Hierarchic adaptive logics

This paper discusses the proof theory, semantics and meta-theory of a class of adaptive logics, called hierarchic adaptive logics. Their specific characteristics are illustrated throughout the paper with the use of one exemplary logic HK, an explicans for reasoning with prioritized belief bases. A generic proof theory for these systems is defined, together with a less complex proof theory for a subclass of them. Soundness and a restricted form of completeness are established with respect to a nonredundant semantics. It is shown that all hierarchic adaptive logics are reflexive, have the strong reassurance property and that a subclass of them is a fixed point for a broad class of premise sets. Finally, they are compared to a different yet related class of adaptive logics.