Multi-Agent Belief Base Revision

We present a generalization of belief base revision to the multi-agent case. In our approach agents have belief bases containing both propositional beliefs and higher-order beliefs about their own beliefs and other agents’ beliefs. Moreover, their belief bases are split in two parts: the mutable part, whose elements may change under belief revision, and the core part, whose elements do not change. We study a belief revision operator inspired by the notion of screened revision. We provide complexity results of model checking for our approach as well as an optimal model checking algorithm. Moreover, we study complexity of epistemic planning formulated in the context of our framework.

System Z for Conditional Belief Bases with Positive and Negative Information

In non-monotonic reasoning, conditional belief bases mostly contain positive information in the form of standard conditionals. However, in practice we are often confronted with negative information, stating that a conditional does \emph{not} hold, i.e. we need a suitable approach for reasoning over belief bases $\Delta$ with positive and negative information. In this paper, we investigate the interaction of positive and negative information in a conditional belief base and establish a property for partitions of $\Delta$ that is equivalent to consistency. Based on this property, we develop a non-trivial extension of system Z for mixed conditional belief bases and provide an algorithm to compute this partition.

Selection Strategies for Inductive Reasoning From Conditional Belief Bases and for Belief Change Respecting the Principle of Conditional Preservation

Given a belief base ∆ consisting of a set of conditionals,there are many different ways an agent may inductivelycomplete the knowledge represented by ∆ to a completeepistemic state; two well-known approaches are given by systemP and system Z, and also each ranking model of ∆ induces afull inference relation. C-representations are special rankingmodels that obey the principle of conditional indifference.Inductive reasoning using c-representations can be done withrespect to all c-representations, with respect to a subclass of,e.g., minimal c-representations, or with respect to singlec-representations. In this paper, we present and investigateselection strategies for determining single c-representations tobe used for inductive reasoning from belief bases. We developaxioms for specifying characteristics of selection strategies.We illustrate which desirable properties, like syntaxsplitting, are ensured by the axioms, and develop constructionsfor obtaining selection strategies satisfying the axioms.Furthermore, we also present and study the extension of selectionstrategies to c-revisions that follow the principle ofconditional preservation and that have been employed successfullyin various belief change settings.

Credibility-limited Base Revision: New Classes and Their Characterizations

In this paper we study a kind of operator —known as credibility-limited base revisions— which addresses two of the main issues that have been pointed out to the AGM model of belief change. Indeed, on the one hand, these operators are defined on belief bases (rather than belief sets) and, on the other hand, they are constructed with the underlying idea that not all new information is accepted. We propose twenty different classes of credibility-limited base revision operators and obtain axiomatic characterizations for each of them. Additionally we thoroughly investigate the interrelations (in the sense of inclusion) among all those classes. More precisely, we analyse whether each one of those classes is or is not (strictly) contained in each of the remaining ones.

Choosing What to Believe - New Results in Selective Revision

Selective Revision was proposed by Fermé and Hansson as a belief revision operation in which it is possible to accept only a part of the input information. In this paper, we extend Selective Revision to belief bases and also to logics not closed under negation.