The semantics of natural language plurals poses a number of intricate problems – both from a formal and a computational perspective. In this thesis I investigate problems of representing, disambiguating and reasoning with plurals from a computational perspective. The work defines a computationally suitable representation for important plural constructions, proposes a tractable resolution algorithm for semantic plural ambiguities, and integrates an automatic reasoning component for plurals.
My solution combines insights from formal semantics, computational linguistics and automated theorem proving and is based on the following main ideas. Whereas many existing approaches to plural semantics work on a model-theoretic basis using higher-order representation languages I propose a proof-theoretic approach to plural semantics based on a flat first-order semantic representation language thus showing that a trade-off between expressive power and logical tractability can be found. The problem of automatic disambiguation of plurals is tackled by a deliberate decision to drastically reduce recourse to contextual knowledge for disambiguation but rely instead on structurally available and thus computationally manageable information. A further central aspect of the solution lies in carefully drawing the borderline between real ambiguity and mere indeterminacy in the interpretation of plural noun phrases. As a practical result of my computational proof-theoretic approach to plural semantics I can use my methods to perform automated reasoning with plurals by applying advanced first-order theorem provers and model-generators available off-the shelf.
The results are prototypically implemented within the two logic-oriented natural language understanding applications DRoPs and Attempto. DRoPs provides an automatic plural disambiguation component for uncontrolled natural language whereas Attempto works with a constructive disambiguation strategy for controlled natural language. Both systems provide tools for the automated analysis of technical texts allowing users for example to automatically detect inconsistencies, to perform question answering, to check whether a conjecture follows from a text or to find equivalences and redundancies.