Underspecified Discourse Representation Structures and their Logic

The paper adresses the problem of reasoning with ambiguities. Semantic representations are presented that leave scope relations between quantifiers and/or other operators unspecified. Truth conditions are provided for these representations and different consequence relations are judged on the basis of intuitive correctness. Finally inference patterns are presented that operate directly on these underspecified structures, i.e. do not rely on any translation into the set of their disambiguations.