Novel Hopfield Neural Network Model with Election Algorithm for Random 3 Satisfiability

One of the influential models in the artificial neural network (ANN) research field for addressing the issue of knowledge in the non-systematic logical rule is Random k Satisfiability. In this context, knowledge structure representation is also the potential application of Random k Satisfiability. Despite many attempts to represent logical rules in a non-systematic structure, previous studies have failed to consider higher-order logical rules. As the amount of information in the logical rule increases, the proposed network is unable to proceed to the retrieval phase, where the behavior of the Random Satisfiability can be observed. This study approaches these issues by proposing higher-order Random k Satisfiability for k ≤ 3 in the Hopfield Neural Network (HNN). In this regard, introducing the 3 Satisfiability logical rule to the existing network increases the synaptic weight dimensions in Lyapunov’s energy function and local field. In this study, we proposed an Election Algorithm (EA) to optimize the learning phase of HNN to compensate for the high computational complexity during the learning phase. This research extensively evaluates the proposed model using various performance metrics. The main findings of this research indicated the compatibility and performance of Random 3 Satisfiability logical representation during the learning and retrieval phase via EA with HNN in terms of error evaluations, energy analysis, similarity indices, and variability measures. The results also emphasized that the proposed Random 3 Satisfiability representation incorporates with EA in HNN is capable to optimize the learning and retrieval phase as compared to the conventional model, which deployed Exhaustive Search (ES).

Logic Learning in Adaline Neural Network

In this paper, Adaline Neural Network (ADNN) has been explored to simulate the actual signal processing between input and output. One of the drawback of the conventional ADNN is the use of the non-systematic rule that defines the learning of the network. This research incorporates logic programming that consists of various prominent logical representation. These logical rules will be a symbolic rule that defines the learning mechanism of ADNN. All the mentioned logical rule are tested with different learning rate that leads to minimization of the Mean Square Error (MSE). This paper uncovered the best logical rule that could be governed in ADNN with the lowest MSE value. The thorough comparison of the performance of the ADNN was discussed based on the performance MSE. The outcome obtained from this paper will be beneficial in various field of knowledge that requires immense data processing effort such as in engineering, healthcare, marketing, and business.

Systematic Boolean Satisfiability Programming in Radial Basis Function Neural Network

Radial Basis Function Neural Network (RBFNN) is a class of Artificial Neural Network (ANN) that contains hidden layer processing units (neurons) with nonlinear, radially symmetric activation functions. Consequently, RBFNN has extensively suffered from significant computational error and difficulties in approximating the optimal hidden neuron, especially when dealing with Boolean Satisfiability logical rule. In this paper, we present a comprehensive investigation of the potential effect of systematic Satisfiability programming as a logical rule, namely 2 Satisfiability (2SAT) to optimize the output weights and parameters in RBFNN. The 2SAT logical rule has extensively applied in various disciplines, ranging from industrial automation to the complex management system. The core impetus of this study is to investigate the effectiveness of 2SAT logical rule in reducing the computational burden for RBFNN by obtaining the parameters in RBFNN. The comparison is made between RBFNN and the existing method, based on the Hopfield Neural Network (HNN) in searching for the optimal neuron state by utilizing different numbers of neurons. The comparison was made with the HNN as a benchmark to validate the final output of our proposed RBFNN with 2SAT logical rule. Note that the final output in HNN is represented in terms of the quality of the final states produced at the end of the simulation. The simulation dynamic was carried out by using the simulated data, randomly generated by the program. In terms of 2SAT logical rule, simulation revealed that RBFNN has two advantages over HNN model: RBFNN can obtain the correct final neuron state with the lowest error and does not require any approximation for the number of hidden layers. Furthermore, this study provides a new paradigm in the field feed-forward neural network by implementing a more systematic propositional logic rule.

Logic mining in football matches

Sports results forecast has became increasingly popular among the fans nowadays. It made predicting the outcome of a sport’s match, a new and interesting challenge. This paper presented a logic mining technique to model the results (Win Draw / Lose) of the football matches played in English Premier League, Spanish La Liga and France Ligue 1. In this research, a method namely <em>k</em> satisfiability based reverse analysis method (<em>k</em>SATRA) hybridized with Ant Colony Optimization (ACO) was brought forward to obtain the logical relationship among the clubs in these leagues. The logical rule obtained from the football matches was used to categorize the results of future matches. ACO is a population-based and nature-inspired algorithm to decipher several combinatorial optimization problems. <em>k</em>SATRA made use of the advantages of Hopfield Neural Network and k Satisfiability representation. The data set used in this study included the data of 6 clubs from each league, which composed of all league matches from year 2014 to 2018. The effectiveness of <em>k</em>SATRA with ACO in obtaining logical rule in football matches was tested based on root mean square error (RMSE), mean absolute error (MAE), mean absolute percentage error (MAPE) and CPU time. Results acquired from the computer simulation showed the robustness of <em>k</em>SATRA in exhibiting the performance of the clubs.

VIOLATIONS OF THE LAW OF THE EXCLUDED MIDDLE IN MEDIA DISCOURSE

The paper is devoted to the study of violations of one of the laws of formal logic: the law of the excluded middle; those violations are found in modern media discourse. The authors examined the relationship between deviations from the law of non-contradiction (contradiction) and the law of the excluded middle and came to the conclusion that violations of the law of the excluded middle occur in speech only in symbiosis with violations of the law of non-contradiction. The analysis of examples from journalistic tests showed that deviations from the law of the excluded middle can be of two types depending on the reasons for their occurrence. If a logical rule is violated unknowingly, a logical error appears in the text. In the case when the author intentionally goes to damage the logical structure of the utterance, the violation is a technique. In turn, the goals of the addressee predetermine the division of techniques into manipulative (in the case when a recipient should not notice logical inconsistencies) and stylistic ones: tropes and figures (which are designed to influence an addressee openly).