FOLE: The First-order Logical Environment

Abstract

This paper describes the first-order logical environment FOLE. Institutions in general, and logical environments in particular, give equivalent heterogeneous and homogeneous representations for logical systems. As such, they offer a rigorous and principled approach to distributed interoperable information systems via system consequence. Since FOLE is a particular logical environment, this provides a rigorous and principled approach to distributed interoperable first-order information systems. The FOLE represents the formalism and semantics of first-order logic in a classification form. By using an interpretation form, a companion approach defines the formalism and semantics of first-order logical/relational database systems. In a strict sense, the two forms have transformational passages (generalized inverses) between one another. The classification form of first-order logic in the FOLE corresponds to ideas discussed in the Information Flow Framework (IFF). The FOLE representation follows a conceptual structures approach, that is completely compatible with formal concept analysis and information flow.Comment: Conceptual Structures for STEM Research and Education, 20th International Conference on Conceptual Structures, ICCS 2013, Mumbai, India, January 10-12, 2013. Proceedings. Can be found online at: http://link.springer.com/chapter/10.1007%2F978-3-642-35786-2_1