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Concepts and analogies in cybernetics: Mathematical investigations of the role of analogy in concept formation and problem solving; with emphasis for conflict resolution via object and morphism eliminations
This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.We address two problematic areas of cybernetics; nam. Analogical Problem Solving (APS) and Analogical Learning (AL). Both these human faculties do unquestionably require Intelligence. In addition, we point out that shifting of representations is the main unified theme underlying these two intellectual tasks. We focus our attention on the formulation and clarification of the notion of analogy, which has been loosely treated and used in the literature; and also on its role in shifting of representations.
We describe analogizing situations in a new representational scheme, borrowed from mathematics and modified and extended to cater for our targets. We call it k-structure, closely resembling semantic networks and directed graphs; the main components of it are the so-called objects and morphisms. We argue and substantiate the need for such a representation scheme, by analysing what its constituents stand for and by cataloguing its virtues, the main one being its visual appeal and its mathematical clarity, and by listing its disadvantages when it is compared to other representation systems. Emphasis is also given to its descriptive power and usefulness by implementing it in a number of APS and AL situations. Besides representation issues, attention is paid to intelligence mechanisms which are involved in APS and AL. A cornerstone in APS and a fundamental theme in AL is the 'skeletization of k-structures'. APS is conceived as 'harmonization of skeletons'. The methodology we develop involves techniques which are computer implemented and extensively studied in theoretic terms via a proposed theory for extended k-structures. To name but a few: 1. 'the separation of the context of a concept from the concept itself', based on the ideas of k-opens and k-spaces; 2, 'object and morphism elimination' of a controversial nature; and 3. 'conflict or deadlock or dilemma resolution' which naturally arises in a k-structure interaction. The overall system, is then applied to capture the essence of EVANS' (1963) analogy-type problems and WINSTOM (1970) learning-type situations. In our attempt not to be too informal, we use basic notions and terminology from abstract Algebra, Topology and Category theory. We rather tend to be "non-logical" (analogical) in EVANS' and WINSTON's sense; "non-numeric", in MESAROVIC (1970) terms (we rather deal with abstract conceptual entities); "non-linguistic" (we do not touch natural language); and "non-resolution" oriented, in the sense of BLEDSOE (1977). However, we give hints sometimes about logical deductive axiomatic systems, employing First Order Predicate Calculus (FOPC); and about semiotics, by which we denote syntactic-semantic-pragmatic features of our system and issues of the problem domains it is acting upon. We believe in what we call: shift from the traditional 'Heuristic search paradigm' era to the 'Analogy-paradigm' era underlying Artificial Intelligence and Cybernetics. We justify this merely by listing a number of A. I. works, which employ, in some way or another, the concept of analogy, over the last fifteen years or so, where a noticeable peak is obvious during the last years and especially in 1977. Finally, we hope that if the proposed conceptual framework and techniques developed do not straightforwardly constitute some kind of platform for Artificial Intelligence, at least it would give some insights into and illuminate our understanding of the two most fundamental faculties the human brain is occupied with; namely problem solving and learning
Introduction to Gestural Similarity in Music. An Application of Category Theory to the Orchestra
Mathematics, and more generally computational sciences, intervene in several
aspects of music. Mathematics describes the acoustics of the sounds giving
formal tools to physics, and the matter of music itself in terms of
compositional structures and strategies. Mathematics can also be applied to the
entire making of music, from the score to the performance, connecting
compositional structures to acoustical reality of sounds. Moreover, the precise
concept of gesture has a decisive role in understanding musical performance. In
this paper, we apply some concepts of category theory to compare gestures of
orchestral musicians, and to investigate the relationship between orchestra and
conductor, as well as between listeners and conductor/orchestra. To this aim,
we will introduce the concept of gestural similarity. The mathematical tools
used can be applied to gesture classification, and to interdisciplinary
comparisons between music and visual arts.Comment: The final version of this paper has been published by the Journal of
Mathematics and Musi
The semiring-theoretic approach to MV-algebras: a survey
In this paper we review some of the main achievements of the
semiring-theoretic approach to MV-algebras initiated and pursued mainly by the
present authors and their collaborators. The survey focuses mainly on the
connections between MV-algebras and other theories that such a semiringbased
approach enabled, and on an application of such a framework to Digital Image
Processing. We also give some suggestions for further developments by stating
several open problems and possible research lines.Comment: Published versio
Quantale Modules, with Applications to Logic and Image Processing
We propose a categorical and algebraic study of quantale modules. The results
and constructions presented are also applied to abstract algebraic logic and to
image processing tasks.Comment: 150 pages, 17 figures, 3 tables, Doctoral dissertation, Univ Salern
Cities Made of Boundaries: Mapping Social Life in Urban Form
Cities Made of Boundaries presents the theoretical foundation and concepts for a new social scientific urban morphological mapping method, Boundary Line Type (BLT) Mapping. Its vantage is a plea to establish a frame of reference for radically comparative urban studies positioned between geography and archaeology. Based in multidisciplinary social and spatial theory, a critical realist understanding of the boundaries that compose built space is operationalised by a mapping practice utilising Geographical Information Systems (GIS).
Benjamin N. Vis gives a precise account of how BLT Mapping can be applied to detailed historical, reconstructed, contemporary, and archaeological urban plans, exemplified by sixteenth to twenty-first century Winchester (UK) and Classic Maya Chunchucmil (Mexico). This account demonstrates how the functional and experiential difference between compact western and tropical dispersed cities can be explored.
The methodological development of Cities Made of Boundaries will appeal to readers interested in the comparative social analysis of built environments, and those seeking to expand the evidence-base of design options to structure urban life and development
Cities Made of Boundaries
Cities Made of Boundaries presents the theoretical foundation and concepts for a new social scientific urban morphological mapping method, Boundary Line Type (BLT) Mapping. Its vantage is a plea to establish a frame of reference for radically comparative urban studies positioned between geography and archaeology. Based in multidisciplinary social and spatial theory, a critical realist understanding of the boundaries that compose built space is operationalised by a mapping practice utilising Geographical Information Systems (GIS).
Benjamin N. Vis gives a precise account of how BLT Mapping can be applied to detailed historical, reconstructed, contemporary, and archaeological urban plans, exemplified by sixteenth- to twenty-first century Winchester (UK) and Classic Maya Chunchucmil (Mexico). This account demonstrates how the functional and experiential difference between compact western and tropical dispersed cities can be explored.
The methodological development of Cities Made of Boundaries will appeal to readers interested in the comparative social analysis of built environments, and those seeking to expand the evidence-base of design options to structure urban life and development
The reasonable effectiveness of Mathematics and its Cognitive roots 1
“At the beginning, Nature set up matters its own way and, later, it constructed human intelligence in such a way that [this intelligence] could understand it” [Galileo Galilei, 1632 (Opere, p. 298)]. “The applicability of our science [mathematics] seems then as a symptom of its rooting, not as a measure of its value. Mathematics, as a tree which freely develops his top, draws its strength by the thousands roots in a ground of intuitions of real representations; it would be disastrous to cut them off, in view of a short-sided utilitarism, or to uproot them from the ground from which they rose ” [H. Weyl, 1910]. Summary. Mathematics stems out from our ways of making the world intelligible by its peculiar conceptual stability and unity; we invented it and used it to single out key regularities of space and language. This is exemplified and summarised below in references to the main foundational approaches to Mathematics, as proposed in the last 150 years. Its unity is also stressed: in this paper, Mathematics is viewed as a "three dimensiona
Cities Made of Boundaries
Cities Made of Boundaries presents the theoretical foundation and concepts for a new social scientific urban morphological mapping method, Boundary Line Type (BLT) Mapping. Its vantage is a plea to establish a frame of reference for radically comparative urban studies positioned between geography and archaeology. Based in multidisciplinary social and spatial theory, a critical realist understanding of the boundaries that compose built space is operationalised by a mapping practice utilising Geographical Information Systems (GIS).
Benjamin N. Vis gives a precise account of how BLT Mapping can be applied to detailed historical, reconstructed, contemporary, and archaeological urban plans, exemplified by sixteenth- to twenty-first century Winchester (UK) and Classic Maya Chunchucmil (Mexico). This account demonstrates how the functional and experiential difference between compact western and tropical dispersed cities can be explored.
The methodological development of Cities Made of Boundaries will appeal to readers interested in the comparative social analysis of built environments, and those seeking to expand the evidence-base of design options to structure urban life and development
GIS Processing for Geocoding Described Collection Locations
Much useful data is currently not available for use in contemporary geographic information systems because location is provided as descriptive text and not in a recognized coordinate system format. This is particularly true for datasets with significant temporal depth such as museum collections. Development is just beginning on applications that automate the conversion of descriptive text based locations to geographic coordinate values. These applications are a type of geocoding or locator service and require functionality in two domains: natural language processing and geometric calculation. Natural language processing identifies the spatial semantics of the text describing a location and tags the individual text elements according to their spatially descriptive role. This is referred to as geoparsing. Once identified, these tagged text elements can be either converted directly to numeric values or used as pointers to geometric objects that represent geographic features identified in the description. These values and geometries can be employed in a series of functions to determine coordinates for the described location. This is referred to as geoprocessing.
Selection of appropriate text elements from a location description and ancillary data as input is critical for successful geocoding. The traverse, one of many types of location description is selected for geocoding development. Specific text elements with spatial meaning are identified and incorporated into an XML format for use as geoprocessing input. Information associated with the location is added to the XML format to maintain database relations and geoprocessing error checking functionality. ESRI’s ArcGIS 8.3 is used as a development environment where geoprocessing functionality is tested for XML elements using ArcObjects and VBA forms
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