System Consequence (1810.02929v1)

Abstract: This paper discusses system consequence, a central idea in the project to lift the theory of information flow to the abstract level of universal logic and the theory of institutions. The theory of information flow is a theory of distributed logic. The theory of institutions is abstract model theory. A system is a collection of interconnected parts, where the whole may have properties that cannot be known from an analysis of the constituent parts in isolation. In an information system, the parts represent information resources and the interconnections represent constraints between the parts. System consequence, which is the extension of the consequence operator from theories to systems, models the available regularities represented by an information system as a whole. System consequence (without part-to-part constraints) is defined for a specific logical system (institution) in the theory of information flow. This paper generalizes the idea of system consequence to arbitrary logical systems.