Before revision:  The formulation of our vector arithmetic closely reflects the logical structure originating from the symbolic sequential decision making formalism ( classical/STRIPS planning ). Contrary to the conventional wisdom that discrete representation cannot perform well due to the lack of ability to capture the uncertainty, our representation is competitive against the continuous representations in several downstream tasks. We demonstrate that our embedding is directly compatible with the symbolic, classical planning solvers by performing a "paraphrasing" task.
After revision:  The formulation of our vector arithmetic closely reflects the logical structure originating from the symbolic sequential decision making formalism ( classical/STRIPS planning formalism. This makes the embedding directly compatible with the symbolic, classical planning solvers by performing a "paraphrasing" task.