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Automated Proof Search System for Logic of Correlated Knowledge
Haroldas Giedra,
Romas Alonderis
Issue:
Volume 5, Issue 2, June 2020
Pages:
29-42
Received:
4 October 2019
Accepted:
2 March 2020
Published:
14 April 2020
Abstract: Logic of correlated knowledge is one of the latest development in logical systems, allowing to handle information about quantum systems. Quantum system may consist of one or more elementary particles. Associating agent to each particle, we get multi-agent system, where agents can perform observations and get results. Allowing communication between agents, correlations such as quantum entanglement can be extracted. This can not be done by traditional epistemic logic or logic of distributed knowledge. Our main scientific result is proof search system GS-LCK-PROC for logic of correlated knowledge, which lets to reason about knowledge automatically. The core of the system is the sequent calculus GS-LCK with the properties of soundness, completeness, admissibility of cut and structural rules, and invertibility of all rules. The ideas of semantic internalization are used to get such properties for the calculus. The calculus provides convenient means for backward proof search and decision procedure for logic of correlated knowledge. The procedure generates a finite model for each sequent. As a result we get termination of the proof search and decidability of logic of correlated knowledge.
Abstract: Logic of correlated knowledge is one of the latest development in logical systems, allowing to handle information about quantum systems. Quantum system may consist of one or more elementary particles. Associating agent to each particle, we get multi-agent system, where agents can perform observations and get results. Allowing communication between ...
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An Elementary Proof of a Result Ma and Chen
Issue:
Volume 5, Issue 2, June 2020
Pages:
43-46
Received:
15 January 2020
Accepted:
11 February 2020
Published:
23 April 2020
Abstract: In 1956, Je_smanowicz conjectured that, for positive integers m and n with m > n; gcd(m; n) = 1 and m ≢ n (mod 2), the exponential Diophantine equation (m2 -n2)x + (2mn)y = (m2 + n2)z has only the positive integer solution (x; y; z) = (2; 2; 2). Recently, Ma and Chen proved the conjecture if 4 ☓mn and y ≥ 2. In this paper, we provide a proposition that, for positive integers m and n with m > n; gcd(m; n) = 1 and m2 + n2 ≡ 5 (mod 8), the exponential Diophantine equation (m2 -n2)x + (2mn)y = (m2 + n2)z has only the positive integer solution x = y = z = 2 with 2j gcd(x; y). Then we present an elementary and simple proof of the result of Ma and Chen by using Jacobi’s symbols.
Abstract: In 1956, Je_smanowicz conjectured that, for positive integers m and n with m > n; gcd(m; n) = 1 and m ≢ n (mod 2), the exponential Diophantine equation (m2 -n2)x + (2mn)y = (m2 + n2)z has only the positive integer solution (x; y; z) = (2; 2; 2). Recently, Ma and Chen proved the conjecture if 4 ☓mn and y ≥ 2. In this paper, we provide a proposition ...
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Parameter Selection Strategy for Frequent Itemsets in Association Analysis
Issue:
Volume 5, Issue 2, June 2020
Pages:
47-50
Received:
16 March 2020
Accepted:
8 April 2020
Published:
12 May 2020
Abstract: In data mining, association analysis mainly deals with different associations between things. Different degrees of correlation are usually treated differently in performance. In a production society, people are more interested in understanding the strong relationships between things, while ignoring weaker relationships, thereby making meaningful and valuable decisions. However, people must face several problems. For example, how to use parameters to define strong correlation; how to define meaningful parameters, this article uses experiments to explain the main factors affecting the parameters and how to select parameter values. Find the balance point where the application association produces economic value, then this balance point is a more meaningful parameter. The purpose of this article is to find the support and credibility based on association analysis through dichotomy, and compare the application analysis of the same metric value in different scenarios. Experimental results show that selecting the same parameter value in different scenarios' associated demand analysis (such as attribute association analysis) will not produce the same benefit. In the same scenario, the dichotomy method can make the parameter value close to a more meaningful value. Therefore, how to define the parameters of frequent itemsets to produce the maximum benefit is the significance of this article.
Abstract: In data mining, association analysis mainly deals with different associations between things. Different degrees of correlation are usually treated differently in performance. In a production society, people are more interested in understanding the strong relationships between things, while ignoring weaker relationships, thereby making meaningful an...
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Symmetry Analysis of the Fokker Planck Equation
Faya Doumbo Kamano,
Bakary Manga,
Joël Tossa
Issue:
Volume 5, Issue 2, June 2020
Pages:
51-60
Received:
30 January 2020
Accepted:
20 February 2020
Published:
28 May 2020
Abstract: In this work, the infinitesimal criterion of invariance for determining symmetries of partial differential equations is applied to the Fokker Planck equation. The maximum rang condition being satisfied, we determine the Lie point symmetries of this equation. Due to the nature of infinitesimal generators of these symmetries and the stability of Lie brackets, we obtain an infinite number of solutions from which we find examples of solutions for the Fokker Planck equation: other solutions are generated given a particular solution of the equation. Then, the Fokker Planck equation admits a conserved form, hence there is an auxiliary system associated to this equation. We show that this system admits six and an infinite number of infinitesimal generators of point symmetries giving rise to two potential symmetries of the Fokker Planck equation. We then use those potential symmetries to determine solutions of the associated system and therefore provide other solutions of the Fokker Planck equation. Note that these are essentially obtained on the basis of the invariant surface conditions. With respect to these conditions and from the potential symmetries that we have found, we finally show that in particular, some solutions of the considered Fokker Planck equation reduced to the trivial solution (solutions that are zero).
Abstract: In this work, the infinitesimal criterion of invariance for determining symmetries of partial differential equations is applied to the Fokker Planck equation. The maximum rang condition being satisfied, we determine the Lie point symmetries of this equation. Due to the nature of infinitesimal generators of these symmetries and the stability of Lie ...
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