arXiv subjects

Robert E. Kent

Publications and source records attributed to Robert E. Kent.

At least 37 records · Page 2Linked to original sources

arXiv2018

Conceptual Analysis of Hypertext

In this chapter tools and techniques from the mathematical theory of formal concept analysis are applied to hypertext systems in general, and the World Wide Web in particular. Various processes for the conceptual structuring of hypertext are discussed: summarization, conceptual scaling, and the creation of conceptual links. Well-known interchange formats for summarizing networked information resources as resource meta-information are reviewed, and two new interchange formats originating from formal concept analysis are advocated. Also reviewed is conceptual scaling, which provides a principled approach to the faceted analysis techniques in library science classification. The important notion of conceptual linkage is introduced as a generalization of a hyperlink. The automatic hyperization of the content of legacy data is described, and the composite conceptual structuring with hypertext linkage is defined. For the conceptual empowerment of the Web user, a new technique called conceptual browsing is advocated. Conceptual browsing, which browses over conceptual links, is dual mode (extensional versus intensional) and dual scope (global versus local).

cs.AI↗

arXiv2018

Introduction to Dialectical Nets

This paper initiates the dialectical approach to net theory. This approach views nets as special, but very important and natural, dialectical systems. By following this approach, a suitably generalized version of nets, called dialectical nets, can be defined in terms of the "fundamental contradiction" inherent in the structure of closed preorders. Dialectical nets are the least conceptual upper bound subsuming the notions of Petri nets, Kan quantification and transition systems. The nature of dialectical nets is that of logical dynamics, and is succinctly defined and summarized in the statement that "dialectical nets are transition systems relativized to closed preorders, and hence are general predicate transformers".

cs.LO↗

arXiv2018

Conceptual Collectives

The notions of formal contexts and concept lattices, although introduced by Wille only ten years ago, 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" of Wille with the well-known "completion by cuts" of MacNeille. Generalization and abstraction of these formal contexts offers a powerful approach to knowledge representation.

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arXiv2018

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 Montanari and Rossi. 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 Rudolf Wille and his colleagues, 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. Some of the intuitions underlying our approach were discussed in a preliminary fashion by Freuder and Wallace.

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arXiv2018

Rough Concept Analysis

The theory introduced, presented and developed in this paper, is concerned with Rough Concept Analysis. This theory is a synthesis of the theory of Rough Sets pioneered by Zdzislaw Pawlak with the theory of Formal Concept Analysis pioneered by Rudolf Wille. The central notion in this paper of a rough formal concept combines in a natural fashion the notion of a rough set with the notion of a formal concept: "rough set + formal concept = rough formal concept". A follow-up paper will provide a synthesis of the two important data modeling techniques: conceptual scaling of Formal Concept Analysis and Entity-Relationship database modeling.

cs.AI↗

arXiv2018

The IFF Foundation for Ontological Knowledge Organization

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.

cs.DL↗

arXiv2018

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) is concerned with the distribution of knowledge. The foundations of Information Flow is explicitly based upon a mathematical theory known as the Chu Construction in *-autonomous categories and implicitly based upon the mathematics of closed categories. Formal Concept Analysis (FCA) is concerned with the conception and analysis of knowledge. In this paper we connect these two studies by extending the basic theorem of Formal Concept Analysis to the distributed realm of Information Flow. The main results are the categorical equivalence between classifications and concept lattices at the level of functions, and the categorical equivalence between bonds and complete adjoints at the level of relations. With this we hope to accomplish a rapprochement between Information Flow and Formal Concept Analysis.

cs.LO↗

arXiv2018

Conceptual Knowledge Markup Language: An Introduction

Conceptual Knowledge Markup Language (CKML) is an application of XML. Earlier versions of CKML followed rather exclusively the philosophy of Conceptual Knowledge Processing (CKP), a principled approach to knowledge representation and data analysis that "advocates methods and instruments of conceptual knowledge processing which support people in their rational thinking, judgment and acting and promote critical discussion." The new version of CKML continues to follow this approach, but also incorporates various principles, insights and techniques from Information Flow (IF), the logical design of distributed systems. Among other things, this allows diverse communities of discourse to compare their own information structures, as coded in logical theories, with that of other communities that share a common generic ontology. CKML incorporates the CKP ideas of concept lattice and formal context, along with the IF ideas of classification (= formal context), infomorphism, theory, interpretation and local logic. Ontology Markup Language (OML), a subset of CKML that is a self-sufficient markup language in its own right, follows the principles and ideas of Conceptual Graphs (CG). OML is used for structuring the specifications and axiomatics of metadata into ontologies. OML incorporates the CG ideas of concept, conceptual relation, conceptual graph, conceptual context, participants and ontology. The link from OML to CKML is the process of conceptual scaling, which is the interpretive transformation of ontologically structured knowledge to conceptual structured knowledge.

cs.AI↗

arXiv2018

Dialectical logic: the Process Calculus

Dialectical logic is the logic of dialectical processes. The goal of dialectical logic is to reveal the dynamical notions inherent in logical computational systems. The fundamental notions of proposition and truth-value in standard logic are subsumed by the notions of process and flow in dialectical logic. Standard logic motivates the core sequential aspect of dialectical logic. Horn-clause logic requires types and nonsymmetry and also motivates the parallel aspect of dialectical logic. The process logics of Milner and Hoare reveal the internal/external aspects of dialectical logic. The sequential internal aspect of dialectical logic should be viewed as a typed or distributed version of Girard's linear logic with nonsymmetric tensor. The simplest version of dialectical logic is inherently intuitionistic. However, by following Glivenko's approach in standard logic using double negation closure, we can define a classical version of dialectical logic.

cs.LO↗

arXiv2018

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.

cs.LO↗

arXiv2016

Information Flow in Logical Environments

This paper describes information flow within logical environments. The theory of information flow, the logic of distributed systems, was first defined by Barwise and Seligman (Information Flow: The Logic of Distributed Systems. 1997). Logical environments are a semantic-oriented version of institutions. The theory of institutions, which was initiated by Goguen and Burstall (Institutions: Abstract Model Theory for Specification and Programming. 1992), is abstract model theory. Information flow is the flow of information in channels over distributed systems. The semantic integration of distributed systems, be they ontologies, databases or other information resources, can be defined in terms of the channel theory of information flow. As originally defined, the theory of information flow uses only a specific logical environment in order to discuss information flow. This paper shows how information flow can be defined in an arbitrary logical environment.

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arXiv2013

FOLE: The First-order Logical Environment

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.

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arXiv2012

Database Semantics

This paper, the first step to connect relational databases with systems consequence (Kent: "System Consequence" 2009), 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: "Functorial Data Migration" 2012), is linked with work on the Information Flow Framework (IFF) [http://suo.ieee.org/IFF/] 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: "Simplicial databases" 2009)[arXiv:0904.2012]. The unified form, a special case of the distinguished form, corresponds to the theory presented in (Spivak: "Functorial Data Migration" 2012). 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.

cs.DB↗

arXiv2011

The Standard Aspect of Dialectical Logic

Dialectical logic is the logic of dialectical processes. The goal of dialectical logic is to introduce dynamic notions into logical computational systems. The fundamental notions of proposition and truth-value in standard logic are subsumed by the notions of process and flow in dialectical logic. Dialectical logic has a standard aspect, which can be defined in terms of the "local cartesian closure" of subtypes. The standard aspect of dialectical logic provides a natural program semantics which incorporates Hoare's precondition/postcondition semantics and extends the standard Kripke semantics of dynamic logic. The goal of the standard aspect of dialectical logic is to unify the logic of small-scale and large-scale programming.

cs.LO↗

arXiv2011

Digital Libraries, Conceptual Knowledge Systems, and the Nebula Interface

Concept Analysis provides a principled approach to effective management of wide area information systems, such as the Nebula File System and Interface. This not only offers evidence to support the assertion that a digital library is a bounded collection of incommensurate information sources in a logical space, but also sheds light on techniques for collaboration through coordinated access to the shared organization of knowledge.

cs.DL↗

arXiv2011

Conceptual Knowledge Markup Language: The central core

The conceptual knowledge framework OML/CKML needs several components for a successful design. One important, but previously overlooked, component is the central core of OML/CKML. The central core provides a theoretical link between the ontological specification in OML and the conceptual knowledge representation in CKML. This paper discusses the formal semantics and syntactic styles of the central core, and also the important role it plays in defining interoperability between OML/CKML, RDF/S and Ontolingua.

cs.DL↗

arXiv2011

The Information Flow Framework: New architecture

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, equations or relational expressions. The IFF is a descriptive category metatheory. It is descriptive, since it follows the principle of conceptual warrant; it is categorical, since it follows the principle of categorical design; and it is a metatheory, since it provides a framework for all theories.

cs.DL↗

arXiv2011

A KIF Formalization for the IFF Category Theory Ontology

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.

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