We present a state-based regression function for planning domains where an agent does not have complete information and may have sensing actions. We consider binary domains and employ a three-valued characterization of domains with sensing actions to define the regression function. We prove the soundness and completeness of our regression formulation with respect to the definition of progression. More specifically, we show that (i) a plan obtained through regression for a planning problem is indeed a progression solution of that planning problem, and that (ii) for each plan found through progression, using regression one obtains that plan or an equivalent one.

• 03B25 - Decidability of theories and sets of sentences
• 03B35 - Mechanization of proofs and logical operations
• 68T20 - Problem solving in the context of artificial intelligence (heuristics, search strategies, etc.)