Talking about trees, scope and concepts

Language can be ambiguous at all levels – at the level of the word, of the phrase, of the sentence, as well as of the text or dialogue. The source of ambiguity is often lexical or morphological, but ambiguities also emerge when passing from one level of linguistic analysis – morphology, syntax, semantics, pragmatics – to another. This transition from one level of representation to another can, however, also have the opposite effect. It may eliminate ambiguities rather than increase them. The ultimate task for both computational and theoretical linguistics must therefore not only be to describe the sources of ambiguity but also to identify the ways in which these ambiguities can be eliminated again. Any solution of the problem of disambiguation will depend on (i) the way different types of ambiguities are represented, if they are, and (ii) the mode of representation for the non-ambiguous case. Representational approaches represent ambiguities by specific construals. For most of them the modes of ambiguity representation subsumes the mode for disambiguated representations, as is the case for packed representations, feature structures, or UDRSs. Descriptive approaches to ambiguity control move from structural representations to descriptions thereof. Linguistic representations are considered here as determined by a description (in form of a logical theory derived from the input and containing general linguistic knowledge) from which the actual representation or the set of possible representations must be derived. (For syntactic structures such descriptions are given in [3, 12, 13, 15], an extension to type-theoretical semantics can be found in [14], and in [4] we proposed a treatment of lexical ambiguities by integrating ontological knowledge to express selectional restrictions of verbs). Representational and descriptive approaches do, however, not exclude each other. Suppose ambiguities are explicitly represented by some construal, as is the case for, e.g., the partial ordering of UDRS-components. Then a UDRS representing an ambiguous sentence may be derived by a logical description grammar approach as the unique model satisfying the description. This model is related to the set of models representing the readings of the sentence by the different ways to strengthen the partial ordering of UDRS-components to linear ones. If the logical theory contains enough