The proper treatment of linguistic ambiguity in ordinary algebra

Abstract

We present a first algebraic approximation to the semantic content of linguistic ambiguity. Starting from the class of ordinary Boolean algebras, we add to it an ambiguity operator ║ and a small set of axioms which we think are correct for linguistic ambiguity beyond doubt.We then show some important, non-trivial results that follow from this axiomatization, which turn out to be surprising and not fully satisfying from a linguistic point of view. Therefore, we also sketch promising algebraic alternatives.