Defaults and Revision in Structured Theories

Starting from a logic which speciies how to make deductions from a set of sentences (a ``at theory'), a way to generalise this to a partially ordered bag of sentences (a `structured theory') is given. The partial order is used to resolve connicts. If occurs below then is accepted only insofar as it does not connict with. We start with a language L, a set of interpretations M and a satisfaction relation M L. The key idea is to deene, for each structured theory, a pre-order on interpretations. Models of the structured theory are deened to be maximal interpretations in the ordering. They are shown to exist if the logic hL; M; i is compact. A revision operator is deened, which takes a struc-tured theory and a sentence and returns a structured theory. The consequence relation has the properties of weak monotonicity, weak cut and weak reeexivity with respect to this operator, but fails their strong counterparts .