Proceedings of the Twenty-Ninth International Conference on Automated Planning and Scheduling (ICAPS 2019) Symbolic Planning with Axioms David Speck University of Freiburg speckd@cs.uni-freiburg.de Florian Geißer Research School of CS, ANU florian.geisser@anu.edu.au Abstract Axioms are an extension for classical planning models that allow for modeling complex preconditions and goals expo- nentially more compactly. Although axioms were introduced in planning more than a decade ago, modern planning tech- niques rarely support axioms, especially in cost-optimal plan- ning. Symbolic search is a popular and competitive opti- mal planning technique based on the manipulation of sets of states. In this work, we extend symbolic search algorithms to support axioms natively. We analyze different ways of en- coding derived variables and axiom rules to evaluate them in a symbolic representation. We prove that all encodings are sound and complete, and empirically show that the presented approach outperforms the previous state of the art in cost- optimal classical planning with axioms. Introduction In classical planning, most planners support models that de- scribe a state of the world in terms of Boolean or finite- domain variables, such as STRIPS (Fikes and Nilsson 1971) or SAS+ (Bäckström and Nebel 1995). The aim of such planners is to find a sequence of operations that transforms a specified initial state into a desired goal. While these models are already very general, more expressive models like ADL with conditional effects (Pednault 1989) or state-dependent action costs (Geißer, Keller, and Mattmiller 2015) allow a more compact representation of a planning problem. Ax- ioms are another example of such a model extension which allow for modeling complex preconditions and goals com- pactly. Planning with axioms introduces a set of derived variables whose values are not directly influenced by the ac- tions, but are derived from the values of other variables us- ing a set of logical axioms. Thiebaux, Hoffmann, and Nebel (2005) argue that axioms are necessary to model real-world problems in a compact and elegant way, as they allow to model complex action preconditions or goals that cannot be expressed in the original formalism without incurring a super-polynomial growth of plan length or domain descrip- tion size. Although axioms are a feature of PDDL (McDermott et al. 1998; Hoffmann and Edelkamp 2005), the common lan- guage for modeling planning tasks, modern planning tech- Copyright C 2019, Association for the Advancement of Artificial Intelligence (www.aaai.org). All rights reserved. Robert Mattmüller University of Freiburg mattmuel@cs.uni-freiburg.de Álvaro Torralba Saarland University torralba@cs.uni-saarland.de niques rarely support axioms, especially in cost-optimal planning. Most admissible heuristics commonly used in A* search, one of the most prominent approaches to cost- optimal planning, are not defined for their use with ax- ioms. The few heuristics that support axioms are based on naive relaxations that consider axioms as zero-cost actions, which may greatly reduce the informativeness of the heuris- tics. One exception is the axiom-aware delete relaxation heuristic, obtained by applying a model for state constraints to planning with axioms (Ivankovic and Haslum 2015; Haslum et al. 2018). While these heuristics are