Inheritance reasoning : psychological plausibility, proof theory and semantics

Default inheritance reasoning is a propositional approach to nonmonotonic reasoning designed to model reasoning with natural language generics. Inheritance reasoners model sets of natural language generics as directed acyclic graphs, and inference corresponds to the speci cation of paths through those networks. A proliferation of inheritance proof theories exist in the literature along with extensive debate about the most reasonable way to construct inferences, based on intuitions about interpretations of particular inheritance networks. There has not been an accepted semantics for inheritance which uni es the set of possible proof theories, which would help identify truly ill-motivated proof theories. This thesis attempts to clarify the inheritance literature in the three ways indicated in the title: psychological plausibility, proof theory and semantics. The thesis intends to displace debate about the best inferences to draw about a network from logicians' introspections to empirical investigation of how people respond to sets of defaults. The third chapter investigates a range of assumptions made within the literature on default inheritance reasoning and additionally attempts to arbitrate among con icting inheritance reasoners based on the best t with empirical data. This empirical research is among the rst studies which have attempted to inform inheritance proof theory with clues about the way people reason. The second and fourth chapters of the thesis contribute to inheritance proof theory by identifying complexity results that have been misleading, and by de ning some new inheritance systems based in part by the observations made in analyzing the data accumulated in experiments reported in Chapter Three. The main contribution of the proof theoretic chapters is the presentation of a set of de nitions for a range of inheritance reasoners within a well de ned family of path-based systems. It is shown how the reasoners relate to each other in terms of both the conclusions reached as well as in indicating the changes to the de nitions required to obtain the appropriate mutations. Implementations are supplied for a number of these systems. The fth chapter uses this parameterization of inheritance proof theory in providing a uni ed semantics using channel theory, a new mathematical framework designed to model natural regularities and information ow. The essential modeling tool supplied by channel theory is the information channel, an object in the universe that enables information ow and which stands for regularities. The semantics for inheritance uses information channels as the interpretation of inheritance links. Inferences, corresponding to paths through the inheritance networks, are interpreted by composite channels. Thus, various reasoning strategies have a natural interpretation in corresponding restrictions on the putative serial composition of channels. This is the rst uni ed semantics for a family of path-based inheritance reasoners. The thesis concludes by pointing out the various ways in which this work can be extended. ii Acknowledgements I would like to express deep gratitude to Je Horty, Richmond Thomason and David Touretzky for developing such a thick area of nonmonotonic reasoning to explore in a PhD thesis. Thanks to Robin Cooper, for giving me freedom to wallow in this stu as I pleased, and for giving guidance and advice at quite crucial moments, support at even more crucial ones. I'd also like to thank Elisabet Engdahl for additional sound advice through the course of my studies in Edinburgh. Marc Moens has also been quite helpful, more than he knows, by giving me things to read and letting me just get on with it. Lawrence Cavedon, Tsutomu Fujinami, Claire Hewson, Ulrike Hahn and Catherine Collin were all very generous in making time to read and comment on various stages of this material. I also owe thanks to both Je Pelletier and Jon Oberlander for agreeing to formally examine the thesis. I am still completely tickled that it is the Centre for Cognitive Science here in Edinburgh where I've been able to do my PhD, and the Marshall Aid Commemoration Commision has my eternal gratitude for making it possible (as well as Robin's EKN boxes for letting it continue to be). Special thanks to Betty Hughes for making administration of all that quite painless, and for keeping the main o ce so warm & friendly. A lot of people have made Edinburgh a fun experience from a social point of view: Pat Healey, Claire Hewson, Rois n Higgins (I don't think it would have been possible to nish this thesis within the desired timetable if she hadn't been planning to submit a PhD thesis on almost exactly the same day and available for commiseration through late-license pints), Lex Holt, Toma z Erjavec, Jelena Meznaric, Sheila Rock, Andreas Sch oter, and Paul Schweizer are the prime culprits there. Particular thanks are due to Pat and Toma z and especially Claire for putting up with me in collaborations and sundry other ways that are best left unspoken here. I'd quite like to thank whoever invented e-mail for making it possible to keep in such frequent communication with folks across the water { Fred Popowich, Nick Cercone, Marcus Smith, Tony Lopez, Glenn MacDonald, Joerg Ueberla, Chris Wiseman, my parents and Dianna Laurent, my sister and brainstorming partner. It has been really good of my family to still acknowledge my existence when I pass through Louisiana after such lengthy absences, as do so many close friends (Tim & Michelle Murphy, Beth Campbell, Michele Barrere, .) who have long given up on me answering letters by post in a timely fashion. Finally, I'd like to dedicate this thesis to John James Boepple, my best friend from childhood, who was murdered in New Orleans on July 21, 1994. This thesis prevented me from giving him a eulogy at his funeral, so I reckon it belongs to him. iii