The anticipatory and systemic adjointness of e-science computation on the grid

Information systems are anticipatory systems providing knowledge of the real world. If e-science is to operate reactively across the Grid it needs to be integrable with other information systems and e-commerce. Theory suggests that four strong-anticipatory levels of computational types are sufficient to provide ultimate systemic closure with a single strong anticipation. Between the four levels are three layers of adjoint functors that relate each type-pair. A free functor allows selection of a target type at a lower level and its right adjoint determines the higher-level type. Because of the uniqueness a higher-level anticipates a lower level and a lower level a higher. Type anticipation can be provided by left (F) or right (G) adjoint functors (F-1 G). These however are weak anticipation. Strong anticipation needs-both left and right adjoints at each level or by composition of adjoints for the system as a whole (F) over bar(F) over barF -1 G (G) over bar(G) over bar. The ISO standard for the Information Resource Dictionary System (IRDS) is itself an anticipatory system with this four-level architecture of universal types which can be used for design of interoperability across the Grid. The sufficiency of middleware tools for the Grid can be anticipated by reference to this same architecture. Thus for instance RDF, the Resource Description Framework, for the markup language XML seems to lack the top level abstraction of IRDS and to have only left-adjoint functionality and therefore not to qualify as a strong anticipatory system.