Iterated revision and the axiom of recovery: a unified treatment via epistemic states

The axiom of recovery, while capturing a central intuition regarding belief change, has been the source of much controversy. We argue briefly against putative counterexamples to the axiom--while agreeing that some of their insight deserves to be preserved--and present additional recovery-like axioms in a framework that uses epistemic states, which encode preferences, as the object of revisions. This provides a framework in which iterated revision becomes possible and makes explicit the connection between iterated belief change and the axiom of recovery. We provide a representation theorem that connects the semantic conditions that we impose on iterated revision and the additional syntactical properties mentioned. We also show some interesting similarities between our framework and that of Darwiche-Pearl. In particular, we show that the intuitions underlying the controversial (C2) postulate are captured by the recovery axiom and our recovery-like postulates (the latter can be seen as weakenings of (C2).

Some logics of belief and disbelief

The introduction of explicit notions of rejection, or disbelief, into logics for knowledge representation can be justified in a number of ways. Motivations range from the need for versions of negation weaker than classical negation, to the explicit recording of classic belief contraction operations in the area of belief change, and the additional levels of expressivity obtained from an extended version of belief change which includes disbelief contraction. In this paper we present four logics of disbelief which address some or all of these intuitions. Soundness and completeness results are supplied and the logics are compared with respect to applicability and utility.

Relevance Sensitive Non-Monotonic Inference on Belief Sequences

We present a method for relevance sensitive non-monotonic inference from belief sequences which incorporates insights pertaining to prioritized inference and relevance sensitive, inconsistency tolerant belief revision. Our model uses a finite, logically open sequence of propositional formulas as a representation for beliefs and defines a notion of inference from maxiconsistent subsets of formulas guided by two orderings: a temporal sequencing and an ordering based on relevance relations between the conclusion and formulas in the sequence. The relevance relations are ternary (using context as a parameter) as opposed to standard binary axiomatizations. The inference operation thus defined easily handles iterated revision by maintaining a revision history, blocks the derivation of inconsistent answers from a possibly inconsistent sequence and maintains the distinction between explicit and implicit beliefs. In doing so, it provides a finitely presented formalism and a plausible model of reasoning for automated agents.