This paper discusses system consequence, a central idea in the project to lift the theory of info... more 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.
This paper discusses an axiomatic approach for the integration of ontologies, an approach that ex... more This paper discusses an axiomatic approach for the integration of ontologies, an approach that extends to first order logic a previous approach (Kent 2000) based on information flow. This axiomatic approach is represented in the Information Flow Framework (IFF), a metalevel framework for organizing the information that appears in digital libraries, distributed databases and ontologies (Kent 2001). The paper argues that the integration of ontologies is the two-step process of alignment and unification. Ontological alignment consists of the sharing of common terminology and semantics through a mediating ontology. Ontological unification, concentrated in a virtual ontology of community connections, is fusion of the alignment diagram of participant community ontologies -the quotient of the sum of the participant portals modulo the ontological alignment structure.
It's ease of use and the availability of browsers for various platforms have paved the way for th... more It's ease of use and the availability of browsers for various platforms have paved the way for the enormous popularity that the World Wide Web currently enjoys. In the near future, by providing not only easy access to information, but also means for conducting business transactions, the Web could form the base technology for the information superhighway. In such a large distributed information system, resource discovery becomes a critical problem. Recent developments in resource discovery systems, such as Harvest [BDHMS94b] and Whois++ [DeWe94], provide scalable mechanisms for the identification, location and characterization of networked information resources based upon resource meta-information. However, the Web's vast information space can only be handled effectively, when resources are meaningfully classified into coherent conceptual structures. The automatic classification of resource meta-information is at the heart of the wave system [WAVE94], which employs methods from the mathematical theory of concept analysis to analyze and interactively explore the vast information space defined by wide area resource discovery services. In this paper we discuss these methods by interpreting various synoptic and summary interchange formats for resource meta-information, such as the Harvest SOIF and the Whois++ urc, in terms of basic ideas from concept analysis. In so doing, we advocate concept analysis as a principled approach to effective resource discovery.
This paper discusses an axiomatic approach for the integration of ontologies, an approach that ex... more This paper discusses an axiomatic approach for the integration of ontologies, an approach that extends to first order logic a previous approach (Kent 2000) based on information flow. This axiomatic approach is represented in the Information Flow Framework (IFF), a metalevel framework for organizing the information that appears in digital libraries, distributed databases and ontologies (Kent 2001). The paper argues that the integration of ontologies is the two-step process of alignment and unification. Ontological alignment consists of the sharing of common terminology and semantics through a mediating ontology. Ontological unification, concentrated in a virtual ontology of community connections, is fusion of the alignment diagram of participant community ontologies-the quotient of the sum of the participant portals modulo the ontological alignment structure.
The notions of formal contexts and concept lattices, although introduced by Wille only ten years ... more The notions of formal contexts and concept lattices, although introduced by Wille only ten years ago [Wille], already have proven to be of great utility in various applications such as data analysis and knowledge representation. In this paper we give arguments that Wille's original notion of formal context, although quite appealing in its simplicity, now should be replaced by a more semantic notion. This new notion of formal context entails a modified approach to concept construction. We base our arguments for these new versions of formal context and concept construction upon Wille's philosophical attitude with reference to the intensional aspect of concepts. We give a brief development of the relational theory of formal contexts and concept construction, demonstrating the equivalence of concept-lattice construction [Wille] with the well-known completion by cuts [MacNeille]. Generalization and abstraction of these formal contexts offers a powerful approach to knowledge representation.
This paper, the first step to connect relational databases with systems consequence (Kent [5]), i... more This paper, the first step to connect relational databases with systems consequence (Kent [5]), is concerned with the semantics of relational databases. It aims to to study system consequence in the logical/semantic system of relational databases. The paper, which was inspired by and which extends a recent set of papers on the theory of relational database systems (Spivak [6] [7]), is linked with work on the Information Flow Framework (IFF [9]) connected with the ontology standards effort (SUO), since relational databases naturally embed into first order logic. The database semantics discussed here is concerned with the conceptual level of database architecture. We offer both an intuitive and technical discussion. Corresponding to the notions of primary and foreign keys, relational database semantics takes two forms: a distinguished form where entities are distinguished from relations, and a unified form where relations and entities coincide. The distinguished form corresponds to the theory presented in (Spivak [6]). The unified form, a special case of the distinguished form, corresponds to the theory presented in (Spivak [7]). A later paper will discuss various formalisms of relational databases, such as relational algebra and first order logic, and will complete the description of the relational database logical environment.
Due to the rapid growth of the World Wide Web, resource discovery becomes an increasing problem. ... more Due to the rapid growth of the World Wide Web, resource discovery becomes an increasing problem. As an answer to the demand for information management, a third generation of WorldWide Web tools will evolve: information gathering and processing agents. This paper describes wave (Web Analysis and Visualization Environment), a 3D interface for WorldWide Web information visualization and browsing. It uses the mathematical theory of concept analysis to conceptually cluster objects, and to create a three-dimensional layout of information nodes. So-called "conceptual scales" for attributes, such as location, title, keywords, topic, size, or modification time, provide a formal mechanism that automatically classifies and categorizes documents, creating a conceptual information space. A visualization shell serves as an ergonomically sound user interface for exploring this information space.
This paper, the first step to connect relational databases with systems consequence (Kent [5]), i... more This paper, the first step to connect relational databases with systems consequence (Kent [5]), is concerned with the semantics of relational databases. It aims to to study system consequence in the logical/semantic system of relational databases. The paper, which was inspired by and which extends a recent set of papers on the theory of relational database systems (Spivak [6] [7]), is linked with work on the Information Flow Framework (IFF [9]) connected with the ontology standards effort (SUO), since relational databases naturally embed into first order logic. The database semantics discussed here is concerned with the conceptual level of database architecture. We offer both an intuitive and technical discussion. Corresponding to the notions of primary and foreign keys, relational database semantics takes two forms: a distinguished form where entities are distinguished from relations, and a unified form where relations and entities coincide. The distinguished form corresponds to the theory presented in (Spivak [6]). The unified form, a special case of the distinguished form, corresponds to the theory presented in (Spivak [7]). A later paper will discuss various formalisms of relational databases, such as relational algebra and first order logic, and will complete the description of the relational database logical environment.
This chapter discusses the institutional approach for organizing and maintaining ontologies. The ... more 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 institutio...
Systems, scientific and philosophic, come and go. Each method of limited understanding is at leng... more Systems, scientific and philosophic, come and go. Each method of limited understanding is at length exhausted. In its prime each system is a triumphant success: in its decay it is an obstructive nuisance.
This paper, the first step to connect relational databases with systems consequence (Kent [5]), i... more This paper, the first step to connect relational databases with systems consequence (Kent [5]), is concerned with the semantics of relational databases. It aims to to study system consequence in the logical/semantic system of relational databases. The paper, which was inspired by and which extends a recent set of papers on the theory of relational database systems (Spivak [6] [7]), is linked with work on the Information Flow Framework (IFF [9]) connected with the ontology standards effort (SUO), since relational databases naturally embed into first order logic. The database semantics discussed here is concerned with the conceptual level of database architecture. We offer both an intuitive and technical discussion. Corresponding to the notions of primary and foreign keys, relational database semantics takes two forms: a distinguished form where entities are distinguished from relations, and a unified form where relations and entities coincide. The distinguished form corresponds to the theory presented in (Spivak [6]). The unified form, a special case of the distinguished form, corresponds to the theory presented in (Spivak [7]). A later paper will discuss various formalisms of relational databases, such as relational algebra and first order logic, and will complete the description of the relational database logical environment.
This paper discusses the representation of ontologies in the first-order logical environment FOLE... more This paper discusses the representation of ontologies in the first-order logical environment FOLE (Kent 2013). An ontology defines the primitives with which to model the knowledge resources for a community of discourse (Gruber 2009). These primitives, consisting of classes, relationships and properties, are represented by the ERA (entity-relationship-attribute) data model (Chen 1976). An ontology uses formal axioms to constrain the interpretation of these primitives. In short, an ontology specifies a logical theory. This paper is the second in a series of three papers that provide a rigorous mathematical representation for the ERA data model in particular, and ontologies in general, within the first-order logical environment FOLE. The first two papers show how FOLE represents the formalism and semantics of (many-sorted) first-order logic in a classification form corresponding to ideas discussed in the Information Flow Framework (IFF). In particular, the first paper (Kent 2015) provi...
Tarski's semantic definition of truth is the composition of its extensional and intensional a... more Tarski's semantic definition of truth is the composition of its extensional and intensional aspects. Abstract satisfaction, the core of the semantic definition of truth, is the basis for the theory of institutions (Goguen and Burstall). The satisfaction relation for first order languages (the truth classification), and the preservation of truth by first order interpretations (the truth infomorphism), form a key motivating example in the theory of Information Flow (IF) (Barwise and Seligman). The concept lattice notion, which is the central structure studied by the theory of Formal Concept Analysis (FCA) (Ganter and Wille), is constructed by the polar factorization of derivation. The study of classification structures (IF) and the study of conceptual structures (FCA) provide a principled foundation for the logical theory of knowledge representation and organization. In an effort to unify these two areas, the paper "Distributed Conceptual Structures" (Kent arXiv:1810.047...
This paper discusses system consequence, a central idea in the project to lift the theory of info... more 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 ...
The first-order logical environment {\ttfamily FOLE} provides a rigorous and principled approach ... more The first-order logical environment {\ttfamily FOLE} provides a rigorous and principled approach to distributed interoperable first-order information systems. {\ttfamily FOLE} has been developed in two forms: a classification form and an interpretation form. Two papers represent {\ttfamily FOLE} in a classification form corresponding to ideas of the Information Flow Framework discussed in (Kent~\cite{kent:sem:integ:iff:iswc2003}~\cite{kent:sem:integ:iff:dsp04391}) and (IFF~\cite{iff}): the first paper (Kent~\cite{kent:fole:era:found}) provides a foundation that connects elements of the {\ttfamily ERA} data model (Chen) with components of the first-order logical environment {\ttfamily FOLE}; the second paper (Kent \cite{kent:fole:era:supstruc}) provides a superstructure that extends {\ttfamily FOLE} to the formalisms of first-order logic. The formalisms in the classification form of {\ttfamily FOLE} provide an appropriate framework for developing the \textbf{relational calculus}. Two...
This paper discusses relational operations in the first-order logical environment FOLE. Here we d... more This paper discusses relational operations in the first-order logical environment FOLE. Here we demonstrate how FOLE expresses the relational operations of database theory in a clear and implementable representation. An analysis of the representation of database tables/relations in FOLE reveals a principled way to express the relational operations. This representation is expressed in terms of a distinction between basic components versus composite relational operations. The 9 basic components fall into three categories: reflection (2), Booleans or basic operations (3), and adjoint flow (4). Adjoint flow is given for signatures (2) and for type domains (2), which are then combined into full adjoint flow. The basic components are used to express various composite operations, where we illustrate each of these with a flowchart. Implementation of the composite operations is then expressed in an input/output table containing four parts: constraint, construction, input, and output. We expl...
This presentation discusses a new, modular, more mature architecture for the Information Flow Fra... more This presentation discusses a new, modular, more mature architecture for the Information Flow Framework (IFF). The IFF uses institution theory as a foundation for the semantic integration of ontologies. It represents metalogic, and as such operates at the structural level of ontologies. The content, form and experience of the IFF could contribute to the development of a standard ontology for category theory. The foundational aspect of the IFF helps to explain the relationship between the fundamental concepts of set theory and category theory. The development of the IFF follows two design principles: conceptual warrant and categorical design. Both are limitations of the logical expression. Conceptual warrant limits the content of logical expression, by requiring us to justify the introduction of new terminology (and attendant axiomatizations). Categorical design limits the form of logical expression (of all mathematical concepts and constraints) to atomic expressions: declarations, e...
This paper begins the discussion of how the Information Flow Framework can be used to provide a p... more This paper begins the discussion of how the Information Flow Framework can be used to provide a principled foundation for the metalevel (or structural level) of the Standard Upper Ontology (SUO). This SUO structural level can be used as a logical framework for manipulating collections of ontologies in the object level of the SUO or other middle level or domain ontologies. From the Information Flow perspective, the SUO structural level resolves into several metalevel ontologies. This paper discusses a KIF formalization for one of those metalevel categories, the Category Theory Ontology. In particular, it discusses its category and colimit sub-namespaces.
In this paper we introduce the olog, or ontology log, a category-theoretic model for knowledge re... more In this paper we introduce the olog, or ontology log, a category-theoretic model for knowledge representation (KR). Grounded in formal mathematics, ologs can be rigorously formulated and cross-compared in ways that other KR models (such as semantic networks) cannot. An olog is similar to a relational database schema; in fact an olog can serve as a data repository if desired. Unlike database schemas, which are generally difficult to create or modify, ologs are designed to be user-friendly enough that authoring or reconfiguring an olog is a matter of course rather than a difficult chore. It is hoped that learning to author ologs is much simpler than learning a database definition language, despite their similarity. We describe ologs carefully and illustrate with many examples. As an application we show that any primitive recursive function can be described by an olog. We also show that ologs can be aligned or connected together into a larger network using functors. The various methods...
The Information Flow Framework (IFF) is a descriptive category metatheory currently under develop... more The Information Flow Framework (IFF) is a descriptive category metatheory currently under development, which is being offered as the structural aspect of the Standard Upper Ontology (SUO). The architecture of the IFF is composed of metalevels, namespaces and meta-ontologies. The main application of the IFF is institutional: the notion of institutions and their morphisms are being axiomatized in the upper metalevels of the IFF, and the lower metalevel of the IFF has axiomatized various institutions in which semantic integration has a natural expression as the colimit of theories.
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Papers by Robert Kent