A Syllogistic Fragment of English with Ditransitive Verbs in Formal Semantics

In this article, we present acts of a \textit{fragment with ditransitive verbs} which take a subject, a direct object and an indirect object in formal semantics of natural language as in \cite{Yoad}. We consider a syllogistic fragment adding transitive verbs and ditransitive verbs with being excluded negative clauses by referring to a fragment as in \cite{fragment1} and \cite{fragment2}.  We give some properties of the fragment in categorial grammar, meaning, lexicon, syntactic category, semantic type, generalized quantifiers, Montague grammar (Montague semantics) \cite{LarryFormal} and \cite{Montague} and finally an intended model for the fragment. We also restrict the fragment to relative clauses and give entailments in the fragment. We study in model theoretic, truth-conditional and compositional semantics to set the framework of the fragment in formal semantics. We also give some algorithms of reasoners for sentences  and set generator algorithms and their implementation technics in the fragment.