Syllogistic Logics with Verbs

This paper provides sound and complete logical systems for several fragments of English which go beyond syllogistic logic in that they use verbs as well as other limited syntactic material: universally and existentially quantified noun phrases, building on the work of Nishihara, Morita, and Iwata [7]; complemented noun phrases, following our [6]; and noun phrases which might contain relative clauses, recursively, based on McAllester and Givan [4]. The logics are all syllogistic in the sense that they do not make use of individual variables. Variables in our systems range over nouns, and in the last system, over verbs as well.