Belief revision - an axiomatic approach

Belief revision systems aim at keeping a database consistent. They mostly concentrate on how to record and maintain dependencies. We propose an axiomatic system, called MFOT, as a solution to the problem of belief revision. MFOT has a set of proper axioms which selects a set of most plausible and consistent input beliefs. The proposed nonmonotonic inference rule further maintains consistency while generating the consequences of input beliefs. It also permits multiple property inheritance with exceptions. We have also examined some important properties of the proposed axiomatic system. We also propose a belief revision model that is object-centered. The relevance of such a model in maintaining the beliefs of a physician is examined.

Fault identification through the combination of symbolic conflict recognition and Markov Chain-aided belief revision

F. Smith and Q. Shen. Fault identification through the combination of symbolic conflict recognition and Markov Chain-aided belief revision. IEEE Transactions on Systems, Man and Cybernetics, Part A: Systems and Humans, 34(5):649-663, 2004.

Distributed belief revision as applied within a descriptive model of jury deliberations

Belief revision is a well-research topic within AI. We argue that the new model of distributed belief revision as discussed here is suitable for general modelling of judicial decision making, along with extant approach as known from jury research. The new approach to belief revision is of general interest, whenever attitudes to information are to be simulated within a multi-agent environment with agents holding local beliefs yet by interaction with, and influencing, other agents who are deliberating collectively. In the approach proposed, it's the entire group of agents, not an external supervisor, who integrate the different opinions. This is achieved through an election mechanism, The principle of "priority to the incoming information" as known from AI models of belief revision are problematic, when applied to factfinding by a jury. The present approach incorporates a computable model for local belief revision, such that a principle of recoverability is adopted. By this principle, any previously held belief must belong to the current cognitive state if consistent with it. For the purposes of jury simulation such a model calls for refinement. Yet we claim, it constitutes a valid basis for an open system where other AI functionalities (or outer stiumuli) could attempt to handle other aspects of the deliberation which are more specifi to legal narrative, to argumentation in court, and then to the debate among the jurors.

Belief revision as applied within a descriptive model of jury deliberations

Belief revision is a well-researched topic within Artificial Intelligence (AI). We argue that the new model of belief revision as discussed here is suitable for general modelling of judicial decision making, along with the extant approach as known from jury research. The new approach to belief revision is of general interest, whenever attitudes to information are to be simulated within a multi-agent environment with agents holding local beliefs yet by interacting with, and influencing, other agents who are deliberating collectively. The principle of 'priority to the incoming information', as known from AI models of belief revision, is problematic when applied to factfinding by a jury. The present approach incorporates a computable model for local belief revision, such that a principle of recoverability is adopted. By this principle, any previously held belief must belong to the current cognitive state if consistent with it. For the purposes of jury simulation such a model calls for refinement. Yet, we claim, it constitutes a valid basis for an open system where other AI functionalities (or outer stimuli) could attempt to handle other aspects of the deliberation which are more specific to legal narratives, to argumentation in court, and then to the debate among the jurors.

A belief revision framework for revising epistemic states with partial epistemic states

Belief revision performs belief change on an agent’s beliefs when new evidence (either of the form of a propositional formula or of the form of a total pre-order on a set of interpretations) is received. Jeffrey’s rule is commonly used for revising probabilistic epistemic states when new information is probabilistically uncertain. In this paper, we propose a general epistemic revision framework where new evidence is of the form of a partial epistemic state. Our framework extends Jeffrey’s rule with uncertain inputs and covers well-known existing frameworks such as ordinal conditional function (OCF) or possibility theory. We then define a set of postulates that such revision operators shall satisfy and establish representation theorems to characterize those postulates. We show that these postulates reveal common characteristics of various existing revision strategies and are satisfied by OCF conditionalization, Jeffrey’s rule of conditioning and possibility conditionalization. Furthermore, when reducing to the belief revision situation, our postulates can induce Darwiche and Pearl’s postulates C1 and C2.

Rational Partial Choice Functions and Their Application to Belief Revision.

Necessary and sufficient conditions for choice functions to be rational have been intensively studied in the past. However, in these attempts, a choice function is completely specified. That is, given any subset of options, called an issue, the best option over that issue is always known, whilst in real-world scenarios, it is very often that only a few choices are known instead of all. In this paper, we study partial choice functions and investigate necessary and sufficient rationality conditions for situations where only a few choices are known. We prove that our necessary and sufficient condition for partial choice functions boils down to the necessary and sufficient conditions for complete choice functions proposed in the literature. Choice functions have been instrumental in belief revision theory. That is, in most approaches to belief revision, the problem studied can simply be described as the choice of possible worlds compatible with the input information, given an agent’s prior belief state. The main effort has been to devise strategies in order to infer the agents revised belief state. Our study considers the converse problem: given a collection of input information items and their corresponding revision results (as provided by an agent), does there exist a rational revision operation used by the agent and a consistent belief state that may explain the observed results?