The Information Flow Framework: New architecture (1109.0983v1)

Abstract: This presentation discusses a new, modular, more mature architecture for the Information Flow Framework (IFF). The IFF uses institution theory as a foundation for the semantic integration of ontologies. It represents metalogic, and as such operates at the structural level of ontologies. The content, form and experience of the IFF could contribute to the development of a standard ontology for category theory. The foundational aspect of the IFF helps to explain the relationship between the fundamental concepts of set theory and category theory. The development of the IFF follows two design principles: conceptual warrant and categorical design. Both are limitations of the logical expression. Conceptual warrant limits the content of logical expression, by requiring us to justify the introduction of new terminology (and attendant axiomatizations). Categorical design limits the form of logical expression (of all mathematical concepts and constraints) to atomic expressions: declarations, equations or relational expressions. The IFF is a descriptive category metatheory. It is descriptive, since it follows the principle of conceptual warrant; it is categorical, since it follows the principle of categorical design; and it is a metatheory, since it provides a framework for all theories.