Hierarchic adaptive logics

Abstract

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 x , 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.

Adaptive Logic Characterizations of Input/Output Logic

“…• are considered (see e.g., [48,49]). The most straightforward way is to use an adaptive logic based on Ω • defneg = Ω defneg ∪Ω + • .…”

Adaptive strategies and finite-conditional premise sets

“…As a final example, consider the propositional version of the logics for reasoning with "plausible information" [32,33]. 14 These are defined on the basis of a normal modal logic (most often K or T), and have as their set of abnormalities Ω ♦ = {♦A ∧ ¬A | A is an atom or its negation}.…”