Time-Slice Rationality and Self-Locating Belief

The epistemology of self-locating belief concerns itself with how rational agents ought to respond to certain kinds of indexical information. I argue that those who endorse the thesis of Time-Slice Rationality ought to endorse a particular view about the epistemology of self-locating belief, according to which ‘essentially indexical’ information is never evidentially relevant to non-indexical matters. I close by offering some independent motivations for endorsing Time-Slice Rationality in the context of the epistemology of self-locating belief

Belief change in branching time: AGM-consistency and iterated revision

We study belief change branching-time structures. First, we identify a property of branching-time frames that is equivalent to AGM-consistency, which is defined as follows. A frame is AGM-consistent if the partial belief revision function associated with an arbitrary state-instant pair and an arbitrary model based on that frame can be extended to a full belief revision function that satisfies the AGM postulates. Second, we provide a set of modal axioms that characterize the class of AGM-consistent frames within the modal logic introduced in [Bonanno, Axiomatic characterization of the AGM theory of belief revision in a temporal logic, Artificial Intelligence, 2007]. Third, we introduce a generalization of AGM belief revision functions that allows a clear statement of principles of iterated belief revision and discuss iterated revision both semantically and syntactically.iterated belief revision, branching time, information, belief, modal logic, AGM belief revision

Four Logics for Minimal Belief Revision

It is natural to think of belief revision as the interaction of belief and information over time. Thus branching-time temporal logic seems a natural setting for a theory of belief revision. We propose a logic based on three modal operators: a belief operator, an information operator and a next-time operator. Four logics of increasing strength are proposed. The first is a logic that captures the most basic notion of minimal belief revision. The second characterizes the qualitative content of Bayes' rule. The third provides an axiomatization of the AGM theory of belief revision and the fourth provides a characterization of the notion of plausibility ordering of the set of possible worlds.

Axiomatization of the AGM theory of belief revision in a temporal logic

It is natural to think of belief revision as the interaction of belief and information over time. Thus branching-time temporal logic seems a natural setting for a theory of belief revision. We propose two extensions of a modal logic that, besides the ""next-time"" temporal operator, contains a belief operator and an information operator. The first logic is shown to provide an axiomatization of the first six postulates of the AGM theory of belief revision, while the second, stronger, logic provides an axiomatization of the full set of AGM postulates.Belief revision, information, temporal logic, AGM theory

Modeling Belief in Dynamic Systems, Part II: Revision and Update

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.Comment: See http://www.jair.org/ for other files accompanying this articl