Inference in a Boolean Fragment

This paper is a contribution to natural logic, the study of logical systems for linguistic reasoning. We construct a system with the following properties: its syntax is closer to that of a natural language than is first-order logic; it can faithfully represent simple sentences with standard quantifiers, intransitive and transitive verbs, converses (for passive sentences), subject relative clauses (a recursive construct), and conjunction and negation on nouns and verbs. We also give a proof system which is complete and is decidable due to the the finite model property. The fragment itself was inspired by Ivanov and Vakarelov [2]. Our logical system differs from theirs in several respects and is an extension of our system in [6]. At the time of this writing, I know of no strictly larger system than the one in this paper and in [2] which is complete and decidable and which is capable of representing interesting in natural language.