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\ud two styles of dynamic semantics for modal interaction: an update semantics in the style of Veltman [Vel96] and a monoidal semantics in the style\ud of Visser [VV96]. The monoidal style is an improvement on the update\ud style, as it forces us to break down the complex update procedures into\ud elementary operations on locations in memory, thus providing a rational\ud reconstruction of the dynamics underlying the update functions. By means\ud of a translation it is shown that the monoidal semantics of the interaction\ud of modalities preserves all the pleasant properties of the update semantics,\ud among which is the decidability result of [Ver99]
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