Planning with epistemic goals has received attention from both the dynamic logic and planning communities. In the single-agent case, under the epistemic closed-world assumption (ECWA), epistemic planning can be reduced to contingent planning. However, it is inappropriate to make the ECWA in some epistemic planning scenarios, for example, when the agent is not fully introspective, or when the agent wants to devise a generic plan that applies to a wide range of situations. In this paper, we propose a complete single-agent epistemic planner without the ECWA. We identify two normal forms of epistemic formulas: weak minimal epistemic DNF and weak minimal epistemic CNF, and present the progression and entailment algorithms based on these normal forms. We adapt the PrAO algorithm for contingent planning from the literature as the main planning algorithm and develop a complete epistemic planner called EPK. Our experimental results show that EPK can generate solutions effectively for most of the epistemic planning problems we have considered including those without the ECWA.

In contingent planning under partial observability with sensing actions, agents actively use sensing to discover meaningful facts about the world. For this class of problems the solution can be represented as a plan tree, branching on various possible observations. Recent successful approaches translate the partially observable contingent problem into a non-deterministic fully observable problem, and then use a planner for non-deterministic planning. While this approach has been successful in many domains, the translation may become very large, encumbering the task of the non-deterministic planner. In this paper we suggest a different approach - using an online contingent solver repeatedly to construct a plan tree. We execute the plan returned by the online solver until the next observation action, and then branch on the possible observed values, and replan for every branch independently. In many cases a plan tree can be exponential in the number of state variables, but still, the tree has a structure that allows us to compactly represent it using a directed graph. We suggest a mechanism for tailoring such a graph that reduces both the computational effort and the storage space. Furthermore, unlike recent state of the art offline planners, our approach is not bounded to a specific class of contingent problems, such as limited problem width, or simple contingent problems. We present a set of experiments, showing our approach to scale better than state of the art offline planners.

The main focus of our work is the use of classical planning algorithms in service of more complex problems of planning under uncertainty. In particular, we are exploring compilation techniques that allow us to reduce some probabilistic planning problems into variants of classical planning, such as metric planning,resource-bounded planning, and cost-bounded suboptimal planning. Currently, our initial work focuses on \emph{conformant probabilistic planning}. We intend toimprove our current methods by improving our compilation methods, but also by improving the ability of current planners to handle the special features ofour compiled problems. Then, we hope to extend these techniques to handle more complex probabilistic settings, such as problems with stochastic actions andpartial observability.

The problem of on-line planning in partially observable settings involves two problems: keeping track of beliefs about the environment and selecting actions for achieving goals. While the two problems are computationally intractable in the worst case, significant progress has been achieved in recent years through the use of suitable reductions. In particular, the state-of-the-art CLG planner is based on a translation that maps deterministic partially observable problems into fully observable non-deterministic ones. The translation, which is quadratic in the number of problem fluents and gets rid of the belief tracking problem, is adequate for most benchmarks, and it is in fact complete for problems that have width 1. The more recent K-replanner uses translations that are linear, one for keeping track of beliefs and the other for selecting actions using off-the-shelf classical planners. As a result, the K-replanner scales up better but it is not as general. In this work, we combine the benefits of the two approaches - the scope of the CLG planner and the efficiency of the Kreplanner. The new planner, called LW1, is based on a translation that is linear but complete for width-1 problems. The scope and scalability of the new planner is evaluated experimentally by considering the existing benchmarks and new problems.

It has been shown recently that the complexity of belief tracking in deterministic conformant and contingent planning is exponential in a width parameter that is often bounded and small. In this work, we introduce a new width notion that applies to non-deterministic conformant and contingent problems as well. We also develop a belief tracking algorithm for non-deterministic problems that is exponential in the problem width, analyze the width of non-deterministic benchmarks, compare the new notion to the previous one over deterministic problems, and present experimental results.

This work proposes new approaches to contingent planning using alternative belief state representations extended from those in conformant planning and a new AND/OR forward search algorithm, called PrAO, for contingent solutions. Each representation was implemented in a new contingent planner. The important role of belief state representation has been confirmed by the fact that our planners all outperform other stateof- the-art planners on most benchmarks and the comparison of their performances varies across all the benchmarks even using the same search algorithm PrAO and same unsophisticated heuristic scheme. The work identifies the properties of each representation method that affect the performance.

This paper compares in depth the effectiveness of two conjunctive belief state representations in contingent planning: prime implicates and minimal CNF, a compact form of CNF formulae, which were initially proposed in conformant planning research (To et al. 2010a; 2010b). Similar to the development of the contingent planner CNFct for minimal CNF (To et al. 2011b), the present paper extends the progression function for the prime implicate representation in (To et al. 2010b) for computing successor belief states in the presence of incomplete information to handle non-deterministic and sensing actions required in contingent planning. The idea was instantiated in a new contingent planner, called PIct, using the same AND/OR search algorithm and heuristic function as those for CNFct. The experiments show that, like CNFct, PIct performs very well in a wide range of benchmarks. The study investigates the advantages and disadvantages of the two planners and identifies the properties of each representation method that affect the performance.

Planning under uncertainty is one of the most general and hardest problems considered in the area of planning. Uncertainty can take the form of incomplete information, wrong information, multiple action outcomes, and varying action durations. My doctoral thesis concentrates on planning with incomplete knowledge and multiple action outcomes, specifically conformant planning and contingent planning. These problems have attracted the attention of many researchers, resulting in numerous sophisticated planners of different approaches. However, those planners cannot scale up well on the size of problems, mostly due to the representation methods employed in the planners. The doctoral research work provides a systematic methodology for dealing with planning under uncertainty, focusing on the representation of belief states that can be used in a forward search paradigm in the belief space for solutions. A good representation should be compact so that a planner implementing it can perform and scale up well as the larger the formulae, the more the computation and the more the memory consumption (i.e., the slower the system and the less the scalability). On the other hand, it should also have properties that allow for definition of an efficient transition function for computing successor belief states, e.g., checking satisfaction in a DNF formula is easy. Defining a direct complete transition function in presence of incomplete information for a general representation, other than the belief state, is particularly hard due to conditional action effects. To address this, I propose a generic abstract algorithm, called GAA, for defining such function given an arbitrary representation. Using the GAA algorithm, my doctoral thesis investigates the properties of different logical formulae and their applicability in planning under uncertainty as a belief state representation. The results obtained so far are very promissing as the research work developed several highly competitive planners which outperform other state-of-the-art planners in most benchmarks available in the literature.

This paper investigates the effectiveness of two state representations, CNF and DNF, in contingent planning. To this end, we developed a new contingent planner, called CNFct, using the AND/OR forward search algorithm PrAO [To et al., 2011] and an extension of the CNF representation of [To et al., 2010] for conformant planning to handle nondeterministic and sensing actions for contingent planning. The study uses CNFct and DNFct [To et al., 2011] and proposes a new heuristic function for both planners. The experiments demonstrate that both CNFct and DNFct offer very competitive performance in a large range of benchmarks but neither of the two representations is a clear winner over the other. The paper identifies properties of the representation schemes that can affect their performance on different problems.