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.
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