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A Knowledge-Level Approach for Effective Acting, Sensing, and Planning, R. Petrick, Ph.D. Thesis, Department of Computer Science, University of Toronto, 2006.

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In this thesis we investigate a "knowledge-level" approach to the problem of modelling an agent's incomplete knowledge, for the purpose of planning or high-level agent control. We investigate two formal accounts of knowledge, action, and sensing in the situation calculus: the Scherl and Levesque (SL) approach that is based on "possible worlds," and the Demolombe and Pozos Parra (DP) approach that utilizes a set of "knowledge fluents." While the SL approach is expressive, reasoning is computationally more expensive; the DP account treats knowledge change as ordinary fluent change, but restricts its representation to primitive knowledge-level assertions. To relate these two accounts we construct "combined action theories," and prove that a set of primitive knowledge assertions remains identical in both accounts after any sequence of actions. We also extend this equivalence to more complex formulae. These results allow us to compile an expressive class of SL theories into equivalent DP theories that avoid the computational drawbacks of possible world reasoning. Moreover, this correspondence gives us a correctness result for the DP treatment of knowledge and action, in terms of possible worlds.

We also describe a new conditional planner called PKS (Planning with Knowledge and Sensing), that works directly at the knowledge level to construct plans with incomplete information and sensing actions. PKS represents its knowledge by using a collection of databases, each of which models a particular type of knowledge. The contents of each database have a fixed, formal translation to a modal logic of knowledge that defines the planner's knowledge state. Actions are modelled as updates to the databases (i.e., the knowledge state), rather than the world state, which differs from other planners. This representation supports features, like functions, that world-level planners often have difficulty working with. We also describe a preliminary procedure for automatically converting DP actions into PKS actions. Together with our SL equivalence results, this transformation provides an important first step towards the goal of compiling world-level actions into equivalent knowledge-level actions usable by PKS. Finally, we demonstrate PKS's expressiveness and efficiency with a series of planning problems that also illustrate the potential of the knowledge-based approach.