A State-Based Regression Formulation for Domains with Sensing Actions<br> and Incomplete Information

TL;DR

This paper introduces a state-based regression method for planning in domains with sensing actions and incomplete information, ensuring soundness and completeness relative to progression-based solutions.

Contribution

It presents a novel regression formulation for binary domains with sensing actions, with proven theoretical soundness and completeness.

Findings

Regression plans are sound and complete with respect to progression.

The approach handles incomplete information and sensing actions effectively.

The method is validated through formal proofs of correctness.

Abstract

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.