Belief Base Revision Research Articles

Toward credible belief base revision

This paper deals with belief base revision, a form of belief change which consists in restoring consistency with the intention of incorporating a new piece of information from the environment, while minimally modifying the agent's belief state represented by a finite set of propositional formulas. In an effort to guarantee more reliability and rationality for real applications while performing revision, we come up with the idea of credible belief base revision. We define two new formula-based revision operators using tools offered by evidence theory. These operators, uniformly presented in the same spirit as [92,13], stem from consistent sub-bases maximal with respect to credibility instead of set inclusion or cardinality. Logical properties and productivity of inference from these operators are established, along with complexity results.

Iterated Belief Base Revision: A Dynamic Epistemic Logic Approach

AGM’s belief revision is one of the main paradigms in the study of belief change operations. In this context, belief bases (prioritised bases) have been largely used to specify the agent’s belief state - whether representing the agent’s ‘explicit beliefs’ or as a computational model for her belief state. While the connection of iterated AGM-like operations and their encoding in dynamic epistemic logics have been studied before, few works considered how well-known postulates from iterated belief revision theory can be characterised by means of belief bases and their counterpart in dynamic epistemic logic. This work investigates how priority graphs, a syntactic representation of preference relations deeply connected to prioritised bases, can be used to characterise belief change operators, focusing on well-known postulates of Iterated Belief Change. We provide syntactic representations of belief change operators in a dynamic context, as well as new negative results regarding the possibility of representing an iterated belief revision operation using transformations on priority graphs.

Against Grue Mysteries

The paper develops an inductive extension of AGM-style belief base revision theory with the aim of formally implementing Freitag’s (Philos Q 65(259):254–267, 2015, Dialectica 70(2):185–200, 2016) solution to Goodman’s paradox. It shows that the paradox dissolves once belief revision takes place on inductively closed belief bases, rather than on belief sets.

On Revising Fuzzy Belief Bases

We look at the problem of revising fuzzy belief bases, i.e., belief base revision in which both formulas in the base as well as revisioninput formulas can come attached with varying truth-degrees. Working within a very general framework for fuzzy logic which is able to capture certain types of uncertainty calculi as well as truth-functional fuzzy logics, we show how the idea of rational change from crisp base revision, as embodied by the idea of partial meet (base) revision, can be faithfully extended to revising fuzzy belief bases. We present and axiomatise an operation of partial meet fuzzy base revision and illustrate how the operation works in several important special instances of the framework.

Relevance sensitive belief structures

We propose a new relevance sensitive model for representing and revising belief structures, which relies on a notion of partial language splitting and tolerates some amount of inconsistency while retaining classical logic. The model preserves an agent's ability to answer queries in a coherent way using Belnap's fourdvalued logic. Axioms analogous to the AGM axioms hold for this new model. The distinction between implicit and explicit beliefs is represented and psychologically plausible, computationally tractable procedures for query answering and belief base revision are obtained.