N. Belknap's Four-Valued Logic, Belknap Computer and New Proximity Functions for Comparing Discrete Objects

Abstract

The idea of ​​Belknap's four-valued logic is that modern computers should function normally not only with the true values ​​of the input information, but also under the conditions of inconsistency and incompleteness of true failures. Belknap's logic introduces four true values: T (true - true), F (false - false), N (none - nobody, nothing, none), B (both - the two, not only the one but also the other). For ease of work with these true values, the following designations are introduced: (1, 0, n, b). Belknap's logic can be used to obtain estimates of proximity measures for discrete objects, for which the functions Jaccard and Needhem, Russel and Rao, Sokal and Michener, Hamming, etc. are used. In this case, it becomes possible to assess the proximity, recognition and classification of objects in conditions of uncertainty when the true values ​​are taken from the set (1, 0, n, b). Based on the architecture of the Hamming neural network, neural networks have been developed that allow calculating the distances between objects described using true values ​​(1, 0, n, b).
 Keywords: four-valued Belknap logic, Belknap computer, proximity assessment, recognition and classification, proximity function, neural network.