Finite Closed Sets of Functions in Multi-valued Logic
نویسندگان
چکیده
منابع مشابه
Finite Closed Sets of Functions in Multi-valued Logic
The article is devoted to classification of close sets of functions in k-valued logic. We build the classification of finite closed sets. The sets contain only constants and unary functions since sets containing even a two-ary function are infinite. Formulas of the number of finite sets and minimal sets exist for all natural k. We find the numbers of closed sets containing the identity function...
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Using Mal’cev’s preiterative algebra (iterative algebra is not sound) we construct in the first time the natural classification of closed sets of functions in multi-valued logic: every closed set belongs only one class and the classes are disjoint. All contemporary papers construct only intersecting classes. We confirm Post’s thesis that multi-valued logic does not contain anything special in c...
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Granularity of knowledge attracted attention of many researchers recently. This paper concerns this issue from the rough set perspective. Granularity is inherently connected with foundation of rough set theory. The concept of the rough set hinges on classification of objects of interest into similarity classes, which form elementary building blocks (atoms, granules) of knowledge. These granules...
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The minimum number of NOT gates in a logic circuit computing a Boolean function is called the inversion complexity of the function. In 1957, A. A. Markov determined the inversion complexity of every Boolean function and proved that ⌈log 2 (d(f)+ 1)⌉ NOT gates are necessary and sufficient to compute any Boolean function f (where d(f) is the maximum number of value changes from greater to smaller...
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ژورنال
عنوان ژورنال: Pure and Applied Mathematics Journal
سال: 2017
ISSN: 2326-9790
DOI: 10.11648/j.pamj.20170601.13