By Zhaohui Luo
This booklet develops a kind concept, reports its homes, and explains its makes use of in laptop technological know-how. The e-book focuses particularly on how the learn of sort thought may possibly provide a robust and uniform language for programming, software specification and improvement, and logical reasoning. the kind idea constructed the following displays a conceptual contrast among logical propositions and computational info kinds. ranging from an creation of the elemental suggestions, the writer explains the which means and use of the type-theoretic language with proof-theoretic justifications, and discusses numerous matters within the learn of variety idea. the sensible use of the language is illustrated by means of constructing an method of specification and knowledge refinement in sort idea, which helps modular improvement of specification, courses, and proofs. scholars and researchers in desktop technology and common sense will welcome this fascinating new publication.
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Additional resources for Computation and reasoning. A type theory for computer science
Keywords: neural network, transient dynamics, oscillatory metastable states, dynamical bifurcation. 1 Introduction Many neurophysiological experiments [1–4] have indicated that some neural processes related, for example, with performing of diﬀerent cognitive tasks (memory, attention, psychomotor coordination, and so on) are accompanied only by transient activity at the level of individual neurons or small enough groups of neurons. As a result of such processes a certain sequence of transitional activity phases appears in neural network.
Reason. 34, 3–24 (2003) 11. : Theory of Probability: a Critical Introductory Treatment. Wiley, New York (1993) 12. : Contributions to the Analysis of the Sensations (C. M. ). , Chicago (1980) 13. : The Bayesian brain: the role of uncertainty in neural coding and computation. Trends Neur. 27(12), 712–719 (2004) 14. : Conditional probability, fuzzy sets, and possibility: a unifying view. Fuzzy Sets and Systems 144(1), 227–249 (2004) 15. : Object Perception as Bayesian Inference. Annu. Rev. Psychol.
Therefore, perception can be described as a subjective process of Bayesian probabilistic inference [12, 13]. If IM is the intensity of the stimulus of modality M, and XM represents the collection of cells sensitive to it, applying the Bayes’ rule, it derives that p( I M X M ) = p( I M ) p( X M I M ) p( X M ) (1) The term p( I M X M ) represents the “posterior probability”. It is proportional to the product of the “prior probability” p ( I M ) and the “likelihood” p( X M I M ) . p( I M ) is the probability of each perception prior to receiving the stimulus: it represents knowledge of the regularities and it is strongly subjective.