New techniques and completeness results for preferential structures

Preferential structures are probably the best examined semantics for nonmon otonic and deontic logics: in a wider sense, they also provide semantical a pproaches to theory revision and update, and other fields where a preferenc e relation between models is a natural approach. They have been widely used to differentiate the various systems of such logics, and their constructio n is one of the main subjects in the formal investigation of these logics. We introduce new techniques to construct preferential structures for comple teness proofs. Since our main interest is to provide general techniques, wh ich can be applied in various situations and for various base logics (propo sitional and other), we take a purely algebraic approach. which can be tran slated into logics by easy lemmata. In particular, we give a clean construc tion via indexing by trees for transitive structures, this allows us to sim plify the proofs of earlier work by the author, and to extend the results g iven there.