Binding. A simple projection (mapping between state-space components of two environments) that acts as a reduction from one environment to another (see section 7.2.1).
Binding map. A mapping from environment states to bindings (see section 7.2.3).
Cartesian product. For sets: 
is the set of
all pairs (a,b) for 
, 
. For environments: an
environment is the Cartesian product of two other environments iff its
state space is the Cartesian product of their state spaces. Since
the set of actions is left open in this definition, there are many
possible ways of forming products, e.g. serial product, parallel
product, uniform extension, etc. (see section 5.1).
Discrete control problem (DCP). An environment and a set of goal states within it (see section 5).
Environment. A state machine, i.e. , a set of possible states and a set of possible actions mapping states to states. The sets of states and actions need not be finite (see section 5).
Focus. An action is focused on a state component if it only alters that component (see section 7.1.3).
Material. An object (environment) whose state space is a chain (see section 7.1).
Policy. A mapping from states to actions; the formalization of an agent's control structure (see section 5).
Projection. A mapping from the state space of one environment to the state space of another (see section 5.2).
Simple projection. A mapping between state spaces that maps state space components of one environment to state space components of another (see section 5.2).
State component. (For environments whose state spaces are Cartesian products) An element of an environment's state-tuple (see section 5.1).
Solution. A policy solves a DCP from an initial state if, when run from that state, it eventually reaches a goal state (see section 5).
Tool. (Roughly) A state component that can be brought to ready state without altering any other state components (see section 7.1.3).
Uniform reducibility. (Roughly) E' is uniformly reducible to E if it consists of multiple copies of E's objects (see section 7.2.1).