A system of relational syllogistic incorporating full Boolean reasoning

We present a system of relational syllogistic, based on classical propositional logic, having primitives of the following form: Some A are R-related to some B; Some A are R-related to all B; All A are R-related to some B; All A are R-related to all B. Such primitives formalize sentences from natural language like `All students read some textbooks'. Here A and B denote arbitrary sets (of objects), and R denotes an arbitrary binary relation between objects. The language of the logic contains only variables denoting sets, determining the class of set terms, and variables denoting binary relations between objects, determining the class of relational terms. Both classes of terms are closed under the standard Boolean operations. The set of relational terms is also closed under taking the converse of a relation. The results of the paper are the completeness theorem with respect to the intended semantics and the computational complexity of the satisfiability problem.Comment: Available at http://link.springer.com/article/10.1007/s10849-012-9165-

Vagueness and Quantification

This paper deals with the question of what it is for a quantifier expression to be vague. First it draws a distinction between two senses in which quantifier expressions may be said to be vague, and provides an account of the distinction which rests on independently grounded assumptions. Then it suggests that, if some further assumptions are granted, the difference between the two senses considered can be represented at the formal level. Finally, it outlines some implications of the account provided which bear on three debated issues concerning quantification

Decomposing generalized quantifiers

This note explains the circumstances under which a type quantifier can be decomposed into a type quantifier and a set, by fixing the first argument of the former to the latter. The motivation comes from the semantics of Noun Phrases (also called Determiner Phrases) in natural languages, but in this article, I focus on the logical facts. However, my examples are taken among quantifiers appearing in natural languages, and at the end, I sketch two more principled linguistic applications