Rule Space Research Articles

ReLiCADA: Reservoir Computing Using Linear Cellular Automata design algorithm

In this paper, we present a novel algorithm to optimize the design of Reservoir Computing using Cellular Automata models for time series applications. Besides selecting the models’ hyperparameters, the proposed algorithm particularly solves the open problem of Linear Cellular Automaton rule selection. The selection method pre-selects only a few promising candidate rules out of an exponentially growing rule space. When applied to relevant benchmark datasets, the selected rules achieve low errors, with the best rules being among the top 5% of the overall rule space. The algorithm was developed based on mathematical analysis of Linear Cellular Automaton properties and is backed by almost one million experiments, adding up to a computational runtime of nearly one year. Comparisons to other state-of-the-art time series models show that the proposed Reservoir Computing using Cellular Automata models have lower computational complexity and, at the same time, achieve lower errors. Hence, our approach reduces the time needed for training and hyperparameter optimization by up to several orders of magnitude.

Association rule mining with a special rule coding and dynamic genetic algorithm for air quality impact factors in Beijing, China.

Understanding air quality requires a comprehensive understanding of its various factors. Most of the association rule techniques focuses on high frequency terms, ignoring the potential importance of low- frequency terms and causing unnecessary storage space waste. Therefore, a dynamic genetic association rule mining algorithm is proposed in this paper, which combines the improved dynamic genetic algorithm with the association rule mining algorithm to realize the importance mining of low- frequency terms. Firstly, in the chromosome coding phase of genetic algorithm, an innovative multi-information coding strategy is proposed, which selectively stores similar values of different levels in one storage unit. It avoids storing all the values at once and facilitates efficient mining of valid rules later. Secondly, by weighting the evaluation indicators such as support, confidence and promotion in association rule mining, a new evaluation index is formed, avoiding the need to set a minimum threshold for high-interest rules. Finally, in order to improve the mining performance of the rules, the dynamic crossover rate and mutation rate are set to improve the search efficiency of the algorithm. In the experimental stage, this paper adopts the 2016 annual air quality data set of Beijing to verify the effectiveness of the unit point multi-information coding strategy in reducing the rule storage air, the effectiveness of mining the rules formed by the low frequency item set, and the effectiveness of combining the rule mining algorithm with the swarm intelligence optimization algorithm in terms of search time and convergence. In the experimental stage, this paper adopts the 2016 annual air quality data set of Beijing to verify the effectiveness of the above three aspects. The unit point multi-information coding strategy reduced the rule space storage consumption by 50%, the new evaluation index can mine more interesting rules whose interest level can be up to 90%, while mining the rules formed by the lower frequency terms, and in terms of search time, we reduced it about 20% compared with some meta-heuristic algorithms, while improving convergence.

About one problem of optimal control synthesis

This paper tackles the problem of characterizing the natural class, or Riccati rule space, of solutions to a specific equation. Despite the significant theoretical and practical implications, there is limited research exploring the application of spectral decomposition of non-self-adjoint differential operators to explicitly solve this nonlinear Riccati equation. Therefore, investigating operator Riccati equations holds potential to validate the dynamic programming method and address the synthesis problem.

The Application of Big Data Technology in English Teaching Mode Innovation and Effect Analysis

Abstract Big data technology provides a detailed development of English language teaching, which is targeted through the assessment of cognitive level. In this paper, ConvSLSTM is used to describe the problem of learners’ knowledge level and build a cognitive framework. With the support of the framework, “recall rate” was introduced to quantify the English vocabulary test results, PSTM ability was adopted to reflect the acquisition of syntactic variants, and attention control was borrowed to evaluate pronunciation characteristics. Based on the initial quantification mentioned above, a hierarchical-level calculation was accomplished by combining fuzzy logic. Meanwhile, based on the estimation of different sides, a rule space model was created, and some corrections were made to achieve the cognitive diagnosis of the group level. In terms of the syntactic developmental trajectory of the girl learners, the maximum value of the range of syntactic variation of the subjects appeared in the middle and late stages. During the early stages of development, the variation range is between 10-35, and the bandwidth is 25, with very little variation. However, in the middle stage of development, it basically starts to oscillate significantly between 10-85, at which time the bandwidth increases to 75. Big data technology has created a comprehensive measurement framework for learners’ English proficiency.

English Translation Stylistic Features and Syntax Translation with Application of Knowledge Mapping

Abstract Aiming at the problems of excessive instantiation complexity, poor interpretability and low generalization ability of knowledge reasoning techniques, this paper unites inductive logic programming ILP with HET neural network to construct a hybrid logic rule and neural network knowledge graph reasoning model - HETIL model. The ILP is utilized to quantify the first-order logic rules, and the multi-layer rule space is constructed by arranging and combining the rules through logic symbols. The rules are instantiated and fed into the HET network, and the attention coefficients aggregate the node features to complete the end-to-end training and generate the rule learning model. Finally, the validity of the model is verified by machine translation experiments, and the results show that the accuracy of the HETIL model in syntactic structure types is more than 0.8 overall. The accuracy in terms of phrase structure reaches 0.879. The average BLEU value of the HETIL model can reach 29.24, which is 1.51 BLEU points higher than the benchmark model. Therefore, the effect of English translation by applying a knowledge graph is better than traditional machine translation.

ACMKC: A Compact Associative Classification Model Using K-Modes Clustering with Rule Representations by Coverage

The generation and analysis of vast amounts of data have become increasingly prevalent in diverse applications. In this study, we propose a novel approach to address the challenge of rule explosion in association rule mining by utilizing the coverage-based representations of clusters determined by K-modes. We utilize the FP-Growth algorithm to generate class association rules (CARs). To further enhance the interpretability and compactness of the rule set, we employ the K-modes clustering algorithm with a distance metric that binarizes the rules. The optimal number of clusters is determined using the silhouette score. Representative rules are then selected based on their coverage within each cluster. To evaluate the effectiveness of our approach, we conducted experimental evaluations on both UCI and Kaggle datasets. The results demonstrate a significant reduction in the rule space (71 rules on average, which is the best result among all state-of-the-art rule-learning algorithms), aligning with our goal of producing compact classifiers. Our approach offers a promising solution for managing rule complexity in association rule mining, thereby facilitating improved rule interpretation and analysis, while maintaining a significantly similar classification accuracy (ACMKC: 80.0% on average) to other rule learners on most of the datasets.

Concise and interpretable multi-label rule sets

Multi-label classification is becoming increasingly ubiquitous, but not much attention has been paid to interpretability. In this paper, we develop a multi-label classifier that can be represented as a concise set of simple “if-then” rules, and thus, it offers better interpretability compared to black-box models. Notably, our method is able to find a small set of relevant patterns that lead to accurate multi-label classification, while existing rule-based classifiers are myopic and wasteful in searching rules, requiring a large number of rules to achieve high accuracy. In particular, we formulate the problem of choosing multi-label rules to maximize a target function, which considers not only discrimination ability with respect to labels, but also diversity. Accounting for diversity helps to avoid redundancy, and thus, to control the number of rules in the solution set. To tackle the said maximization problem, we propose a 2-approximation algorithm, which circumvents the exponential-size search space of rules using a novel technique to sample highly discriminative and diverse rules. In addition to our theoretical analysis, we provide a thorough experimental evaluation and a case study, which indicate that our approach offers a trade-off between predictive performance and interpretability that is unmatched in previous work.

Dynamic scheduling for flexible job shop using a deep reinforcement learning approach

Due to the influence of dynamic changes in the manufacturing environment, a single dispatching rule (SDR) cannot consistently attain better results than other rules for dynamic scheduling problems. Dynamic selection of the most appropriate rule from several SDRs based on the Deep Q-Network (DQN) offers better scheduling performance than using an individual SDR. However, the discreteness of action space caused by the DQN and the simplicity of the action as an SDR limit the selection range and restrict performance improvement. Thus, in this paper, we propose a scheduling method based on deep reinforcement learning for the dynamic flexible job-shop scheduling problem (DFJSP), aiming to minimize the mean tardiness. Firstly, a Markov decision process with composite scheduling action is provided to elaborate the flexible job-shop dynamic scheduling process and transform the DFJSP into an RL task. Subsequently, a composite scheduling action aggregated by SDRs and continuous weight variables is designed to provide a continuous rule space and SDR weight selection. Moreover, a reward function related to mean tardiness performance criteria is designed such that maximizing the cumulative reward is equivalent to minimizing the mean tardiness. Finally, a policy network with states as inputs and weights as outputs is constructed to generate the scheduling decision at each decision point. Also, the deep deterministic policy gradient (DDPG) algorithm is used to train the policy network to select the most appropriate weights at each decision point, thereby aggregating the SDRs into a better rule. Results from numerical experiments reveal that the proposed scheduling method achieves significantly better scheduling results than an SDR and the DQN-based method in dynamically changeable manufacturing environments.

Intelligent Height Adjustment Method of Shearer Drum Based on Rough Set Significance Reduction and Fuzzy Rough Radial Basis Function Neural Network

The intelligent adjustment method of the shearer drum is the key technology to improve the intelligent level and safety degree of fully mechanized mining face. This paper proposes a shearer drum intelligent height adjustment model based on rough set significance attribute reduction (AR) and fuzzy rough radial basis function neural network (FRRBFNN) optimized by adaptive immune genetic algorithm (AIGA). The model first selects the parameters of shearer process monitoring based on the importance attribute reduction algorithm of rough set, and establishes the attribute reduction set of shearer operation characteristic parameters and the drum height decision rule base. Next, a fuzzy rough radial basis function neural network determined by the decision rule space is proposed. By introducing the fuzzy rough membership function as the connection weight, the network can accurately describe the complex nonlinear relationship between the working characteristic parameters of the attribute shearer and the drum height, and measure the uncertainty of the coal seam distribution. Finally, to further optimize the performance of FRRBFNN, the adaptive immune genetic algorithm is introduced to optimize its parameters, to build a high-precision shearer drum height prediction system. For the evaluation method of the model, we use three indicators: mean absolute error, mean absolute percentage error, and root mean square error. Based on the measured data in Yujialiang area, Shaanxi Province, the experimental results show that—compared with the FRRBFNN and support vector regression (SVR) models, a gated current neural network (GRU), a radial basis function neural network (RBF), the memory strengthen long short-term memory (MSLSTM) model, and the adaptive fuzzy reasoning Petri net (AFRPN)—the MAE of the AR-AIGA-FRBFNN model for predicting the height of the left and right rollers are 18.3 mm and 17.2 mm, respectively; the MAPE is 0.96% and 0.93%, respectively; and the RMSE is 21.2 mm and 22.4 mm, respectively. The AR-AIGA-FRBFNN model is therefore more effective than the other considered methods.

Adaptive Spatial Complex Fuzzy Inference Systems With Complex Fuzzy Measures

Fuzzy inference systems, in general, and complex fuzzy inference systems, in particular, play an increasingly important role in many fields, such as change detection, image classification, recognition problems, etc. Despite being the well-known technique to solve with time series data, the rulebase still has the considered limitation because of the directly affecting the results as well as the processing time of these methods. To overcome this limitation, this study proposes an Adaptive spatial complex inference system that can automatically infer and adapt to the new remotely sensed image. In the proposed model, to predict the image of time t + 1, the system will generate a new rulebase according to this expected image. This new rulebase and the previous Co-Spatial-CFIS+ rulebase are evaluated using a complex fuzzy measure. This measure is built by determining the intersection domain between two rule spaces; this intersection value estimates removing, merging, or adding a newly generated rule into the current rulebase. Finally, a more suitable set of rules is obtained for image prediction. To illustrate the efficiency of the proposed approach, it is applied to the remote sensing cloud image data of the U.S. Navy. Our model evaluated the model’s effectiveness in comparison to the state-of-the-art along studies in detecting changes in remote sensing cloud images. Moreover, the findings of the experiments revealed that the proposed model could improve the change detection results in terms of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</i> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> , RMSE, time-consuming, and the number of rules.

Using multivalued logic for qualitative data analysis

В статье рассматривается логический подход к анализу данных для решения задачи классификации. Исследуемые данные представляют собой совокупность объектов и их признаков. Как правило, это разрозненная разнородная информация, и ее недостаточно для разумного применения вероятностных моделей. Поэтому рассматриваются логические алгоритмы, которые при определенных условиях могут оказаться более адекватными. Для выразительного формального представления отношений между объектами и их атрибутами используется многозначная логика, а количество значений зависит от конкретного атрибута. Поэтому предлагается система операций над переменными с разными областями определения. В результате строится решающая функция, которая является классификатором объектов, присутствующих в изучаемых данных. Анализируются свойства и возможности этой функции. Показано, что логическая функция, являющаяся конъюнкцией в пространстве правил, связывающих заданные объекты с их характерными признаками, однозначно характеризует исходные данные, делит предметную область на классы, обладает свойствами модифицируемости, удовлетворяет требованиям полноты и непротиворечивости в заданная область. В работе также предлагается алгоритм его реализации The article considers a logical approach to data analysis for solving the classification problem. The studied data is a set of objects and their features. As a rule, this is disparate heterogeneous information, and it is not enough for a reasonable application of probabilistic models. Therefore, logical algorithms are considered, which, under certain conditions, may be more adequate. For an expressive formal representation of the relationship between objects and their attributes, multivalued logic is used, and the number of values depends on the particular attribute. Therefore, a system of operations on variables with different domains is proposed. As a result, a decision function is built, which is a classifier of objects present in the studied data. The properties and possibilities of this function are analyzed. It is shown that a logical function, which is a conjunction in the space of rules that connect given objects with their characteristic features, unambiguously characterizes the initial data, divides the subject area into classes, has modifiability properties, satisfies the requirements of completeness and consistency in the given area. The paper also proposes an algorithm for its implementation.

Homotopies in Multiway (Nondeterministic) Rewriting Systems as n-Fold Categories

We investigate algebraic and compositional properties of abstract multiway rewriting systems, which are archetypical structures underlying the formalism of the Wolfram model. We demonstrate the existence of higher homotopies in this class of rewriting systems, where homotopical maps are induced by the inclusion of appropriate rewriting rules taken from an abstract rulial space of all possible such rules. Furthermore, we show that a multiway rewriting system with homotopies up to order n may naturally be formalized as an n-fold category, such that (upon inclusion of appropriate inverse morphisms via invertible rewriting relations) the infinite limit of this structure yields an ∞-groupoid. Via Grothendieck’s homotopy hypothesis, this ∞-groupoid thus inherits the structure of a formal homotopy space. We conclude with some comments on how this computational framework of homotopical multiway systems may potentially be used for making formal connections to homotopy spaces upon which models relevant to physics may be instantiated.

The Effect of “Directness” of the Distance Metric to Produce Compact and Accurate Associative Classification Models

Machine learning techniques are ever prevalent as datasets continue to grow daily. Associative classification (AC), which combines classification and association rule mining algorithms, plays an important role in understanding big datasets that generate a large number of rules. Clustering, on the other hand, can contribute by reducing the rule space to produce compact models. The above-mentioned facts were the main motivation for this research work. We propose a new distance (similarity) metric based on “direct” and “indirect” measures and explain the overall importance of this method, which can produce compact and accurate models. Specifically, we aim to employ agglomerative hierarchical clustering to develop new associative classification models that contain a lower number of rules. Furthermore, a new strategy (based on the cluster center) is presented to extract the representative rule for each cluster. Twelve real-world datasets were evaluated experimentally for accuracy and compactness, and the results were compared to those of previously established associative classifiers. The results show that our method outperformed the other algorithms in terms of classifier size on most of the datasets, while still being as accurate in classification.

Liquid Democracy with Ranked Delegations

Liquid democracy is a novel paradigm for collective decision-making that gives agents the choice between casting a direct vote or delegating their vote to another agent. We consider a generalization of the standard liquid democracy setting by allowing agents to specify multiple potential delegates, together with a preference ranking among them. This generalization increases the number of possible delegation paths and enables higher participation rates because fewer votes are lost due to delegation cycles or abstaining agents. In order to implement this generalization of liquid democracy, we need to find a principled way of choosing between multiple delegation paths. In this paper, we provide a thorough axiomatic analysis of the space of delegation rules, i.e., functions assigning a feasible delegation path to each delegating agent. In particular, we prove axiomatic characterizations as well as an impossibility result for delegation rules. We also analyze requirements on delegation rules that have been suggested by practitioners, and introduce novel rules with attractive properties. By performing an extensive experimental analysis on synthetic as well as real-world data, we compare delegation rules with respect to several quantitative criteria relating to the chosen paths and the resulting distribution of voting power. Our experiments reveal that delegation rules can be aligned on a spectrum reflecting an inherent trade-off between competing objectives.

The Rules-Boundaries-Behaviours (RBB) framework for farmers' adoption decisions of sustainable agricultural practices

Farmers are often reluctant to adopt sustainable agricultural practices despite a thorough formal regulatory framework combating unsustainable behaviour. To date, the literature in this area has largely focused on the behavioural aspects of decision-making, with an emphasis on monetary compensation. This paper is an exploratory attempt to develop a new theory for farmers' adoption decisions of sustainable agricultural practices that takes into account both its enablers and its barriers. With an exploratory position, the case of Germany is used as a seminal context for building this new theory that we refer to as the Rules-Boundaries-Behaviours (RBB) framework. The basis for the development of the theory is a systematic literature review taking into account 48 peer-reviewed articles published between 1995 and 2021. The RBB framework illustrates that farmers’ behavioural factors are restricted by boundary conditions (limitations in the personal, farm, farm operation, and environmental spheres), and that these behavioural and boundary conditions are contextually embedded in a complex in/formal rule space. A guideline for the use of the RBB framework in future studies is proposed and an extension of the methodological toolbox with engaged fieldwork is suggested.

Development of a New Learning Progression Verification Method based on the Hierarchical Diagnostic Classification Model: Taking Grade 5 Students’ Fractional Operations as an Example

AbstractLearning progressions can reflect students’ continuous in‐depth thinking development paths, and their establishment is an iterative process from the construction of hypothetical learning progressions to the verification of that hypotheses. Considering the limitations of the existing verification method of learning progressions based on a rule space model, this study put forward a new validating method based on the hierarchical diagnostic classification model (HDCM) and developed a learning progression with grade 5 students’ fraction operations as an example. An expert group first abstracted the attributes and then developed a hypothesized learning progression. Next, the HDCM was used to analyze the test data collected from 817 fifth‐grade students, followed by the revision of the learning progression hypothesis. Results showed that (1) the fractional operations involved five attributes: basic operation (A1), reduction of a fraction (A2), changing fractions to a common denominator (A3), split with mix number (A4), and borrowing (A5); (2) the constructed learning progression featured four levels: Level 1 with A1, Level 2 with both A1 and A2, Level 3 with the first four attributes, and Level 4 with all five attributes.

The popular song in the socio-cultural space of modern Russia: transformation of codes and meanings (based on content analysis materials)

Popular music is one of the instruments of influence on the masses, which raises the importance of tracking the direction of changes in the ideas, broadcast in popular songs. The relevance of this topic relates to the inclusion of Russia in global processes, when intercultural integration becomes one of the factors of transformation of the socio-cultural space under the influence of new rules and patterns of musical life. The purpose of this study is to analyze changes in the codes and meanings of popular songs of modern Russia. The novelty of the study is as follows. Based on the content analysis, general trends in the transformation of codes and meanings of popular songs in Russia from 1990 to 2021 are shown. The growth of listening to popular songs and comments on it was revealed, which indicates the scaling of the impact on the audience, especially on representatives of the younger generation. A decrease in the average age of performers was recorded. It is determined that the main theme of the songs is the theme of love, which is often presented in a tragic or vulgar context. Socially significant positive topics (patriotism, politics, childhood, youth, family) occur in fragments or in isolated cases. An increase in the number of lines of songs with a constant number of words since 2001 has been revealed with a drop in the share of disclosure of the theme of songs, which indicates the destruction of speech and general cultural norms, the desire of performers to “hype”, the growth of popularity, commercial benefits, and not to convey the meaning of the lyrics. The specifics of the song genre in Russia are shown for three periods: 1990-2000, 2001-2010, and 2011-2021. The “roaring”, “heavy-hearted” nineties with a sense of the breakdown of the social system, habitual personal relationships and social ties are replaced by pop “zero” with expectations of positive changes, freedom. The period since 2011 is characterized by a wide variety of stylistic trends and not just significant banality and mediocrity of the text, but also the glorification and justification of deviant behavior, the predominance of pessimistic and sexualized mood, aggression, turning into an insult. This leads to the fact that the song, as a “public singing” that unites and elevates people, becomes dysfunctional, destructive, destroying the personality (especially the emerging one), social ties, the social system, the socio-cultural space of the country as a space of norms and rules. The direction of further research is related to the development of methodological recommendations on the criteria for censoring the musical space in order to restore the speech norm and the traditional Russian system of values.

Theoretical Model of the Structure of Freedom in Psychology

The modern stage of the development of psychological knowledge reveals new opportunities for a more complete consideration of the phenomenon of freedom in psychology, primarily by studying the spiritual dimension of consciousness. There are four layers of consciousness associated with the development of freedom: spiritual, value, reflexive, and existential. It is shown that most authors consider freedom mainly in the reflexive layer of consciousness, linking it with awareness, meaningfulness of life, self-management. There are fewer studies that affect the value layer of consciousness, where freedom is associated with the desire for self-realization, the choice of personal values and meanings; studies of the existential layer, where freedom is considered as a choice of opportunities in the space of culture, the space of social norms and rules. The article presents the approach of V.P. Zinchenko and G.V. Ozhiganova, who showed the importance of the spiritual layer of consciousness, its priority role in relation to the value, reflexive and existential layers. The spiritual layer of consciousness and the corresponding spiritual freedom are poorly studied in psychology, as are the types of freedom and its structural components. Freedom is understood by the author as a component of human consciousness, a product and result of the development of spiritual, value, reflexive and existential layers of consciousness, consisting in the conscious overcoming of external and internal obstacles in the course of life for the purpose of self-realization and spiritual self-improvement. Based on the theoretical analysis of the literature, the author&amp;apos;s model of the structure of freedom as a component of human consciousness is proposed, which describes the structure of two types of freedom: external and internal. The appearance of freedom is determined to a greater extent by the existential, reflexive, value-based, to a lesser extent spiritual layers of consciousness, aimed at self-realization and self-actualization. Interior view of freedom is determined to a greater extent by the spiritual, value and reflexive, to a lesser extent by the existential layer of consciousness, aimed at spiritual self-improvement and personal growth. The theoretical model of the structure of freedom as a component of human consciousness proposed by the author can serve as the basis for the study of freedom in psychology.

Le jeu est à l’espace ce que le récit est au temps. Une anthropologie ricœurienne du jeu comme mimèsis spatiale

By studying the logic that unites play, the rules of games and the body of players, this article intends to highlight a spatial mimesis through play and games. It consists of carrying out a Ricœurian anthropology of play and game, taking Ricœur's analysis of the relationship between time and narrative as a model. The article then shows that play prefigures the physical space as a lived space, that game configures a space of rules and that the player's body is refigured by the spatiality of the rules of the game. This application of the ternary model of Ricœurian mimesis thus allows a unified understanding of play and games by space, and of space by play and games.

Using multivalued logic for qualitative data analysis

The paper considers a logical approach to data analysis to solve the classification problem. The studied data is a set of objects and their features. As a rule, this is scattered heterogeneous information and it is not enough for a reasonable application of probabilistic models. Therefore, logical algorithms are considered, which under certain conditions may be more adequate. For an expressive formal representation of the relationship between objects and their attributes, multivalued logic is used, and the number of values depends on a specific attribute. Therefore, a system of operations is proposed for variables with different domains of definition. As a result, a decisive function is built, which is a classifier of objects that are present in the studied data. The properties and capabilities of this function are analyzed. It is shown that the logical function, which is a conjunction in the space of rules connecting given objects with their characteristic features, uniquely characterizes the initial data, divides the subject area into classes, possesses modifiability properties, meets the requirements of completeness and consistency in a given area. The paper also proposes an algorithm for its implementation.