | | |-> ---> dog | |-> PP ---> ---> in | |-> NP ---> SNP ---> ---> the | |-> --- park S ---> NP ---> SNP ---> ---> John | |-> VP ---> ---> met | |-> NP ---> SNP ---> ---> a | | | |-> ---> man | |-> and | |-> SNP ---> ---> a | |-> ---> dog | |-> PP ---> ---> in | |-> NP ---> SNP ---> ---> the | |-> --- park That is, the prepositional phrase "in the park" be part of the VP "met ... in the park" or of the NP "the dog in the park." B. There are an immense number of parse trees for these sentences. Below are five. Tree 1: S ---> NP ---> SNP ---> ---> John | |-> VP ---> ---> sent | |-> NP ---> SNP ---> ---> email | |-> PP ---> ---> to | | | |-> NP ---> SNP ---> ---> the | | | | | |-> ---> author | |-> and | | | |-> SNP ---> ---> the | | | |-> ---> publisher | | | |-> PP ---> ---> of | | | |-> NP ---> SNP ---> ---> the | | | |-> -> text | |-> PP ---> ---> about | |-> NP ---> SNP ---> ---> an | | |-> ---> error | |-> PP ---> ---> in | |-> NP ---> SNP ---> ---> the | |-> -> table | |-> PP1 Abbreviation PP1: PP ---> ---> of | |-> NP ---> SNP ---> ---> contents Tree # 2: S ---> NP ---> SNP ---> ---> John | |-> VP ---> ---> sent | |-> NP ---> SNP ---> ---> email | |-> PP ---> ---> to | | | |-> NP ---> SNP ---> ---> the | | | | | |-> ---> author | |-> and | | | |-> SNP ---> ---> the | | | |-> ---> publisher | |-> PP ---> ---> of | | | |-> NP ---> SNP ---> ---> the | | | |-> -> textbook | |-> PP ---> ---> about | | | |-> NP ---> SNP ---> ---> an | | | | |-> ---> error | |-> PP ---> ---> in | | | |-> NP ---> SNP ---> ---> the | | | |-> -> table | |-> PP ---> ---> of | |-> NP ---> SNP ---> ---> contents Tree # 3: S ---> NP ---> SNP ---> ---> John | |-> VP ---> ---> sent | |-> NP ---> SNP ---> ---> email | | | |-> PP ---> ---> to | | | |-> NP ---> SNP ---> ---> the | | | |-> ---> author | |-> and | |-> SNP ---> ---> the | |-> ---> publisher | |-> PP ---> ---> of | |-> NP ---> SNP ---> ---> the | |-> -> text | |-> PP2 Abbreviation PP2: PP ---> ---> about | |-> NP -> SNP ---> ---> an | |-> ---> error | |-> PP ---> ---> in | |-> NP -> SNP ---> ---> the | |-> -> table | |-> PP ---> ---> of | |-> NP -> SNP -> -> contents Tree # 4: S ---> NP ---> SNP ---> ---> John | |-> VP ---> ---> sent | |-> NP ---> SNP ---> ---> email | |-> PP ---> ---> to | |-> NP ---> SNP ---> ---> the | | | |-> ---> author |-> and | |-> SNP ---> ---> the | |-> ---> publisher | |-> PP ---> ---> of | | | |-> NP ---> SNP ---> ---> the | | | |-> -> text | |-> PP ---> ---> about | | | |-> NP -> SNP ---> ---> an | | | |-> -> error | | | |-> PP3 | |-> PP ---> ---> of | |-> NP ---> SNP ---> ---> contents Abbreviation: PP3: PP ---> ---> in | |-> NP ---> SNP ---> ---> the | |-> -> table Tree # 5: S ---> NP ---> SNP ---> ---> John | |-> VP ---> ---> sent | |-> NP ---> SNP ---> ---> email | | | |-> PP ---> ---> to | | | | | |-> NP ---> SNP ---> ---> the | | | | | | | |-> ---> author | | |-> and | | | | | |-> SNP ---> ---> the | | | | | |-> ---> publisher | | | |-> PP ---> ---> of | | | |-> NP ---> SNP ---> ---> the | | | |-> -> textbook | |-> PP ---> ---> about | |-> NP ---> SNP ---> ---> an | |-> ---> error | |-> PP ---> ---> in | | | |-> NP ---> SNP ---> ---> the | | | |-> -> table | |-> PP ---> ---> of | |-> NP -> SNP -> -> contents C. The parse given for this sentence by the grammar is S ---> NP ---> SNP ---> ---> Nine | | | | | |-> ---> men | |-> and | | | |-> SNP ---> ---> women | |-> VP ---> ---> serve | |-> PP ---> ---> on | |-> NP ---> SNP ---> ---> the | |-> ---> Supreme | |-> ---> Court The problem with this parse is that "Nine" modifies "men", meaning that there are nine men and some indeterminate number of women on the Supreme Court. The indended meaning that there are nine people on the court has the adjective "nine" modifying "men and women" but that is not possible in this grammar, since an adjective can only be part of an SIMPLE-NP, which cannot contain a conjunction. (The same problem appears in the sentence in part B. "Of the textbook" presumably is intended to modify "the author and the publisher" but it cannot in this grammar.) Another difficulty, which some students found, is that "Supreme Court" is arguably a proper noun, rather than an adjective and a noun.