By a fragment of a natural language, we understand a
collection of sentences forming a naturally delineated subset of
that language and equipped with a semantics commanding the general
assent of its native speakers. By the semantic complexity of
such a fragment, we understand the computational complexity of
deciding whether any given set of sentences in that fragment
represents a logically possible situation. In earlier papers by the
first author, the semantic complexity of various fragments of
English involving at most transitive verbs was investigated. The present paper considers various fragments of English involving
ditransitive verbs and determines their semantic complexity.