We consider a model-based diagnosis approach to the diagnosis of plans. Here, a plan performed by some agent(s) is considered as a system to be diagnosed. We introduce a simple formal model of plans and plan execution where it is assumed that the execution of a plan can be monitored by making partial observations of plan states. These observed states are used to compare them with states predicted based on (normal) plan execution. Deviations between observed and predicted states can be explained by qualifying some plan steps in the plan as behaving abnormally. A diagnosis is a subset of plan steps qualified as abnormal that can be used to restore the compatibility between the predicted and the observed partial state. Besides minimum and subset minimal diagnoses, we argue that in plan-based diagnosis maximum informative diagnoses should be considered as preferred diagnoses, too. The latter ones are diagnoses that make the strongest predictions with respect to partial states to be observed in the future. We show that in contrast to minimum diagnoses, finding a (subset minimal) maximum informative diagnosis can be achieved in polynomial time. Finally, we show how these diagnoses can be found efficiently if the plan is distributed over a number of agents.

We discuss the application of Model Based Diagnosis in agent-based planning. We model a plan as a system to be diagnosed and assume that agents can monitor the execution of the plan by making partial observations during plan execution. These observations are used by the agents to explain plan deviations (errors) by qualifying some action instances as behaving abnormally. We prefer those qualifications that are maximum informative, i.e. explain as much as possible. Since in a plan several instances of the same action might occur, an error occurring in one instance might be used to predict the occurrence of the same error in an action instance to be executed later on. To account for such correlations, we introduce causal rules to generate diagnoses from action instances qualified as abnormally and we introduce Pareto minimal causal diagnoses as the right extension of classical minimal diagnoses.Next, we consider the multi-agent perspective where each agent is responsible for a part of the total plan, we show how plan-diagnoses of these partial plans are related to diagnoses of the total plan and how global diagnoses can be obtained in a distributed way.

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Diagnosis of plan failures is an important subject in both single-and multi-agent planning. Plan diagnosis can be used to deal with plan failures in three ways: (i) to provide information necessary for the adjustment of the current plan or for the development of a new plan, (ii) to point out which equipment and/or agents should be repaired or adjusted to avoid further violation of the plan execution, and (iii) to identify the agents responsible for planexecution failures. We introduce two general types of plan diagnosis: primary plan diagnosis identifying the incorrect or failed execution of actions, and secondary plan diagnosis that identifies the underlying causes of the faulty actions. Furthermore, three special cases of secondary plan diagnosis are distinguished, namely agent diagnosis, equipment diagnosis and environment diagnosis.

The interest in the concept of entropic forces has risen considerably since E. Verlinde proposed to interpret the force in Newton s second law and Gravity as entropic forces [1]. Brownian motion, the motion of a small particle (pollen) driven by random impulses from the surrounding molecules, may be the first example of a stochastic process in which such forces are expected to emerge. In this note it is shown that at least two types of entropic force can be identified in the case of 3D Brownian motion (or random walk). This yields simple derivations of known results of Brownian motion, Hook s law and, applying an external (non-radial) force, Curie s law and the Langevin-Debye equation.Comment: 11 pages, 1 figur