Towards a Logic of Ambiguous Expressions 1 Coping with Ambiguous Information

Ambiguity has more than once been identiied as the main single obstacle for various natural language processing tasks (e.g., Bar-Hillel 1960, Car-bonel and Hayes 1987). Surprisingly, however, the logical properties of ambiguous expressions have not been studied in much depth. The reason is, presumably, that ambiguity is not a real phenomenon, but rather what you see when you look at a real phenomenon (namely: an utterance) with insuucient knowledge about it (that is: disregarding its linguistic or non-linguistic context). This view is represented in a pure form by Barwise and Perry, who claim that although sentences can be ambiguous, utterances cannot (Barwise and Perry 1983). Each particular utterance of an expression is an utterance of it in a certain \way" that removes all ambiguity. In accordance with this idea, if ambiguity is treated in practical systems, it is usually treated in the same manner in which an illness is treated: to get rid of it. This is called the resolution of ambiguity. The result of resolution is a formula from which all ambiguity has been removed and which does its job (database query, or whatever) in standard ways. However, complete ambiguity resolution is not always possible. It is of little use to ask whether an utterance situation must, in principle, always contain enough information to aaord complete disambiguation. What counts is that in practice, often not enough information is available to an interpreter. This holds whether the interpreter is a person or a computer. Various authors have argued that semantic theories attribute so many interpretations to sentences, that to assume that interpreters can always retrieve the intended meaning amounts to believing in miracles. 1 In addition , a human interpreter may perceive an utterance incompletely, or lack 1 This includes older work, such as van Lehn (1978), Bobrow and Webber (1980), and Hobbs (1983). Hobbs, for example, claimed that people can understand, and yet not fully disambiguate a sentence like In most democratic countries most politicians can fool most of the people on almost every issue most of the time, given all the 120 diierent scope orders that its NPs can have (Hobbs 1983).