Towards a pragmatic explanation for the prevalence of upward-monotonicity in natural language: some results on communicative stability, the strongest answer condition, and exhaustification
Émile Enguehard
May 2025 

In natural language, logical functions that have the formal property of upward-monotonicity are pervasive. This is most visible in the prevalence of upward-monotonic operators in the logical lexicon. The object of this paper is to point out that this upward-monotonic bias has important consequences for the composition of the alternative sets used in theories of pragmatics, and to argue for the view first proposed by Bar-Lev and Katzir (2022: Linguistic Inquiry) that the function of the bias is to guarantee that alternative sets have certain properties. We argue that it is desirable for sets of alternatives to verify the strongest-answer condition, because it is equivalent to the condition that the exhaustification algorithms that have been proposed in the literature to derive scalar implicatures turn the set into a partition of logical space. Then, we show that in certain formal settings, a strongest-answer condition on alternative sets predicts the upward-monotonic bias, assuming those sets are derived as predicted by the structural theory of alternatives. Putting these things together, the bias lets speakers be maximally informative for a given set of alternatives. Because the strongest-answer condition is also equivalent to Bar-Lev and Katzir's stability condition, defined in the context of probabilistic models of pragmatics, our argument can be seen as a generalization of their approach, for which we offer independent motivation.

Format:	[ pdf ]
Reference:	lingbuzz/009015 (please use that when you cite this article)
Published in:	To appear in Linguistics and Philosophy. Earlier versions at https://ling.auf.net/lingbuzz/007288
keywords:	universals, logical lexicon, monotonicity, pragmatics, exhaustification, semantics, semantics
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