Clones of Self-Dual and Self-K-Al Functions in K-valued Logic
Issue:
Volume 6, Issue 2, April 2017
Pages:
59-70
Received:
17 February 2017
Accepted:
24 February 2017
Published:
10 March 2017
Abstract: We give a classification of dual functions, they are m-al functions. We call a function m-al with respect to an operator if the operator lives any function unchanged after m times of using the operator. And 2 ≤ m ≤ k. Functions with different m have very different properties. We give theoretical results for clones of self-dual (m = 2) and self- -al (m = k) functions in k-valued logic at k ≤ 3. And we give numerical results for clones of self-dual and self-3-al functions in 3-valued logic. In particular, the inclusion graphs of clones of self-dual and of self-3-al functions are not a lattice.
Abstract: We give a classification of dual functions, they are m-al functions. We call a function m-al with respect to an operator if the operator lives any function unchanged after m times of using the operator. And 2 ≤ m ≤ k. Functions with different m have very different properties. We give theoretical results for clones of self-dual (m = 2) and self- -al...
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Generalization of Kalmar’s Proof of Deducibility in Two Valued Propositional Logic into Many Valued Logic
Chubaryan Anahit,
Khamisyan Artur
Issue:
Volume 6, Issue 2, April 2017
Pages:
71-75
Received:
13 February 2017
Accepted:
15 March 2017
Published:
22 March 2017
Abstract: This paper focuses on the problem of constructing of some standard Hilbert style proof systems for any version of many valued propositional logic. The generalization of Kalmar’s proof of deducibility for two valued tautologies inside classical propositional logic gives us a possibility to suggest some method for defining of two types axiomatic systems for any version of 3-valued logic, completeness of which is easy proved direct, without of loading into two valued logic. This method i) can be base for direct proving of completeness for all well-known axiomatic systems of k-valued (k≥3) logics and may be for fuzzy logic also, ii) can be base for constructing of new Hilbert-style axiomatic systems for all mentioned logics.
Abstract: This paper focuses on the problem of constructing of some standard Hilbert style proof systems for any version of many valued propositional logic. The generalization of Kalmar’s proof of deducibility for two valued tautologies inside classical propositional logic gives us a possibility to suggest some method for defining of two types axiomatic syst...
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Shallow Water 1D Model for Pollution River Study
Antoine Celestin Kengni Jotsa,
Vincenzo Angelo Pennati,
Antonio Di Guardo,
Melissa Morselli
Issue:
Volume 6, Issue 2, April 2017
Pages:
76-88
Received:
25 February 2017
Accepted:
23 March 2017
Published:
15 April 2017
Abstract: In this paper a finite element 1D model for shallow water flows with distribution of chemical substances is presented. The deterministic model, based on unsteady flow and convection-diffusion-decay of the pollutants, allows for evaluating in any point of the space-time domain the concentration values of the chemical compounds. The numerical approach followed is computationally cost-effectiveness respect both the stability and the accuracy, and by means of it is possible to foresee the evolution of the concentrations.
Abstract: In this paper a finite element 1D model for shallow water flows with distribution of chemical substances is presented. The deterministic model, based on unsteady flow and convection-diffusion-decay of the pollutants, allows for evaluating in any point of the space-time domain the concentration values of the chemical compounds. The numerical approac...
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