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

Graph Theory and Universal Grammar

Tese arquivada ao abrigo da Portaria nº 227/2017 de 25 de Julho-Registo de Grau EstrangeiroIn the last few years, Noam Chomsky (1994; 1995; 2000; 2001) has gone quite far in the direction of simplifying syntax, including eliminating X-bar theory and the levels of D-structure and S-structure entirely, as well as reducing movement rules to a combination of the more primitive operations of Copy and Merge. What remain in the Minimalist Program are the operations Merge and Agree and the levels of LF (Logical Form) and PF (Phonological form). My doctoral thesis attempts to offer an economical theory of syntactic structure from a graph-theoretic point of view (cf. Diestel, 2005), with special emphases on the elimination of category and projection labels and the Inclusiveness Condition (Chomsky 1994). The major influences for the development of such a theory have been Chris Collins’ (2002) seminal paper “Eliminating labels”, John Bowers (2001) unpublished manuscript “Syntactic Relations” and the Cartographic Paradigm (see Belletti, Cinque and Rizzi’s volumes on OUP for a starting point regarding this paradigm). A syntactic structure will be regarded here as a graph consisting of the set of lexical items, the set of relations among them and nothing more

Semantic networks

AbstractA semantic network is a graph of the structure of meaning. This article introduces semantic network systems and their importance in Artificial Intelligence, followed by I. the early background; II. a summary of the basic ideas and issues including link types, frame systems, case relations, link valence, abstraction, inheritance hierarchies and logic extensions; and III. a survey of ‘world-structuring’ systems including ontologies, causal link models, continuous models, relevance, formal dictionaries, semantic primitives and intersecting inference hierarchies. Speed and practical implementation are briefly discussed. The conclusion argues for a synthesis of relational graph theory, graph-grammar theory and order theory based on semantic primitives and multiple intersecting inference hierarchies

Rethinking Analyticity: A defence of philosophy as a conceptual discipline

This thesis argues that for a concept of analyticity--and an attendant analytic-synthetic distinction--to be workable, we must acknowledge its essential normative dimension. Indeed, I point out that contemporary debates surrounding so-called metaphysical and epistemic conceptions of analyticity are importantly misguided for failing to see the significance in this point: that analytic sentences express norms, not descriptions. Moreover, I argue that no sentence can--in one and the same use--function both normatively and descriptively. These thoughts are marshalled to show that the positions of Timothy Williamson and Paul Boghossian on analytic truth are jointly untenable, despite appearing to be opposite ends of a debate. In later chapters, I seek to show the positive contribution of these insights. First, I demonstrate how John McDowell's arguments against the Myth of the Given point us both toward seeing analytic truth as a precondition for empirical description and away from Robert Brandom's inferentialist understanding of conceptual content. And second, finally, I show that Mark Wilson's innovative work on conceptual change in various applied fields can complement the approach I endorse; i.e., that normativity and conceptual change interact rather than conflict

Transcendental-Phenomenological Proof and Descriptive Metaphysics

Following P.F. Strawson's reading of Kant, the majority of the literature on transcendental arguments seeks to divorce such arguments from their original Kantian context. This thesis is concerned with Mark Sacks's recent defence of transcendental arguments, which takes a different approach. A critique is given of Sacks's work and extensions and modifications of his approach are recommended. It is proposed that certain difficulties encountered by Kant's transcendentally-ideal approach can be overcome with Hegelian solutions

Transcendental-Phenomenological Proof and Descriptive Metaphysics

Following P.F. Strawson's reading of Kant, the majority of the literature on transcendental arguments seeks to divorce such arguments from their original Kantian context. This thesis is concerned with Mark Sacks's recent defence of transcendental arguments, which takes a different approach. A critique is given of Sacks's work and extensions and modifications of his approach are recommended. It is proposed that certain difficulties encountered by Kant's transcendentally-ideal approach can be overcome with Hegelian solutions

Archaeological knowledge and its representation an inter-disciplinary study of the problems of knowledge representation

The thesis is a study of archaeology viewed from a perspective informed by (a) social constructionist theory and pragmatism; (b) techniques of Belief and Knowledge Representation developed by Artificial Intelligence research and (c) the conception of history and historical practice propounded by the philosopher, historian and archaeologist, R.G. Collingwood. It is argued that Gibsonian affordances and von Uexkull's notion of the Umwelt, recently discussed by Rom Harré, provide the basis for a description and understanding of human action and agency. Further, belief and knowledge representation techniques embodied in Expert Systems and Intelligent Tutoring Systems provide a means of implementing models of human action which may bridge intentionality and process and thereby provide a unifying learning environment in which the relationships of language, social action and material transformation of the physical world can be explored in a unified way. The central claim made by the thesis is that Collingwood's logic (dialectic) of Question & Answer developed in 1917 as a hermeneutic procedure, may be seen as a fore-runner of Newell and Simon's Heuristic Search, and thereby amenable to modem approaches to problem solving. Collingwood's own approach to History/ Archaeology is grounded on many shared ideas with pragmatism and a social constructionist conception of mind and is conducted within a problem solving framework. Collingwood is therefore seen as a three-way bridge between Social Psychology, Artificial Intelligence and Archaeology. The thesis concludes that Social Psychology, Artificial Intelligence and Archaeology can be integrated through the use of Intelligent Tutoring Systems informed by a Collingwoodian perspective on Archaeology, Mind and History - construed as Mind's self-knowledge