Generalized planning is about finding plans that solve collections of planning instances, often infinite collections, rather than single instances. Recently it has been shown how to reduce the planning problem for generalized planning to the planning problem for a qualitative numerical problem; the latter being a reformulation that simultaneously captures all the instances in the collection. An important thread of research thus consists in finding such reformulations, or abstractions, automatically. A recent proposal learns the abstractions inductively from a finite and small sample of transitions from instances in the collection. However, as in all inductive processes, the learned abstraction is not guaranteed to be correct for the whole collection. In this work we address this limitation by performing an analysis of the abstraction with respect to the collection, and show how to obtain formal guarantees for generalization. These guarantees, in the form of first-order formulas, may be used to 1) define subcollections of instances on which the abstraction is guaranteed to be sound, 2) obtain necessary conditions for generalization under certain assumptions, and 3) do automated synthesis of complex invariants for planning problems. Our framework is general, it can be extended or combined with other approaches, and it has applications that go beyond generalized planning.

It may (2010) to estimate the probability of each possible goal be that one agent needs to monitor the activities of another based on the difference between the cost of the best plan agent, attempt to assist the other agent, or simply avoid getting for the goal given the observed actions, Cost(G O), and the in the way while performing its own duties. For all of cost of the best plan for the goal without the observed actions, these cases the agent needs to be able to realize what the Cost(G O). The big difference here is that the observations other agent is doing. In the absence of full and timely communication only indirectly give us probabilities for actions in of plans and goals, goal and plan recognition becomes the plan graph. We therefore first construct a Bayesian Network essential. Many goal recognition techniques allow the (BN) to estimate these action probabilities, and then sequence of observations to be incomplete, but few consider use this probability information in the plan graph to compute the possibility of noisy observations. In practice, this is not expected cost for each goal, given the observations.

Goal Recognition is the task of inferring an actor's goals given some or all of the actor's observed actions. There is considerable interest in Goal Recognition for use in intelligent personal assistants, smart environments, intelligent tutoring systems, and monitoring user's needs. In much of this work, the actor's observed actions are compared against a generated library of plans. Recent work by Ramirez and Geffner makes use of AI planning to determine how closely a sequence of observed actions matches plans for each possible goal. For each goal, this is done by comparing the cost of a plan for that goal with the cost of a plan for that goal that includes the observed actions. This approach yields useful rankings, but is impractical for real-time goal recognition in large domains because of the computational expense of constructing plans for each possible goal. In this paper, we introduce an approach that propagates cost and interaction information in a plan graph, and uses this information to estimate goal probabilities. We show that this approach is much faster, but still yields high quality results.