Nonmonotonic Probabilistic Logics between Model-Theoretic Probabilistic Logic and Probabilistic Logic under Coherence

Recently, it has been shown that probabilistic entailment under coherence is weaker than model-theoretic probabilistic entailment. Moreover, probabilistic entailment under coherence is a generalization of default entailment in System P. In this paper, we continue this line of research by presenting probabilistic generalizations of more sophisticated notions of classical default entailment that lie between model-theoretic probabilistic entailment and probabilistic entailment under coherence. That is, the new formalisms properly generalize their counterparts in classical default reasoning, they are weaker than model-theoretic probabilistic entailment, and they are stronger than probabilistic entailment under coherence. The new formalisms are useful especially for handling probabilistic inconsistencies related to conditioning on zero events. They can also be applied for probabilistic belief revision. More generally, in the same spirit as a similar previous paper, this paper sheds light on exciting new formalisms for probabilistic reasoning beyond the well-known standard ones.Comment: 10 pages; in Proceedings of the 9th International Workshop on Non-Monotonic Reasoning (NMR-2002), Special Session on Uncertainty Frameworks in Nonmonotonic Reasoning, pages 265-274, Toulouse, France, April 200

Probabilistic Default Reasoning with Conditional Constraints

We propose a combination of probabilistic reasoning from conditional constraints with approaches to default reasoning from conditional knowledge bases. In detail, we generalize the notions of Pearl's entailment in system Z, Lehmann's lexicographic entailment, and Geffner's conditional entailment to conditional constraints. We give some examples that show that the new notions of z-, lexicographic, and conditional entailment have similar properties like their classical counterparts. Moreover, we show that the new notions of z-, lexicographic, and conditional entailment are proper generalizations of both their classical counterparts and the classical notion of logical entailment for conditional constraints.Comment: 8 pages; to appear in Proceedings of the Eighth International Workshop on Nonmonotonic Reasoning, Special Session on Uncertainty Frameworks in Nonmonotonic Reasoning, Breckenridge, Colorado, USA, 9-11 April 200

REBA: A Refinement-Based Architecture for Knowledge Representation and Reasoning in Robotics

This paper describes an architecture for robots that combines the complementary strengths of probabilistic graphical models and declarative programming to represent and reason with logic-based and probabilistic descriptions of uncertainty and domain knowledge. An action language is extended to support non-boolean fluents and non-deterministic causal laws. This action language is used to describe tightly-coupled transition diagrams at two levels of granularity, with a fine-resolution transition diagram defined as a refinement of a coarse-resolution transition diagram of the domain. The coarse-resolution system description, and a history that includes (prioritized) defaults, are translated into an Answer Set Prolog (ASP) program. For any given goal, inference in the ASP program provides a plan of abstract actions. To implement each such abstract action, the robot automatically zooms to the part of the fine-resolution transition diagram relevant to this action. A probabilistic representation of the uncertainty in sensing and actuation is then included in this zoomed fine-resolution system description, and used to construct a partially observable Markov decision process (POMDP). The policy obtained by solving the POMDP is invoked repeatedly to implement the abstract action as a sequence of concrete actions, with the corresponding observations being recorded in the coarse-resolution history and used for subsequent reasoning. The architecture is evaluated in simulation and on a mobile robot moving objects in an indoor domain, to show that it supports reasoning with violation of defaults, noisy observations and unreliable actions, in complex domains.Comment: 72 pages, 14 figure