In M. Amblard, P. de Groote, S. Pogodalla & C. Retoré (eds.), Logical Aspects of Computational Linguistics. Celebrating 20 Years of LACL (1996–2016). Springer. pp. 191-210 (2016)

Alda Mari
Institut Jean Nicod
We show that actuality entailments arise with goal-oriented modality only and endorse Belnap’s view of that goal-oriented modals use historical accessibility with a fixed past and an open future. This modal-theoretic assumption allows us to spell out the precise modal-temporal configuration in which the actuality entailment arises and our predictions are borne out by the data, cross-linguistically. We also show that, when any assumption about the identity of worlds at branching point is leveled - which appears to be the case with generic deontic and opportunity modals, the actuality entailments disappear. We also predict that the entailment disappears with prospectivity. Finally, we argue that modal sentences giving rise to actuality entailments are informative, insofar as the contribution of the modality survives as a presupposition that the modal base is non-homogeneous.
Keywords acuality entailments  dynamic modality  presupposition
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Backwards and Forwards in the Modal Logic of Agency.Nuel Belnap - 1991 - Philosophy and Phenomenological Research 51 (4):777-807.

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