This paper describes the first-order logical environment FOLE. Institutions in general (Goguen and Burstall [4]), 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 (Kent [6]). 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 (Kent [7]) 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 [12]). The FOLE representation follows a conceptual structures approach, that is completely compatible with formal concept analysis (Ganter and Wille [2]) and information flow (Barwise and Seligman [1]).
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