Theoretical Foundations of Ternary Logic Application in Logical-Probabilistic Method for Assessment of Socio-Economic System Reliability

Karasev, V. B.

doi:10.1109/itms52826.2021.9615326

2021 62nd International Scientific Conference on Information Technology and Management Science of Riga Technical University (IT 2021

DOI: 10.1109/itms52826.2021.9615326

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Theoretical Foundations of Ternary Logic Application in Logical-Probabilistic Method for Assessment of Socio-Economic System Reliability

V. B. Karasev

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“…Then, these are used to build a combination of any other state as the ternary predicate as well as handling the ternary the whole system state. Th reliability functions are also written as a three-valued logic predicate [58].…”

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confidence: 99%

Lattice Structure of Some Closed Classes for Three-Valued Logic and Its Applications

Kalimulina

2021

Mathematics

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This paper provides a brief overview of modern applications of nonbinary logic models, where the design of heterogeneous computing systems with small computing units based on three-valued logic produces a mathematically better and more effective solution compared to binary models. For application, it is necessary to implement circuits composed of chipsets, the operation of which is based on three-valued logic. To be able to implement such schemes, a fundamentally important theoretical problem must be solved: the problem of completeness of classes of functions of three-valued logic. From a practical point of view, the completeness of the class of such functions ensures that circuits with the desired operations can be produced from an arbitrary (finite) set of chipsets. In this paper, the closure operator on the set of functions of three-valued logic that strengthens the usual substitution operator is considered. It is shown that it is possible to recover the sublattice of closed classes in the general case of closure of functions with respect to the classical superposition operator. The problem of the lattice of closed classes for the class of functions T2 preserving two is considered. The closure operators R1 for the functions that differ only by dummy variables are considered equivalent. This operator is withiin the scope of interest of this paper. A lattice is constructed for closed subclasses in T2={f|f(2,…,2)=2}, a class of functions preserving two.

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Lattice Structure of Some Closed Classes for Three-Valued Logic and Its Applications

Kalimulina

2021

Mathematics

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Theoretical Foundations of Ternary Logic Application in Logical-Probabilistic Method for Assessment of Socio-Economic System Reliability

Cited by 1 publication

References 4 publications

Lattice Structure of Some Closed Classes for Three-Valued Logic and Its Applications

Lattice Structure of Some Closed Classes for Three-Valued Logic and Its Applications

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