Independence -- the study of what is relevant to a given problem of reasoning -- has received an increasing attention from the AI community. In this paper, we consider two basic forms of independence, namely, a syntactic one and a semantic one. We show features and drawbacks of them. In particular, while the syntactic form of independence is computationally easy to check, there are cases in which things that intuitively are not relevant are not recognized as such. We also consider the problem of forgetting, i.e., distilling from a knowledge base only the part that is relevant to the set of queries constructed from a subset of the alphabet. While such process is computationally hard, it allows for a simplification of subsequent reasoning, and can thus be viewed as a form of compilation: once the relevant part of a knowledge base has been extracted, all reasoning tasks to be performed can be simplified.

We study the logic of comparative concept similarity $\CSL$ introduced by Sheremet, Tishkovsky, Wolter and Zakharyaschev to capture a form of qualitative similarity comparison. In this logic we can formulate assertions of the form " objects A are more similar to B than to C". The semantics of this logic is defined by structures equipped by distance functions evaluating the similarity degree of objects. We consider here the particular case of the semantics induced by \emph{minspaces}, the latter being distance spaces where the minimum of a set of distances always exists. It turns out that the semantics over arbitrary minspaces can be equivalently specified in terms of preferential structures, typical of conditional logics. We first give a direct axiomatisation of this logic over Minspaces. We next define a decision procedure in the form of a tableaux calculus. Both the calculus and the axiomatisation take advantage of the reformulation of the semantics in terms of preferential structures.

We investigate the problem of reasoning in the propositional fragment of MBNF, the logic of minimal belief and negation as failure introduced by Lifschitz, which can be considered as a unifying framework for several nonmonotonic formalisms, including default logic, autoepistemic logic, circumscription, epistemic queries, and logic programming. We characterize the complexity and provide algorithms for reasoning in propositional MBNF. In particular, we show that entailment in propositional MBNF lies at the third level of the polynomial hierarchy, hence it is harder than reasoning in all the above mentioned propositional formalisms for nonmonotonic reasoning. We also prove the exact correspondence between negation as failure in MBNF and negative introspection in Moore's autoepistemic logic.

The study of belief change has been an active area in philosophy and AI. In recent years two special cases of belief change, belief revision and belief update, have been studied in detail. In a companion paper (Friedman & Halpern, 1997), we introduce a new framework to model belief change. This framework combines temporal and epistemic modalities with a notion of plausibility, allowing us to examine the change of beliefs over time. In this paper, we show how belief revision and belief update can be captured in our framework. This allows us to compare the assumptions made by each method, and to better understand the principles underlying them. In particular, it shows that Katsuno and Mendelzon's notion of belief update (Katsuno & Mendelzon, 1991a) depends on several strong assumptions that may limit its applicability in artificial intelligence. Finally, our analysis allow us to identify a notion of minimal change that underlies a broad range of belief change operations including revision and update.