A Graphical Model-Based Representation for Classical AI Plans using Category Theory

Angeline Aguinaldo, William Regli

Keywords: category theory, PDDL, model-based representation, explainable ai

TL;DR: The compositional property and graphical syntax described in category theory can be used to represent PDDL solutions in the context of the domain file to improve comprehensibility.

Abstract: Classical AI planners provide solutions to planning problems in the form of long and opaque text outputs. To aid in the generalization of planning solutions, it is necessary to have a rich and comprehensible representation for both human and computers beyond the current line-by-line text notation. In particular, it is desirable to encode the trace of literals throughout the plan to capture the dependencies between actions selected. The approach of this paper is to view the actions as maps between literals and the selected plan as a composition of those maps. The mathematical theory, called category theory, provides the relevant structures for capturing maps, their compositions, and maps between compositions. We employ this theory to propose an algorithm agnostic, model-based representation for domains, problems, and plans expressed in the commonly used planning description language, PDDL. This category theoretic representation is accompanied by a graphical syntax in addition to a linear notation, similar to algebraic expressions, that can be used to infer literals used at every step of the plan. This provides the appropriate constructive abstraction and facilitates comprehension for human operators. In this paper, we demonstrate this on a plan with the Blocksworld domain.