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.

A framework for managing uncertain inputs: An axiomization of rewarding

The success postulate in belief revision ensures that new evidence (input) is always trusted. However, admitting uncertain input has been questioned by many researchers. Darwiche and Pearl argued that strengths of evidence should be introduced to determine the outcome of belief change, and provided a preliminary definition towards this thought. In this paper, we start with Darwiche and Pearl’s idea aiming to develop a framework that can capture the influence of the strengths of inputs with some rational assumptions. To achieve this, we first define epistemic states to represent beliefs attached with strength, and then present a set of postulates to describe the change process on epistemic states that is determined by the strengths of input and establish representation theorems to characterize these postulates. As a result, we obtain a unique rewarding operator which is proved to be a merging operator that is in line with many other works. We also investigate existing postulates on belief merging and compare them with our postulates. In addition, we show that from an epistemic state, a corresponding ordinal conditional function by Spohn can be derived and the result of combining two epistemic states is thus reduced to the result of combining two corresponding ordinal conditional functions proposed by Laverny and Lang. Furthermore, when reduced to the belief revision situation, we prove that our results induce all the Darwiche and Pearl’s postulates as well as the Recalcitrance postulate and the Independence postulate.

Revising Partial Pre-Orders with Partial Pre-Orders: A Unit-Based Revision Framework

Belief revision studies strategies about how agents revise their belief states when receiving new evidence. Both in classical belief revision and in epistemic revision, a new input is either in the form of a (weighted) propositional formula or a total
pre-order (where the total pre-order is considered as a whole).
However, in some real-world applications, a new input can be a partial pre-order where each unit that constitutes the partial pre-order is important and should be considered individually. To address this issue, in this paper, we study how a partial preorder representing the prior epistemic state can be revised by another partial pre-order (the new input) from a different perspective, where the revision is conducted recursively on the individual units of partial pre-orders. We propose different revision operators (rules), dubbed the extension, match, inner and outer revision operators, from different revision points of view. We also analyze several properties for these operators.

Probabilistic Planning in AgentSpeak using the POMDP framework.

AgentSpeak is a logic-based programming language, based on the Belief-Desire-Intention (BDI) paradigm, suitable for building complex agent-based systems. To limit the computational complexity, agents in AgentSpeak rely on a plan library to reduce the planning problem to the much simpler problem of plan selection. However, such a plan library is often inadequate when an agent is situated in an uncertain environment. In this paper, we propose the AgentSpeak+ framework, which extends AgentSpeak with a mechanism for probabilistic planning. The beliefs of an AgentSpeak+ agent are represented using epistemic states to allow an agent to reason about its uncertain observations and the uncertain effects of its actions. Each epistemic state consists of a POMDP, used to encode the agent’s knowledge of the environment, and its associated probability distribution (or belief state). In addition, the POMDP is used to select the optimal actions for achieving a given goal, even when facing uncertainty.