Interaction of modalities in discourse : a monoidal account

Abstract

The topic of the present paper is the interaction of modalities in discourse. We make some initial observations about this phenomenon and discuss some connections with other discourse phenomena. Then we present two styles of dynamic semantics for modal interaction: an update semantics in the style of Veltman [Vel96] and a monoidal semantics in the style of Visser [VV96]. The monoidal style is an improvement on the update style, as it forces us to break down the complex update procedures into elementary operations on locations in memory, thus providing a rational reconstruction of the dynamics underlying the update functions. By means of a translation it is shown that the monoidal semantics of the interaction of modalities preserves all the pleasant properties of the update semantics, among which is the decidability result of [Ver99].