FOLE: The First-order Logical Environment

TL;DR

FOLE introduces a rigorous logical environment for first-order logic, enabling heterogeneous and homogeneous representations for distributed, interoperable information systems with formal semantics and transformational capabilities.

Contribution

This paper presents FOLE, the first comprehensive logical environment for first-order logic, integrating formalism, semantics, and transformational mappings for distributed information systems.

Findings

Provides a classification-based formalism for first-order logic

Defines semantics via interpretation form compatible with databases

Establishes transformational passages between formalism and semantics

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.