Knowledge updates: Semantics and complexity issues

Abstract

We consider the problem of how an agent's knowledge can be updated. We propose a formal method of knowledge update on the basis of the semantics of modal logic S5. In our method, an update is specified according to the minimal change on both the agent's actual world and knowledge. We discuss general minimal change properties of knowledge update and show that our knowledge update operator satisfies all Katsuno and Mendelzon's update postulates. We characterize several specific forms of knowledge update which have important applications in reasoning about change of agents' knowledge. We also examine the persistence property of knowledge and ignorance associated with knowledge update.

Introspective Forgetting

“…According to (Zhang and Zhou, 2008), we have that ψ → ∀pϕ is valid iff (in their notation) KF orget({ψ}, p) → ϕ is valid-this is similar to the intended generalization to modal logic of the notion Fg(ψ, p) in . In (Zhang and Zhou, 2008) it is also observed that by constraining the ψ-models to those also satisfying ¬Kp∧¬K¬p (some sort of belief expansion following the belief contraction induced by going to all (P −p)-bisimilar models), we can enforce ignorance about p as in (Baral and Zhang, 2005). This relates introspective forgetting to unawareness forgetting.…”

“…Their work was built upon by Lang, Liberatore and Marquis with their in-depth study on the computational costs of transforming theories by variable forgetting , or rather the costs of determining the independence of parts of a theory from specific variables. Baral and Zhang joined this battleground for more explicit operators for knowledge and belief with their (Baral and Zhang, 2005), wherein the result of an agent forgetting a variable results in her (explicit) ignorance of that variable's value, and in (Zhang and Zhou, 2008), in progress, Zhang and Zhou make an original and interesting backtrack to the ideas of (Lin and Reiter, 1994) by suggesting bisimulation invariance except for the forgotten variable, in order to model forgetting. Forgetting has been generalized to logic programs in Zhang et al, 2005;Eiter and Wang, 2006) and to description logics in (Zhao et al, 2007).…”

Postulates for revising BDI structures

“…Notice that we have said nothing about the representation of such structures, which is a key issue if we try to understand the complexity of revision operations (Baral and Zhang 2005). We must first consider how the value and cost functions are represented, since naive representations of them (listing all input/output pairs that define the function) is not practical.…”

“…In fact, update can be a computationally complex process (Baral and Zhang 2005); the point is to factor out this complexity from the analysis of updating an agent's overall mental state, so that we get an understanding of the inherent complexity of this process. 2.…”

A Logic Approach for LTL System Modification

“…They listed ten update operations, based on propositional logic and further characteristics. Recently, the update of the knowledge base is enhanced by the modality update by Baral and Zhang [1]. They discussed knowledge update and its minimal change, based on modal logic S5.…”