The ERA of FOLE: Superstructure

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) provided a "foundation" that connected elements of the ERA data model with components of the first-order logical environment FOLE, and this second paper provides a "superstructure" that extends FOLE to the formalisms of first-order logic. The third paper will define an "interpretation" of FOLE in terms of the transformational passage, first described in (Kent 2013), from the classification form of first-order logic to an equivalent interpretation form, thereby defining the formalism and semantics of first-order logical/relational database systems (Kent 2011). The FOLE representation follows a conceptual structures approach, that is completely compatible with Formal Concept Analysis (Ganter and Wille 1999) and Information Flow (Barwise and Seligman 1997)

The ERA of FOLE: Foundation

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 entity-relationship-attribute ERA 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 first 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, this first paper provides a foundation that connects elements of the ERA data model with components of the first-order logical environment FOLE, and the second paper provides a superstructure that extends FOLE to the formalisms of first-order logic. The third paper defines an interpretation of FOLE in terms of the transformational passage, first described in (Kent 2013), from the classification form of first-order logic to an equivalent interpretation form, thereby defining the formalism and semantics of first-order logical/relational database systems (Kent 2011). The FOLE representation follows a conceptual structures approach, that is completely compatible with formal concept analysis (Ganter and Wille 1999) and information flow (Barwise and Seligman 1997)

The FOLE Table

This paper continues the discussion of the representation of ontologies in the first-order logical environment FOLE. According to Gruber, an ontology defines the primitives with which to model the knowledge resources for a community of discourse. These primitives, consisting of classes, relationships and properties, are represented by the entity-relationship-attribute ERA data model of Chen. An ontology uses formal axioms to constrain the interpretation of these primitives. In short, an ontology specifies a logical theory. A series of three papers by the author provide a rigorous mathematical representation for the ERA data model in particular, and ontologies in general, within FOLE. The first two papers, which provide a foundation and superstructure for FOLE, represent the formalism and semantics of (many-sorted) first-order logic in a classification form corresponding to ideas discussed in the Information Flow Framework (IFF). The third paper will define an interpretation of FOLE in terms of the transformational passage, first described in (Kent, 2013), from the classification form of first-order logic to an equivalent interpretation form, thereby defining the formalism and semantics of first-order logical/relational database systems. Two papers will provide a precise mathematical basis for FOLE interpretation: the current paper develops the notion of a FOLE relational table following the relational model of Codd, and a follow-up paper will develop the notion of a FOLE relational database. Both of these papers expand on material found in the paper (Kent, 2011). Although the classification form follows the entity-relationship-attribute data model of Chen, the interpretation form follows the relational data model of Codd. In general, the FOLE representation uses a conceptual structures approach, that is completely compatible with formal concept analysis and information flow.Comment: 48 pages, 21 figures, 9 tables, submitted to T.A.C. for review in August 201

Institutionalising Ontology-Based Semantic Integration

We address what is still a scarcity of general mathematical foundations for ontology-based semantic integration underlying current knowledge engineering methodologies in decentralised and distributed environments. After recalling the first-order ontology-based approach to semantic integration and a formalisation of ontological commitment, we propose a general theory that uses a syntax-and interpretation-independent formulation of language, ontology, and ontological commitment in terms of institutions. We claim that our formalisation generalises the intuitive notion of ontology-based semantic integration while retaining its basic insight, and we apply it for eliciting and hence comparing various increasingly complex notions of semantic integration and ontological commitment based on differing understandings of semantics

Two Decades of Maude

This paper is a tribute to José Meseguer, from the rest of us in the Maude team, reviewing the past, the present, and the future of the language and system with which we have been working for around two decades under his leadership. After reviewing the origins and the language's main features, we present the latest additions to the language and some features currently under development. This paper is not an introduction to Maude, and some familiarity with it and with rewriting logic are indeed assumed.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech