Robert E. Kent

Distributed Conceptual Structures

The theory of distributed conceptual structures, as outlined in this paper, is concerned with the distribution and conception of knowledge. It rests upon two related theories, Information Flow and Formal Concept Analysis, which it seeks to unify. Information Flow (IF) [2] is concerned with the distribution of knowledge. The foundations of Information Flow are explicitly based upon the Chu Construction in *- autonomous categories [1] and implicitly based upon the mathematics of closed categories [6]. Formal Concept Analysis (FCA) [3] is concerned with the conception and analysis of knowledge. In this paper, we connect these two studies by categorizing the basic theorem of Formal Concept Analysis, thus extending it to the distributed realm of Information Flow. The main result is the representation of the basic theorem as a categorical equivalence at three different levels of functional and relational constructs. This representation accomplishes a rapprochement between Information Flow and Formal Concept Analysis.

The First-Order Logical Environment

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]).

System Consequence

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.

Formal concept analysis with many-sorted attributes

This paper unites two problem-solving traditions in computer science: (1) constraint-based reasoning; and (2) formal concept analysis. For basic definitions and properties of networks of constraints, we follow the foundational approach of U. Montanari and P. Rossi (1988). This paper advocates distributed relations as a more semantic version of networks of constraints. The theory developed here uses the theory of formal concept analysis pioneered by R. Wille and his colleagues (1992), as a key for unlocking the hidden semantic structure within distributed relations. Conversely, this paper offers distributed relations as a seamless many-sorted extension to the formal contexts of formal concept analysis.<<ETX>>

The Institutional Approach

This chapter discusses the institutional approach for organizing and maintaining ontologies. The theory of institutions was named and initially developed by Joseph Goguen and Rod Burstall. This theory, a metatheory based on category theory, regards ontologies as logical theories or local logics. The theory of institutions uses the category-theoretic ideas of fibrations and indexed categories to develop logical theories. Institutions unite the lattice approach of Formal Concept Analysis of Ganter and Wille with the distributed logic of Information Flow of Barwise and Seligman. The institutional approach incorporates locally the lattice of theories idea of Sowa from the theory of knowledge representation. The Information Flow Framework, which was initiated within the IEEE Standard Upper Ontology project, uses the institutional approach in its applied aspect for the comparison, semantic integration and maintenance of ontologies. This chapter explains the central ideas of the institutional approach to ontologies in a careful and detailed manner.