Related papers: Conceptua: Institutions in a Topos
Truth refers to the satisfaction relation used to define the semantics of model-theoretic languages. The satisfaction relation for first order languages (truth classification), and the preservation of truth by first order interpretations…
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…
The theory of institutions is framed as an indexed/fibered duality, where the indexed aspect specifies the fibered aspect. Tarski represented truth in terms of a satisfaction relation. The theory of institutions encodes satisfaction as its…
The IFF approach for the notion of "lattice of theories" uses the idea of a concept lattice from Formal Concept Analysis (Ganter and Wille) and the idea of the truth classification from Information Flow (Barwise and Seligman). The IFF…
This paper is a tutorial on Formal Concept Analysis (FCA) and its applications. FCA is an applied branch of Lattice Theory, a mathematical discipline which enables formalisation of concepts as basic units of human thinking and analysing…
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,…
The notion of concept has been studied for centuries, by philosophers, linguists, cognitive scientists, and researchers in artificial intelligence (Margolis & Laurence, 1999). There is a large literature on formal, mathematical models of…
This paper discusses the representation of ontologies in the first-order logical environment {\ttfamily FOLE}. An ontology defines the primitives with which to model the knowledge resources for a community of discourse. These primitives…
Human knowledge is made up of the conceptual structures of many communities of interest. In order to establish coherence in human knowledge representation, it is important to enable communication between the conceptual structures of…
Formal Concept Analysis (FCA) is a mathematical framework for knowledge representation and discovery. It performs a hierarchical clustering over a set of objects described by attributes, resulting in conceptual structures in which objects…
Formal Concept Analysis (FCA) is an approach to creating a conceptual hierarchy in which a \textit{concept lattice} is generated from a \textit{formal context}. That is, a triple consisting of a set of objects, $G$, a set of attributes,…
This paper discusses the representation of ontologies in the first-order logical environment {\ttfamily FOLE}. An ontology defines the primitives with which to model the knowledge resources for a community of discourse. These primitives…
The definition is a common form of human expert knowledge, a building block of formal science and mathematics, a foundation for database theory and is supported in various forms in many knowledge representation and formal specification…
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…
We study the structure of the partial order induced by the definability relation on definitions of truth for the language of arithmetic. Formally, a definition of truth is any sentence $\alpha$ which extends a weak arithmetical theory…
The notion of class is ubiquitous in computer science and is central in many formalisms for the representation of structured knowledge used both in knowledge representation and in databases. In this paper we study the basic issues…
The sharing of ontologies between diverse communities of discourse allows them to compare their own information structures with that of other communities that share a common terminology and semantics - ontology sharing facilitates…
Formal concept analysis has grown from a new branch of the mathematical field of lattice theory to a widely recognized tool in Computer Science and elsewhere. In order to fully benefit from this theory, we believe that it can be enriched…
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).…
A model of knowledge representation is described in which propositional facts and the relationships among them can be supported by other facts. The set of knowledge which can be supported is called the set of cognitive units, each having…