Belief Change without Compactness

Abstract

Dealing with dynamics is a vital problem in Artificial Intelligence (AI). An intelligent system should be able to perceive and interact with its environment to perform its tasks satisfactorily. To do so, it must sense external actions that might interfere with its tasks, demanding the agent to self-adapt to the environment dynamics. In AI, the field that studies how a rational agent should change its knowledge in order to respond to a new piece of information is known as Belief Change. It assumes that an agent’s knowledge is specified in an underlying logic that satisfies some properties including compactness: if an information is entailed by a set X of formulae, then this information should also be entailed by a finite subset of X. Several logics with applications in AI, however, do not respect this property. This is the case of many temporal logics such as LTL and CTL. Extending Belief Change to these logics would provide ways to devise self-adaptive intelligent systems that could respond to change in real time. This is a big challenge in AI areas such as planning, and reasoning with sensing actions. Extending belief change beyond the classical spectrum has been shown to be a tough challenge, and existing approaches usually put some constraints upon the system, which are either too restrictive or dispense some of the so desired rational behaviour an intelligent system should present. This is a summary of the thesis “Belief Change without Compactness” by Jandson S Ribeiro. The thesis extends Belief Change to accommodate non-compact logics, keeping the rationality criteria and without imposing extra constraints. We provide complete new semantic perspectives for Belief Change by extending to non-compact logics its three main pillars: the AGM paradigm, the KM paradigm and Non-monotonic Reasoning.

Keywords

• Belief Revision
• Belief Update
• Comapctness
• Non-Monotonic Reasoning