Proof Systems for Planning Under Cautious Semantics

Planning with incomplete knowledge becomes a very active research area since late 1990s. Many logical formalisms introduce sensing actions and conditional plans to address the problem. The action language \(\mathcal{A}_{K}\) invented by Son and Baral is a well-known framework for this purpose. In this paper, we propose so-called cautious and weakly cautious semantics for \(\mathcal{A}_{K}\), in order to allow an agent to generate and execute reliable plans in safety-critical environments. Intuitively speaking, cautious and weakly cautious semantics enable the agent to know exactly what happens after the execution of an action. Computational complexity analysis shows that cautious semantics reduces the reasoning complexity of \(\mathcal{A}_{K}\), it is also worth to point out that many useful domains could still be expressed with this setting. Another important contribution of our work is the development of Hoare style proof systems. These proof systems are served as inference mechanisms for the verification of conditional plans, and proved to be sound and complete. In addition, they could also be used for plan generation, in the sense that constructing a derivation is indeed a procedure to finding a plan. We point out that the proof systems posses a nice property for off-line planning, that is, the agent could generate and store short proofs in her spare time, and perform quick plan query by easily constructing a long proof from the stored shorter ones (under the assumption that sufficient proofs are stored).