Reasoning with natural language

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.

../../../_images/image0281.svg

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.

../../../_images/image0301.svg

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].