Logic programming under the answer-set semantics nowadays deals with numerous different notions of program equivalence. This is due to the fact that equivalence for substitution (known as strong equivalence) and ordinary equivalence are different concepts. The former holds, given programs P and Q, iff P can be faithfully replaced by Q within any context R, while the latter holds iff P and Q pro...

Conditions of information independence are important in information economics and game theory. We present notions of partial independence in Bayesian environments, and study their relationships to notions of common knowledge.

In recent work, Stalnaker proposes a logical framework in which belief is realized as a weakened form of knowledge [30]. Building on Stalnaker’s core insights, and using frameworks developed in [11] and [4], we employ topological tools to refine and, we argue, improve on this analysis. The structure of topological subset spaces allows for a natural distinction between what is known and (roughly...

The AGM postulates [4], [1] are widely regarded to have captured much of what is involved in the process of rational belief revision. Recently however, Parikh [7] observed that despite their success, the AGM postulates are rather liberal in their treatment of the notion of relevance. More precisely, Parikh argues that during belief revision a rational agent does not change her entire belief cor...