12.7. Reasoning with natural language

Solution 7.1 

Redraw the parse tree of Figure 7.1 in the manner of an SLD proof tree, where ‘resolvents’ are partially parsed sentences such as

[the],[rapid],noun,verb_phrase

and ‘clauses’ are grammar rules.

Solution 7.2 

Draw the search space generated by the grammar in Section 7.1 for a top-down parse, if grammar rules are applied to sentences from left to right. Discuss the similarities and differences with SLD-trees.

The search space is partly drawn below; the lower part, which contains all possible verb phrases, re-appears at three other nodes as indicated.

This search space is basically a propositional SLD-tree, with fully parsed sentences corresponding to success branches (failure branches occur only when for some syntactic category no grammar rules are specified).

Solution 7.4 

Extend the following grammar rules with arguments expressing their interpretation:

verb_phrase     --> transitive_verb,proper_noun.
transitive_verb --> [likes].

The transitive verb defines a binary mapping Y=>X=>L, which is applied to the meaning of the proper noun:

verb_phrase(M)                    --> transitive_verb(Y=>M),proper_noun(Y).
transitive_verb(Y=>X=>likes(X,Y)) --> [likes].