Formal Alternatives as a Solution to the Proviso Problem

This paper investigates a particular problem concerning presupposition accommodation. Let ψ and X be sentences, and suppose ψ presupposes X . We represent this as ψ{X}.1 Suppose the speaker and hearer of a conversation are in context c. Suppose further that the speaker wishes to update the context cwith the information in ψ, an operation we represent as c[ψ{X}]. ψ{X} imposes a requirement on c that has to be met for the update to take place: c already has to entail X . In terms of update operations, this means that if we try updating c with X , we just get back c: c[X ] = c. When this condition is met, we say that c satisfies X , or that c is a fixed point for [X ]. But what if c is not a fixed point for [X ]? What happens when the condition is not met? There are at least two possible outcomes: (i) either communication breaks down, or (ii) we make some repair [Y ] to c so that update will be defined after all, i.e. we update c with Y , c[Y ], so that c[Y ] ends up satisfying X . Call this repair process accommodation Lewis (1979). We then update the new context resulting from accommodation of Y with ψ,c[Y ][ψ]. The question I explore in these pages is: Is there anything more to say about this repair process than simply “do something?” By detailed investigation of a particular puzzle in the theory of presupposition accommodation, this paper will: (i) Present empirical evidence that there are formal restrictions on the allowable repairs [Y ] that can be made, and (ii) Derive the restricted set of allowable repairs from the instructions encoded in the contextchange potentials defined in Heim (1983). We will see that the derivation of the set of alternatives makes crucial reference to the formal descriptions of context-change potentials (context-change potential descriptions, or CCPDs). Thus, the system