The Planning Process: Mappings between State and Decision Spaces

The planning process is modelled as an information processing system. The inputs to the system comprise observations of the state of the environment, and the outputs are goals and plans to guide actions in the environment. The processor consists of two interacting subsystems: the one carrying descriptions about material states is called the state space and the other holding information about decisions and values is called the decision space. The memory of the planning system stores its history: its ‘experiences’ both of its external and of its internal environments. The ‘facts’ which inform the planning system are represented as a relation between the state space and the decision space. Such a relation induces a pair of functions which is known to form a Galois connection between two sets. Compositions of these two functions are closure operators which define closure systems on the decision space and the state space, respectively. Each of these functions when restricted to the closure systems is an isomorphism. Isomorphic elements are paired together and the collection of such pairs forms a Galois lattice. A Galois lattice presents to the planners an overall view of the current ‘situation’ of the environment. Each element of the Galois lattice relates a set of ‘systems’ represented in the state space to a set of ‘values’ used to evaluate ‘systems’ in the decision space. The planning process is then viewed as a transformation of the Galois lattice which represents the current ‘situation’ to another Galois lattice which represents the desirable ‘situation’.