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

Interpreting the Quantum Wave Function in Terms of 'Interacting Faculties'

In this article we discuss the problem of finding an interpretation of quantum mechanics which provides an objective account of physical reality. In the first place we discuss the problem of interpretation and analyze the importance of such an objective account in physics. In this context we present the problems which arise when interpreting the quantum wave function within the orthodox formulation of quantum mechanics. In connection to this critic, we expose the concept of 'entity' as an epistemological obstruction. In the second part of this paper we discuss the relation between actuality and potentiality in classical and quantum physics, and continue to present the concept of 'ontological potentiality' which is distinguished from the generic Aristotelian notion of potentiality in terms of 'becoming actual'. In this paper our main aim is to provide an objective interpretation of quantum mechanics which allows us to discuss the meaning of physical reality according to the theory. For this specific propose we present the concept of 'faculty' in place of the concept of 'entity'. Within our theory of faculties, we continue to discuss and interpret two paradigmatic experiments of quantum mechanics such as the double-slit and Schrodinger's cat.Comment: 34 page

On Engineering Support for Business Process Modelling and Redesign

Currently, there is an enormous (research) interest in business process redesign (BPR). Several management-oriented approaches have been proposed showing how to make BPR work. However, detailed descriptions of empirical experience are few. Consistent engineering methodologies to aid and guide a BPR-practitioner are currently emerging. Often, these methodologies are claimed to be developed for business process modelling, but stem directly from information system design cultures. We consider an engineering methodology for BPR to consist of modelling concepts, their representation, computerized tools and methods, and pragmatic skills and guidelines for off-line modelling, communicating, analyzing, (re)designing\ud business processes. The modelling concepts form the architectural basis of such an engineering methodology. Therefore, the choice, understanding and precise definition of these concepts determine the productivity and effectiveness of modelling tasks within a BPR project. The\ud current paper contributes to engineering support for BPR. We work out general issues that play a role in the development of engineering support for BPR. Furthermore, we introduce an architectural framework for business process modelling and redesign. This framework consists of a coherent set of modelling concepts and techniques on how to use them. The framework enables the modelling of both the structural and dynamic characteristics of business processes. We illustrate its applicability by modelling a case from service industry. Moreover, the architectural framework supports abstraction and refinement techniques. The use of these techniques for a BPR trajectory are discussed

Combinatorial Information Theory: I. Philosophical Basis of Cross-Entropy and Entropy

This study critically analyses the information-theoretic, axiomatic and combinatorial philosophical bases of the entropy and cross-entropy concepts. The combinatorial basis is shown to be the most fundamental (most primitive) of these three bases, since it gives (i) a derivation for the Kullback-Leibler cross-entropy and Shannon entropy functions, as simplified forms of the multinomial distribution subject to the Stirling approximation; (ii) an explanation for the need to maximize entropy (or minimize cross-entropy) to find the most probable realization; and (iii) new, generalized definitions of entropy and cross-entropy - supersets of the Boltzmann principle - applicable to non-multinomial systems. The combinatorial basis is therefore of much broader scope, with far greater power of application, than the information-theoretic and axiomatic bases. The generalized definitions underpin a new discipline of ``{\it combinatorial information theory}'', for the analysis of probabilistic systems of any type. Jaynes' generic formulation of statistical mechanics for multinomial systems is re-examined in light of the combinatorial approach. (abbreviated abstract)Comment: 45 pp; 1 figure; REVTex; updated version 5 (incremental changes

The fundamental cycle of concept construction underlying various theoretical frameworks

In this paper, the development of mathematical concepts over time is considered. Particular reference is given to the shifting of attention from step-by-step procedures that are performed in time, to symbolism that can be manipulated as mental entities on paper and in the mind. The development is analysed using different theoretical perspectives, including the SOLO model and various theories of concept construction to reveal a fundamental cycle underlying the building of concepts that features widely in different ways of thinking that occurs throughout mathematical learning