One Semiring to Rule Them All1

In this paper we look at the well known phenomenon of conjunction fallacies (Tversky & Kahneman, 1983) from a linguistic perspective. We are particularly interested in understanding the impact of this phenomenon on our understanding of compositionality, a core assumption of contemporary linguistic theories about language meaning. We will argue that contra Hertwig, Benz, and Krauss (2008), conjunction fallacies do not arise because of the ambiguity of coordinating conjunctions such as and, but rather because there are two different strategies available for computing the composite likelihood of a collection of events. Crucially, in our analysis the two strategies are two variants of the same underlying general structure that simultaneously allows subjects 1. to reason in purely logical terms; 2. to follow the rules of probability and 3. to commit fallacies depending on the conditions under which they evaluate linguistic expressions relating uncertain events. We will explain the choice between the two strategies in terms of cognitive/computational economy and the consequences of overestimating the likelihood of an event.