Abstracting over Semantic Theories

ing over Semantic Theories Alexander Guy Brockway Holt Doctor of Philosophy University of Edinburgh 1993 Abstract The topic of this thesis is abstraction over theories of formal semantics for natural language. It is motivated by the belief that a metatheoretical perspective can contribute both to a better theoretical understanding of semantic theories, and to improved practical mechanisms for developing theories of semantics and combining them with theories of syntax. The argument for a new way to understand semantic theories rests partly on the present di culty of accurately comparing and classifying theories, as well as on the desire to easily combine theories that concentrate on di erent areas of semantics. There is a strong case for encouraging more modularity in the structure of semantic theories, to promote a division of labour, and potentially the development of reusable semantic modules. A more abstract approach to the syntax-semantics interface holds out the hope of further bene ts, notably a degree of guaranteed semantic coherence via types or constraints. Two case studies of semantic abstraction are presented. First, alternative characterizations of intensional abstraction and predication are developed with respect to three di erent semantic theories, but in a theory-independent fashion. Second, an approach to semantic abstraction recently proposed by Johnson and Kay is analyzed in detail, and the nature of its abstraction described with formal speci cations. Finally, a programme for modular semantic speci cations is described, and applied to the area of quanti cation and anaphora, demonstrating successfully that theory-independent devices can be used to simultaneously abstract across both semantic theories and syntax-semantics interfaces. iThe topic of this thesis is abstraction over theories of formal semantics for natural language. It is motivated by the belief that a metatheoretical perspective can contribute both to a better theoretical understanding of semantic theories, and to improved practical mechanisms for developing theories of semantics and combining them with theories of syntax. The argument for a new way to understand semantic theories rests partly on the present di culty of accurately comparing and classifying theories, as well as on the desire to easily combine theories that concentrate on di erent areas of semantics. There is a strong case for encouraging more modularity in the structure of semantic theories, to promote a division of labour, and potentially the development of reusable semantic modules. A more abstract approach to the syntax-semantics interface holds out the hope of further bene ts, notably a degree of guaranteed semantic coherence via types or constraints. Two case studies of semantic abstraction are presented. First, alternative characterizations of intensional abstraction and predication are developed with respect to three di erent semantic theories, but in a theory-independent fashion. Second, an approach to semantic abstraction recently proposed by Johnson and Kay is analyzed in detail, and the nature of its abstraction described with formal speci cations. Finally, a programme for modular semantic speci cations is described, and applied to the area of quanti cation and anaphora, demonstrating successfully that theory-independent devices can be used to simultaneously abstract across both semantic theories and syntax-semantics interfaces. i Acknowledgements Most of all, I owe a great debt to my supervisor, Ewan Klein, for his kindness, tolerance, inspiration and continual encouragement. It has been a privilege to spend the last ve years in the Centre for Cognitive Science. For discussions and arguments that have shaped the ideas which follow I thank all those that I have known here, but especially David Adger, David Beaver, Patrick Blackburn, Lawrence Cavedon, Robin Cooper, Martin Emms, Ian Lewin, Suresh Manandhar, Michael Newton, Mike Reape, Sheila Rock, Catrin Siân Rhys, Peter Ruhrberg and Henk Zeevat. Beyond Edinburgh I would like to thank Mark Ryan, and to record the in uence of George Bealer's inspiring lectures at Leuven in 1990. I am grateful to everyone who has worked to make CCS such a good place to be, in particular Robert Dale, Elisabet Engdahl, Betty Hughes, Ewan Klein and Jeremy Olsen. To Jeremy and the rest of the computing team|thanks for an environment that I have relied on time and time again. This thesis would have been impossible without nancial support from the UK Science and Engineering Research Council, for which I am most grateful. It would have been hard to complete it without the occasional work kindly o ered to me by Robert Dale and Jeremy Olsen. To my family and to my friends, for all your support|thank you very much. Finally, I thank Chris Mellish and Henk Zeevat, my examiners, for their constructive suggestions.