Logical Foundations for the Infrastructure of the Information Market

Abstract

The European knowledge-based economy has a complex product to market to the rest of the world. Techniques of the past, based on the closed-world assumption, have proved useful in many types of local information systems. However, theory and practice suggest that this approach may be inadequate for the infrastructure required. In databases the relational model through SQL has maintained wide dominance in business data processing. However, interoperability between different databases, even when based on the relational model, is proving a major problem. Predicate logic (consistent and complete to first-order) has many advantages for practical application. Interoperability however requires higher order logic as the arguments themselves are relations and functions. Higher order logic in the context of set theory behaves less satisfactorily according to Gödel’s theorems as such logic cannot satisfy all three of soundness, completeness and effectiveness. This may be a fundamental reason why interoperability is proving to be so difficult. This paper looks at underlying problems and suggests that they may be avoided by the use of categorial higher order logic. Cartesian categories are complete, consistent and decidable. They can be employed as an engineering technique to construct a general architecture of interoperability.