Simple Logical Rules Research Articles

Performance Analysis of PI, T1NFC, and T2NFC of Indirect Vector Control-Based Induction Motor Using DSpace-2812

A type 2 Neuro-Fuzzy torque controller for indirect vector control (IVC) based induction motor (IM) driving is presented in this work. In various operating modes, a linear fixed-gain proportional-integral (PI) based speed controller is employed in indirect vector control of an IM drive (IMD). To achieve high performance, the PI controller (PIC) requires precise and accurate gain parameters. The PIC gain values have been tuned for a specific operating point and may not perform satisfactorily when the load torque and operating point change. To enhance dynamic performance over a wide speed range and reduce load torque ripple, the PIC is replaced by a Type-1 neuro-fuzzy logic controller (T1NFC). The T1FLC is simple, easy to use, and successful at dealing with nonlinear control systems without the use of complex mathematical equations. Instead, it relies on simple logical rules that are decided by an expert. The T1NFC is replaced by a Type-2 neuro-fuzzy logic controller to enhance controller performance. Owing to the availability of three-dimensional control with type-reduction technique (i.e. Type-2 fuzzy sets and Type-2 reducer set) in the defuzzification process, the T2NFC effectively handles the large footprint of uncertainties compared to the T1NFC, whereas the T1NFC have only Type-1 fuzzy sets and a single membership function. The T2NFC using MATLAB Simulink is used to observe the induction motor performance characteristics like, stator phasor current, torque, and speed under various operating situations. T2NFC controllers provide better driving performance characteristics than PI and T1NFC controllers. When associated to the PI and T1NFC controllers, the suggested T2NFC greatly reduce the amount of ripple in the torque and stator current of the IM drive. Practical validation is also performed with a 3.7 KW IM drive and a DSP 2812 controller for real-time examination of the drive parameters.

Multi-criteria risk evaluation model for developing ventilator-associated pneumonia.

Ventilator-associated pneumonia is a hospital-acquired infection of the lungs occurring in mechanically ventilated patients. An active risk management approach can prevent the occurrence of the disease and promote positive organizational changes, subsequently decreasing mortality and hospitalization costs. Using scientific and clinical practice knowledge, a risk evaluation model was developed to identify patients more at risk of developing the disease. For this purpose, a Decision Expert qualitative multi-criteria decision method was used, in which alternatives are evaluated according to predetermined hierarchically arranged criteria. Characteristics of each evaluated alternative are described by the members of an interdisciplinary expert team and are represented by the values of the basic criteria. Values of hierarchically higher aggregated criteria are computed in an upwards fashion according to utility functions, which are defined as simple logical rules. This method is integrated into a software solution, DEXi. The approach is applicable to vastly diverse decision problems and has been successfully used before for health-related decision support. The designed model was tested using actual clinical data. Evaluations of alternatives that most distinctly demonstrated the functionality of the evaluation model were selected and are presented in the results. The evaluation model is intended to assist a holistic evaluation of the risk of developing ventilator-associated pneumonia, by considering patient-related risk factors and the use of preventive measures. The model incorporates nursing-specific data that have hitherto been poorly utilized in preventing ventilator-associated pneumonia and promotes the active engagement of nurses in confronting this interdisciplinary healthcare problem, which has gained more prominence with the onset of COVID-19 disease.

Fairness in Resource Distribution: Relationship between Children’s Moral Reasoning and Logical Reasoning

Abstract Introduction: The aim of this study is to examine children’s moral reasoning and logical reasoning processes and the relationship between these two mechanisms. In the present study the focus is on the relationship between the factors such as fair sharing, equality, merit, ownership, opportunity in the resource allocation and logical reasoning among the children aged 5-7. Methods: In this study, which aims to examine how the logical thinking skills differ according to the children’s moral reasoning process, a survey design approach was used. Participants were 92 children aged 5 (female N=13, male N=14) and aged 6 (female N=17, male N=18), aged 7 (female N=17, male N=13). The data collected from the moral and logical reasoning tasks were analyzed in two steps. At the first step the answers of the participants were scored. At the second step their justifications were categorized. To test out hypotheses we used two general linear models to examine the age effects of Age (5-7 years) and Reasoning (equality, ownership, merit, opportunity) on children’s evaluations of the vignette characters’ actions. Age-related changes in children’s evaluation and their logical reasoning skills related to initial distribution and transfer status were analyzed by the variance analysis. Results: Based on the findings of the study it can be stated that the children in the age group of 6-7 evaluated negatively the reward distribution based on the outcomes due to their concerns about the inequality in the opportunities and the violation of the principle of equality. The findings of the study indicate that there is no significant difference in children’s logical thinking skills depending on their age. As a result of the study, it is found that although there is no direct relationship between the moral and logical reasoning processes of children, the children who can reject the AC type inference predominantly emphasize the principle of equality. Although there is no significant relationship between moral reasoning and logical reasoning processes, it can be said that children with higher levels of logical reasoning much more frequently emphasize the principle of equality in moral reasoning process. Discussion: Research indicates that children aged around 5 consider the reward distribution based on the outcomes fair. Older children, on the other hand, evaluate the inequalities in resource distribution as unfair. These findings support the results of the study suggesting that older children consider inequal source distribution both at the first case and at the transfer cases unfair. The children’s approval or disapproval of the transfer varies based on their reasoning processes. They support transfer if they emphasize the principle of equality, but they do not support it if their focus is on the principle of ownership. Older children are found to have a commitment to the principle of equality, and the difference between the 5-year age group and the 6-7-year age group is remarkable in this regard. Similar findings are reported in the previous studies, and it is generally stated that younger children are more selfish and that the tendency to distribute resources equally becomes dominant due to the increase in the age of children. Although there is no significant relationship between moral reasoning and logical reasoning processes, it can be said that children with higher levels of logical reasoning emphasize the principle of equality in moral reasoning process much more frequently. Conclusion: Cognitivists argue that cognition and particularly reasoning have significant roles in making moral decisions. It suggests that children whose logical thinking skills are higher than others understand the necessity of equality to ensure fairness. The basic information on logic should be taught and introduced to the children from an early age. In addition, children should be ensured to use these methods through connections with both daily life and other courses at schools. It is thought that having basic logic knowledge by children will affect positively their cognitive, affective and social development. In order to examine this effect, a logic program including simple logic rules and basic inference types should be developed and the effects of such programs on the cognitive, affective and social development of children should be examined.

Çocukların Eşit Paylaşım Davranışının Mantıksal Düşünme Becerileriyle İlişkisi

Bu araştırmanın amacı, çocukların eşit paylaşımı tercih etme/etmeme durumlarına göre, mantıksal düşünme becerilerinin nasıl farklılaştığını incelemektir. Bu kapsamda, çocukların eşit paylaşımda bulunma/bulunmama davranışlarına göre mantıksal düşünme becerilerinin nasıl farklılaştığı ve bu sürecin yaşa bağlı değişimi incelenmiştir. Bu araştırmaya okul öncesi ve ilkokul düzeyinde eğitim görmekte olan 5-7 yaş aralığındaki 104 çocuk katılmıştır. Veri toplama sürecinde çocukların eşit paylaşım davranışlarını incelemek amacıyla iki farklı içeriğe sahip (şeker ve etiket paylaşımı) etkinlikten yararlanılmıştır. Çocukların mantıksal düşünme becerilerini incelemek amacıyla iki farklı çıkarım türünden oluşan üç soru sorulmuştur. Araştırma sonucunda, hem çıkartma hem de şeker kullanılan uygulamalarda çocukların büyük bir çoğunluğunun eşit paylaşım davranışı gerçekleştirdiği görülmüştür. Eşit paylaşımda bulunan çocuklar bu tercihlerinin sebebini genellikle adalet konusuna vurgu yaparak açıklamıştır. Çocukların yaşlarındaki artışa bağlı olarak eşit paylaşım davranışının arttığı görülmüştür. Araştırma sonucunda çocukların özellikle alternatif öncüller üretmelerini gerektiren çıkarım türlerinde zorlandıkları görülmüştür. Bunun yanında çocukların mantıksal düşünme becerilerinde görülen farklılaşmanın eşit paylaşım davranışı sergileme durumuyla ilişkisi incelenmiştir. Kaynak olarak şeker seçildiğinde, eşit paylaşımı tercih eden çocukların yaşça büyük olduğu ve mantıksal düşünme becerilerinin de daha gelişmiş olduğu tespit edilmiştir. Çocukların temel düzey mantık bilgisine sahip olmalarının bilişsel, duyuşsal ve sosyal boyutta gelişimlerini olumlu yönde etkileyeceği düşünülmektedir. Bu etkiyi incelemek amacıyla basit mantık kurallarını ve temel çıkarım türlerini içeren bir mantık programı hazırlanarak çocukların bilişsel, duyuşsal ve sosyal boyutlardaki gelişimlerine etkisi incelenmelidir.

Optimization of Association Rules for Students' Data: A Soft Set

Association rule (AR) mining is a common method to find the associations between objects in a transaction or in a data set, which is simple logical rules, determine the critical relationship among the objects. The rule generation is difficult if it satisfies a predefined threshold value. To trace the relationship is very important for domains to reveal crucial and hidden information from the data set. Some critical relationship of the objects may appear rarely and to trace them using classical methods are difficult one. The apriori algorithm (AA) with hashing technique along with the PDI algorithm is used to find the appropriate ARs from the students’ dataset. Since soft set is a tool for handling imprecise parameterized data, the soft set concept is used in optimization process to get optimized ARs. In this paper, the ARs are optimized using soft set for further analysis.

A Three-Level Fuzzy-2 DTC of Induction Motor Drive Using SVPWM

This paper presents proportional integral direct torque control (PIDTC) and fuzzy-2 DTC (F2DTC) of the induction motor (IM) drive using space vector pulse width modulation (SVPWM) for three-level diode-clamped inverter (TDCI). The above control schemes have been implemented in the laboratory using 2 HP IM through a DSPACE DS-1104 controller. The control schemes are capable to balance the dc-link capacitor voltages of TDCI by selecting an optimum voltage vector without using an extra controller. However, the three-level PIDTC of an IM gives poor transient performance during starting, loading, and speed reversal with considerable current and voltage total harmonic distortion (THD). In addition, it takes more time to reach the steady state with large spikes on capacitor voltages during the load or speed variation. This is due to poor performance of the PI controllers (speed and torque). In F2DTC, the conventional PI controllers are replaced by Mamdani-type fuzzy-2 controllers using a centroid method with simple logical rules. The simulated and experimental performance show that F2DTC for the three-level inverter-fed IM drive provides a fast dynamic response, less current and voltage THDs, considerable less distortion in flux and torque, and fewer spikes on capacitor voltages as compared to PIDTC.

Fuzzy rule‐based decision support system for evaluation of long‐established forest restoration projects

Although the importance of monitoring and evaluation of restoration actions is increasingly acknowledged, availability of accurate, quantitative monitoring data is very rare for most restoration areas, particularly for long‐established restoration projects. We propose using fuzzy rule‐based expert systems to evaluate the degree of success of restoration actions when available information on project results and impacts largely relies on expert‐based qualitative assessments and rough estimates of quantitative values. These systems use fuzzy logic to manage the uncertainty present in the data and to integrate qualitative and quantitative information. To illustrate and demonstrate the potential of fuzzy rule‐based systems for restoration evaluation, we applied this approach to seven forest restoration projects implemented in Spain between 1897 and 1952, using information compiled in the REACTION database on Mediterranean forest restoration projects. The information available includes both quantitative and expert‐based qualitative data, and covers a wide variety of indicators grouped into technical, structural, functional, and socioeconomic criteria. The fuzzy rule‐based system translates expert knowledge of restoration specialists and forest managers into a set of simple logic rules that integrate information on individual indicators into more general evaluation criteria. The rule‐based approach proposed here can be readily applicable to any kind of restoration project, provided that some information, even if vague and uncertain, is available for a variety of assessment indicators. The evaluation of long‐established forest restoration projects implemented in Spain revealed important asymmetries in the degree of restoration success between technical, structural, functional, and socioeconomic criteria.

Copper Loss and Torque Ripple Minimization in Switched Reluctance Motors Considering Nonlinear and Magnetic Saturation Effects

The discrete torque generation mechanism and inherently nonlinear magnetic characterization of switched reluctance motors lead to unacceptable torque ripples and limit the application of these motors. In this study, a phase current profiling technique and torque sharing function are proposed in consideration of magnetic saturation effects and by minimizing power loss in the commutation area between the adjacent phases. Constant torque trajectories are considered in incoming and outgoing phase current planes based on nonlinear T-i-theta curves obtained from experimental measurements. Optimum points on constant torque trajectories are selected by improving drive efficiency and minimizing copper loss in each rotor position. A novel analytic invertible function is introduced to express phase torque based on rotor position and its corresponding phase current. The optimization problem is solved by the proposed torque function, and optimum torque sharing functions are derived. A modification method is also introduced to enhance the torque ripple-free region based on simple logic rules. Compared with conventional torque sharing functions, the resultant reference current from the proposed method has less peak and effective values and exhibits lower copper loss. Experimental and simulation results from a four-phase 4 KW 8/6 SRM validate the effectiveness of the proposed method.

An Algorithmic Approach to Inferring Cross-Ontology Links while Mapping Anatomical Ontologies

Automated and semi-automated mapping and the subsequently merging of two (or more) anatomical ontologies can be achieved by (at least) two direct procedures. The first concerns syntactic matching between the terms of the two ontologies; in this paper, we call this direct matching (DM). It relies on identities between the terms of the two input ontologies in order to establish cross-ontology links between them. The second involves consulting one or more external knowledge sources and utilizing the information available in them, thus providing additional information as to how terms (concepts) from the two input ontologies are related/linked to each other. Each of the two ontologies is aligned to an external knowledge source and links representing synonymy, is-a parent-child, and part-of parent-child relations, are drawn between the ontology and the knowledge source. These links are then run through a set of simple logical rules in order to come up with cross-ontology links between the two input ontologies. This method is known as semantic matching. It proves useful and reasonably accurate; in this paper, we call it the source matching predictions (SMP) procedure.Not all cross-ontology links that semantically (i.e., from a biological/anatomical standpoint) exist between the two input ontologies will be discovered by either DM or SMP. To improve the discovery of cross-ontology links we propose a novel algorithmic procedure which involves a probability-like scoring scheme. This procedure is called the child matching predictions (CMP) procedure. Describing the DM, SMP, CMP procedures, and particularly the CMP procedure in formal terms is the main goal of this paper.

An Argumentation-Driven Model for Flexible and Efficient Persuasive Negotiation

The purpose of this paper is to propose a formal description and implementation of a negotiation protocol between autonomous agents using persuasive argumentation. This protocol is designed to be simple and computationally efficient. The computational efficiency is achieved by specifying the protocol as a set of simple logical rules that software agents can easily combine. These latter are specified as a set of computational dialogue games about which agents can reason. The protocol converges by checking the termination conditions. The paper discusses the formal properties of the protocol and addresses, as proof of concept, the implementation issues using an agent-oriented platform equipped with logical programming mechanisms.

Modeling and Control of Fluid Transportation Operations in Production Plants With Petri Nets

In industrial plants various material flows take place, connecting processing and storing units to accomplish specific product routings. For example, chemical and batch plants are characterized by fluid exchange between tanks, reactors, filters, distillation columns, etc. Such fluid transportation operations may involve the use of many elementary transporting resources (e.g., pipes and valves), which can be extremely complicated to manage, especially in the case of concurrent material transfer and possibly conflicting commands. A systematic modeling and control approach for such operations is proposed based on Petri nets, which employs aggregate transportation resources denoted lines, for which suitable definitions of dependency and compatibility are provided. The actual management of valves is demanded to a specific control module, which computes valve commands with simple logical rules on the basis of the marking of resource places in the supervisor Petri net. The hierarchical and modular control architecture separates the resource allocation and deadlock avoidance problems from the physical device management, thus limiting system complexity. The general ideas discussed in this brief have been exemplified with a simple batch process example drawn from the literature.

Multibiometrics for face recognition

Fusion is a popular practice to combine multiple sources of biometric information to achieve systems with greater performance and flexibility. In this paper various approaches to fusion within a multibiometrics context are considered and an application to the fusion of 2D and 3D face information is discussed. An optimal method for fusing the accept/reject decisions of individual biometric sources by means of simple logical rules is presented. Experimental results on the FRGC 2D and 3D face data show that the proposed technique performs effectively without the need for score normalization.

Composite Time Lines: A Means to Leverage Resolving Power from Radioisotopic Dates and Biostratigraphy

Species origination and extinction events far outnumber radioisotopically dated events in the ancient stratigraphic record. In order to calibrate rapid rates of Mesozoic and Paleozoic change and to estimate the ages of paleobiologic events it would be ideal to have multiple dated events in single stratigraphic sections. This condition is rarely realized and the practical alternative is to build composite sections that combine information from many different locations. The compositing process takes advantage of all available evidence of relative age to produce high resolution time lines; i.e. ordered sequences of individual events whose average spacing is much finer than the duration of biostratigraphic zones and can approach the uncertainty intervals of the highest precision radioisotopic dates. Dated events are included in the compositing process from the outset. As a result the sequencing procedure is more efficient and the dated events find their optimal positions in the time line independent of any biostratigraphic zonal schemes. The sequencing procedures follow simple logical rules that may be learned from tiny data sets. When usefully large numbers of events are involved, however, the sequencing must be undertaken by computer and there is seldom a unique solution that best fits the field data. The range of positions in sequence that an event may occupy across the full set of equally best-fit solutions is a measure of the resolving power of the event. As new high-precision dates and detailed range charts continue to become available, the quality of the time lines will improve and they will become increasingly viable alternatives to zonal time scales in the older parts of the Phanerozoic.

Computational intelligence methods for rule-based data understanding

In many applications, black-box prediction is not satisfactory, and understanding the data is of critical importance. Typically, approaches useful for understanding of data involve logical rules, evaluate similarity to prototypes, or are based on visualization or graphical methods. This paper is focused on the extraction and use of logical rules for data understanding. All aspects of rule generation, optimization, and application are described, including the problem of finding good symbolic descriptors for continuous data, tradeoffs between accuracy and simplicity at the rule-extraction stage, and tradeoffs between rejection and error level at the rule optimization stage. Stability of rule-based description, calculation of probabilities from rules, and other related issues are also discussed. Major approaches to extraction of logical rules based on neural networks, decision trees, machine learning, and statistical methods are introduced. Optimization and application issues for sets of logical rules are described. Applications of such methods to benchmark and real-life problems are reported and illustrated with simple logical rules for many datasets. Challenges and new directions for research are outlined.

A new methodology of extraction, optimization and application of crisp and fuzzy logical rules

A new methodology of extraction, optimization, and application of sets of logical rules is described. Neural networks are used for initial rule extraction, local or global minimization procedures for optimization, and Gaussian uncertainties of measurements are assumed during application of logical rules. Algorithms for extraction of logical rules from data with real-valued features require determination of linguistic variables or membership functions. Contest-dependent membership functions for crisp and fuzzy linguistic variables are introduced and methods of their determination described. Several neural and machine learning methods of logical rule extraction generating initial rules are described, based on constrained multilayer perceptron, networks with localized transfer functions or on separability criteria for determination of linguistic variables. A tradeoff between accuracy/simplicity is explored at the rule extraction stage and between rejection/error level at the optimization stage. Gaussian uncertainties of measurements are assumed during application of crisp logical rules, leading to "soft trapezoidal" membership functions and allowing to optimize the linguistic variables using gradient procedures. Numerous applications of this methodology to benchmark and real-life problems are reported and very simple crisp logical rules for many datasets provided.

A rule-plus-exception model for classifying objects in continuous-dimension spaces

The authors propose a rule-plus-exception (RULEX) model for how observers classify stimuli residing in continuous-dimension spaces. The model follows in the spirit of the discrete-dimension version of RULEX developed by Nosofsky, Palmeri, and McKinley (1994). According to the model, observers learn categories by forming simple logical rules along single dimensions and by remembering occasional exceptions to those rules. In the continuous-dimension version of RULEX, the rules are formalized in terms of linear decision boundaries that are orthogonal to the coordinate axes of the psychological space. In addition, a similarity-comparison process governs whether stored exceptions are used to classify an object. The model provides excellent quantitative fits both to averaged classification transfer data and to distributions of generalizations observed at the individual-participant level. The modeling analyses suggest that, when multiple rules are available for solving a problem, averaged classification data often represent a probabilistic mixture of idiosyncratic rule-plus-exception strategies.

Methodological aspects of using decision trees to characterise leiomyomatous tumors

The aim of the present work is to present the potential uses of a classification technique labeled the "decision tree" for tumor characterisation when faced with a large number of features. The decision tree technique enables multifeature logical classification rules to be produced by determining discriminatory values for each feature selected. In this report, we propose a methodology that used decision trees to compare and evaluate the information contributed by different types of features for tumor characterisation. This methodology is able to produce a set of hypotheses related to a diagnosis and or prognosis problem. For example, hypotheses can be producted (on the basis of a set of descriptive features) to explain why tumor cases belong to a given histopathological group. To illustrate our purpose, this methodology was applied to the difficult problem of leiomyomatous tumour diagnosis. The aim was to illustrate what kind of diagnostic information can be extracted from a sample data set including 23 smooth muscle tumors (14 benign leiomyomas and 9 malignant leiomyosarcomas) described by a large set of computer-assisted, microscope-generated features. Three groups of features were used relating to: (1) ploidy level determination (10 features), (2) quantitative chromatin pattern description (15 features), and (3) immunohistochemically related antigen specificities (6 features). All these features were quantified by digital cell image analysis. The results suggest that an objective distinction between leiomyomas and leiomyosarcomas can be established by means of simple logical rules depending on only a few features among which the immunohistochemically revealed antigen expression of desmin plays a preponderant part. One of the combinations of features proposed by the methodology is interesting for pathologists, because it includes two features describing the appearance of a nucleus in terms of chromatin distribution homogeneity and density, two features widely used by pathologists in tumor-grading systems.

Perennial legumes for the high rainfall zone of eastern Australia. 2. Persistence and potential adaptation zones

Cultivars and accessions of a range of perennial legumes were evaluated in small plot field trials at 4 on-farm locations on the Northern Tablelands of New South Wales. Variable establishment from seed resulted in good stands at 2 sites, and moderate to poor stands at the other 2 sites. In spite of this, trends in behaviour of individual species were apparent even where stands were very poor. This was exemplified by the gradual improvement in frequency of Trifolium medium at the most montane site. Trifolium ambiguum and Coronilla varia were most persistent across all sites. Good stands of Lotus corniculatus, L. pedunculatus, T. pratense and Medicago sativa thinned out within several years with M. sativa most persistent. Astragalus cicer thinned out rapidly on the relatively acidic soils but maintained a good stand at 1 site on a deep, free-draining granite. From these results and known climatic responses, simple logical rules were constructed to predict potential legume adaptation zones for eastern Australia. The zones of adaptation for the range of species are compared with a nominal zone for T. repens to identify areas where legume persistence might be improved with additional species.

Identification of High Versus Lower Risk Clinical Subgroups in a Group of Adult Patients with Supratentorial Anaplastic Astrocytomas

The present work investigates whether computer-assisted techniques can contribute any significant information to the characterization of astrocytic tumor aggressiveness. Two complementary computer-assisted methods were used. The first method made use of the digital image analysis of Feulgen-stained nuclei, making it possible to compute 15 morphonuclear and 8 nuclear DNA content-related (ploidy level) parameters. The second method enabled the most discriminatory parameters to be determined. This second method is the Decision Tree technique, which forms part of the Supervised Learning Algorithms. These two techniques were applied to a series of 250 supratentorial astrocytic tumors of the adult. This series included 39 low-grade (astrocytomas, AST) and 211 high-grade (47 anaplastic astrocytomas, ANA, and 164 glioblastomas, GBM) astrocytic tumors. The results show that some AST, ANA and GBM did not fit within simple logical rules. These "complex" cases were labeled NC-AST, NC-ANA and NC-GBM because they were "non-classical" (NC) with respect to their cytological features. An analysis of survival data revealed that the patients with NC-GBM had the same survival period as patients with GBM. In sharp contrast, patients with ANA survived significantly longer than patients with NC-ANA. In fact, the patients with ANA had the same survival period as patients who died from AST, while the patients with NC-ANA had a survival period similar to those with GBM. All these data show that the computer-assisted techniques used in this study can actually provide the pathologist with significant information on the characterization of astrocytic tumor aggressiveness.

Rule-plus-exception model of classification learning.

The authors propose a rule-plus-exception model (RULEX) of classification learning. According to RULEX, people learn to classify objects by forming simple logical rules and remembering occasional exceptions to those rules. Because the learning process in RULEX is stochastic, the model predicts that individual Ss will vary greatly in the particular rules that are formed and the exceptions that are stored. Averaged classification data are presumed to represent mixtures of these highly idiosyncratic rules and exceptions. RULEX accounts for numerous fundamental classification phenomena, including prototype and specific exemplar effects, sensitivity to correlational information, difficulty of learning linearly separable versus nonlinearly separable categories, selective attention effects, and difficulty of learning concepts with rules of differing complexity. RULEX also predicts distributions of generalization patterns observed at the individual subject level.