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Mathematical Models of Interactive Computing
, 1999
"... : Finite computing agents that interact with an environment are shown to be more expressive than Turing machines according to a notion of expressiveness that measures problemsolving ability and is specified by observation equivalence. Sequential interactive models of objects, agents, and embedded s ..."
Abstract

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: Finite computing agents that interact with an environment are shown to be more expressive than Turing machines according to a notion of expressiveness that measures problemsolving ability and is specified by observation equivalence. Sequential interactive models of objects, agents, and embedded systems are shown to be more expressive than algorithms. Multiagent (distributed) models of coordination, collaboration, and true concurrency are shown to be more expressive than sequential models. The technology shift from algorithms to interaction is expressed by a mathematical paradigm shift that extends inductive definition and reasoning methods for finite agents to coinductive methods of set theory and algebra. An introduction to models of interactive computing is followed by an account of mathematical models of sequential interaction in terms of coinductive methods of nonwellfounded set theory, coalgebras, and bisimulation. Models of distributed information flow and multiagent inter...
Church’s Thesis and the Conceptual Analysis of Computability
 Notre Dame Journal of Formal Logic
, 2007
"... ..."
Digital Paradoxes in Learning Theories
"... Abstract—As a learning theory tries to borrow from science a framework to found its method, it shows paradoxes and paralysing contraddictions. This results, on one hand, from adopting a learning/teaching model as it were a mere “transfer of data” (mechanical learning approach), and on the other hand ..."
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Abstract—As a learning theory tries to borrow from science a framework to found its method, it shows paradoxes and paralysing contraddictions. This results, on one hand, from adopting a learning/teaching model as it were a mere “transfer of data” (mechanical learning approach), and on the other hand from borrowing the complexity theory (an indeterministic and nonlinear model), that risks to vanish every educational effort. This work is aimed at describing existing criticism, unveiling the antinomic nature of such paradoxes, focussing on a view where neither the mechanical learning perspective nor the chaotic and nonlinear model can threaten and jeopardize the educational work. Author intends to go back over the steps that led to these paradoxes and to unveil their antinomic nature. Actually this could serve the purpose to explain some current misunderstandings about the real usefulness of Ict within the youth’s learning process and growth. Keywords—Antinomy, complexity, Leibniz, paradox. I.