First-order preference theories and their applications

technical reportThis dissertation begins with a logical analysis of the notion of preference. Earlier approaches to logical analysis of preference are surveyed and their shortcomings pointed out. Next, a family of modal logics of preference is presented with soundness and completeness results for both the propositional and first order cases. These logics of preference turn out to be remarkably expressive. In the rest of the thesis, the formal tools developed in the first part are used to give a computational account of nonmonotoncity in deductive reasoning as symbolic optimization. A few results on complexity are given. In the domain of logic programming, preference logics give a totally declarative account of negation as failure. Further, we propose a syntactic extension to Horn clauses that embodies the notion of constraint relazation. The relaxation regimes are accorded their due status in the model theory, and they also give guidelines for devising a fair computation rule for the SLD-interpreter. The strong similarities between preferences and obligations, in particular, their normative nature, allows the construction of a preference based deontic logic that is free of the paradoxes of standard deontic logic. Finally, a brief outline of the larger context (and the problem that motivated this research) in which this research was performed, i.e., a declarative account of document structures, is given