A Uniform Abstraction Framework for Generalized Planning

Abstract

Generalized planning aims at finding a general solution for a set of similar planning problems. Abstractions are widely used to solve such problems. However, the connections among these abstraction works remain vague. Thus, to facilitate a deep understanding and further exploration of abstraction approaches for generalized planning, it is important to develop a uniform abstraction framework for generalized planning. Recently, Banihashemi et al. proposed an agent abstraction framework based on the situation calculus. However, expressiveness of such an abstraction framework is limited. In this paper, by extending their abstraction framework, we propose a uniform abstraction framework for generalized planning. We formalize a generalized planning problem as a triple of a basic action theory, a trajectory constraint, and a goal. Then we define the concepts of sound abstractions of a generalized planning problem. We show that solutions to a generalized planning problem are nicely related to those of its sound abstractions. We also define and analyze the dual notion of complete abstractions. Finally, we review some important abstraction works for generalized planning and show that they can be formalized in our framework.

Automated Verification of Propositional Agent Abstraction for Classical Planning via CTLK Model Checking

“…Inspired by sound abstraction and complete abstraction for situation calculus models [Cui, Liu, and Luo 2021], we define sound abstraction and complete abstraction for LTSs. Definition 9.…”

Abstracting Noisy Robot Programs

“…Similarly, Saribatur and Eiter (2021) use abstraction in Answer Set Programming to reduce the search space, improving solver performance. Cui, Liu, and Luo (2021) leverage abstraction for generalized planning, i.e., for finding general solutions for a set of similar planning problems. Abstraction has also been used to analyze causal models (Rubenstein et al 2017;Banihashemi, Khan, and Soutchanski 2022).…”