Tim Fernando - Negations framed in context

In this work, I provide a frame-theoretic account of a recent paper [NCK] by Nairn, Condoravdi and Karttunen, analyzing implicatives, factives and counterfactives such as those in (1) and (2).

(1a)    Ed forgot to close the door.

(1b)    Ed did not forget to close the door.

(2a)    Ed forgot that the door was closed.

(2b)    Ed did not forget that the door was closed.

(1a) implies Ed did NOT close the door, (1b) implies the opposite. Both (2a) and (2b) imply the door WAS closed. In the terminology of [NCK], forget to is a two-way implicative reversing the polarity of its complement, whereas forget that is a factive preserving polarity.
   The relevance of negation in (1) and (2) to frames lies in two familiar positions about the presuppositions of p. The first is that these are captured by the disjunction, p or not p, for a suitable notion of not. And the second is that these are requirements on a context for p to convey a proposition. This second view (going back to Karttunen) has a clean formal implementation in proof-theoretic type systems inspired by “propositions-as-types” (e.g. [R], [C1]). In [C1], Cooper encodes contexts as records that are essentially recursive attribute-value structures, i.e. frames. Moreover, going back to examples (1) and (2) above, we can, under propositions-as-types, step from notions of truth (as in propositions such as the door was closed in (2)) to more general notions of type membership (covering the property to close the door in (1)). The difference between propositions and properties is arguably crucial to the observation that forget that is factive whereas forget to is a polarity reversing two-way implicative.
   The frame-theoretic account I give of [NCK] uses implications from type theory to encode classifications such as the factivity of forget that. Moreover, these implications compose to yield the behavior predicted in [NCK] of multiply embedded constructions such as (3).

   (3)     Ed did not forget to force Dave to leave.

The implication from (3) that Dave left follows, in my account, from stringing together implications encoding classifications from [NCK]. In type theory, implications correspond to function types. In [C2], function types are used to encode frames of mind, the domain in which provides a handle on presuppositions. The present work ties all this with negations framed in context.

References

[C1] R. Cooper, Records and record types in semantic theory,  Journal of Logic and Computation 15 (2) 99-112, 2005.

[C2] R. Cooper, Austinian truth, attitudes and type theory, Research on Language and Computation 3 (4) 333-362, 2005.

[NCK] R. Nairn, C. Condoravdi and L.Karttunen, Computing relative polarity for textual inference, Inference in Computational Semantics-5, 2006.

[R] A. Ranta, Type-Theoretical Grammar, Oxford, 1994.