Harrison-Trainor

AAAI Conferences

Qualitative and quantitative approaches to reasoning about uncertainty can lead to different logical systems for formalizing such reasoning, even when the language for expressing uncertainty is the same. In the case of reasoning about relative likelihood, with statements of the form φ ψ expressing that φ is at least as likely as ψ, a standard qualitative approach using preordered preferential structures yields a dramatically different logical system than a quantitative approach using probability measures. In fact, the standard preferential approach validates principles of reasoning that are incorrect from a probabilistic point of view. However, in this paper we show that a natural modification of the preferential approach yields exactly the same logical system as a probabilistic approach--not using single probability measures, but rather sets of probability measures. Thus, the same preferential structures used in the study of non-monotonic logics and belief revision may be used in the study of comparative probabilistic reasoning based on imprecise probabilities.


Iterated Belief Change Due to Actions and Observations

Journal of Artificial Intelligence Research

In action domains where agents may have erroneous beliefs, reasoning about the effects of actions involves reasoning about belief change. In this paper, we use a transition system approach to reason about the evolution of an agent's beliefs as actions are executed. Some actions cause an agent to perform belief revision while others cause an agent to perform belief update, but the interaction between revision and update can be non-elementary. We present a set of rationality properties describing the interaction between revision and update, and we introduce a new class of belief change operators for reasoning about alternating sequences of revisions and updates. Our belief change operators can be characterized in terms of a natural shifting operation on total pre-orderings over interpretations. We compare our approach with related work on iterated belief change due to action, and we conclude with some directions for future research.


Iterated Belief Change Due to Actions and Observations

Journal of Artificial Intelligence Research

In action domains where agents may have erroneous beliefs, reasoning about the effects of actions involves reasoning about belief change. In this paper, we use a transition system approach to reason about the evolution of an agent's beliefs as actions are executed. Some actions cause an agent to perform belief revision while others cause an agent to perform belief update, but the interaction between revision and update can be non-elementary. We present a set of rationality properties describing the interaction between revision and update, and we introduce a new class of belief change operators for reasoning about alternating sequences of revisions and updates. Our belief change operators can be characterized in terms of a natural shifting operation on total pre-orderings over interpretations. We compare our approach with related work on iterated belief change due to action, and we conclude with some directions for future research.


Iterated Belief Change Due to Actions and Observations

AAAI Conferences

In action domains where agents may have erroneous beliefs, reasoning about the effects of actions involves reasoning about belief change. In this paper, we use a transition system approach to reason about the evolution of an agent's beliefs as actions are executed. Some actions cause an agent to perform belief revision while others cause an agent to perform belief update, but the interaction between revision and update can be nonelementary. We present a set of rationality properties describing the interaction between revision and update, and we introduce a new class of belief change operators for reasoning about alternating sequences of revisions and updates. Our belief change operators can be characterized in terms of a natural shifting operation on total pre-orderings over interpretations. We compare our approach with related work on iterated belief change due to action, and we conclude with some directions for future research.


Dependency-Directed Reconsideration Belief Base Optimization for Truth Maintenance Systems

AAAI Conferences

We define reconsideration, a non-prioritized belief change operation on a finite set of base beliefs. Reconsideration is a hindsight belief change repair that eliminates negative effects caused by the order of previously executed belief change operations. Beliefs that had previously been removed are returned to the base if there no longer are valid reasons for their removal. This might result in less preferred beliefs being removed, and additional beliefs being returned. The end product is an optimization of the belief base, converting the results of a series of revisions to the very base that would have resulted from a batch revision performed after all base beliefs were entered/added. Reconsideration can be done by examining the entire set of all base beliefs (both currently believed and retracted) -- or, if the believed base is consistent, by examining all retracted beliefs for possible return. This, however, is computationally expensive. We present a more efficient, TMSfriendly algorithm, dependency-directed reconsideration (DDR), which can produce the same results by examining only a dynamically determined subset of base beliefs that are actually affected by changes made since the last base optimization process. DDR is an efficient, anytime, belief base optimizing algorithm that eliminates operation order effects.