. Function composition operator: .
. A projection (p. ).
. The inverse of , i.e. the set of states that map to a given state under (p. ).
. (For a simple projection ). A generalized inverse. Since only maps certain components of S' to S, is s' with those components replaced by their corresponding components in s (p. ).
. For a simple reduction from an environment E' to E, the function mapping an action a from E to the action that implements it in E' (p. ).
. The chain-environment of n states (p. ).
E. An environment.
. G a goal of E and E' uniformly reducible to E. The existential goal of G in E': the set of all E'-states that map to a goal state under some binding (p. ).
. The serial product. The Cartesian product of and in which actions from the two environments must be taken separately (p. ).
. The parallel product. The Cartesian product of and in which actions from the two environments must be taken simultaneously (p. ).
. (E' an environment uniformly reducible to E) The leftmost-ready binding map from E' to E (p. ).
p. A policy.
. The standard policy for single-material environment E and goal G (p. ).
. The singleton environment (the environment with exactly one state). Used to represent a self-resetting tool (p. ).