Explanation of current black box machine learning models is a significant challenge. The attempts to address it range from explaining black-box models to building interpretable models in the first place. Visualization, visual knowledge discovery, and visual representation learning methods are emerging methods allowing domain experts to be actively involved in model discovery and explanation without being machine learning experts. Glyph visualization makes this process more intuitive and easier for domain experts and users. However, glyphs have their own challenges of occlusion and relatively low dimensional data that they can represent. This paper proposes a method to ease these limitations with suggested animated flocks of colored "bird" glyphs for interpretable classification based on clustering that uses hyper-rectangles/hyperblocks. This paper shows that the proposed glyph approach expands significantly the dimensionality of data that simple glyphs can represent up to 16 attributes while simultaneously providing an increased capacity for preattentive perception by intelligent agents. It is shown that this method produces minimally occluded interpretable glyphs for interpretable input data which enable quick identification of class patterns to aid with classification tasks.

Building on existing work with Hyperblocks, which classify data using minimum and maximum bounds for each attribute, we focus on enhancing interpretability, decreasing training time, and reducing model complexity without sacrificing accuracy. This system allows subject matter experts (SMEs) to directly inspect and understand the model’s decision logic without requiring extensive machine learning expertise. To reduce Hyperblock complexity while retaining performance, we introduce a suite of algorithms for Hyperblock simplification. These include removing redundant attributes, removing redundant blocks through overlap analysis, and creating disjunctive units. These methods eliminate unnecessary parameters, dramatically reducing model size without harming classification power. We increase robustness by introducing an interpretable fallback mechanism using k-Nearest Neighbor (k-NN) classifiers for points not covered by any block, ensuring complete data coverage while preserving model transparency. Our results demonstrate that interpretable models can scale to high-dimensional, large-volume datasets while maintaining competitive accuracy. On benchmark datasets such as WBC (9-D), we achieve strong predictive performance with significantly reduced complexity. On MNIST (784-D), our method continues to improve through tuning and simplification, showing promise as a transparent alternative to black-box models in domains where trust, clarity, and control are crucial.

The visualization of multi-dimensional data with interpretable methods remains limited by capabilities of both high-dimensional lossless visualizations that do not suffer from occlusion and that are computationally capable by parameterized visualization. This paper proposes a low to high dimensional data supporting framework using lossless Concentric Coordinates which are a more compact generalization of Parallel Coordinates along with former Circular Coordinates. These are forms of the General Line Coordinates visualizations which directly support machine learning algorithm visualization and facilitate human interaction. This paper demonstrates the benefits of these methods with multiple case studies.

There are significant difficulties for the acceptance of black-box Machine Learning (ML) models by subject matter experts (SMEs) despite significant achievements of many black-box models. A promising way to address this problem is by building a trustable, qualitative, interpretable models for the task based on SME knowledge. Such qualitative models can work as qualitative explainers of black-box models or as sanity checks for them. In this paper, qualitative models operate with ordinal attributes, which can be Boolean or k-valued attributes with a small$k$. Humans easier understand and reason with such attributes that with continuous numeric attributes with many more values. Some ML tasks do not have sufficient training data. Building qualitative models with a SME (“expert models”) is a way to solve these tasks solely with a SME's knowledge. The proposed Monotone Ordinal Expert Knowledge Acquisition (MOEKA) system allows building “expert models” through interview phases with the SME. Monotonicity is a key property of the system that is tested and used to shorten the interview process with a SME along with new methods for selecting the order of questions. MOEKA rather directly approximates domain knowledge in contrast with other ML explainers, which approximate black-box ML models. MOEKA can be also used as a method of database searching. Several case studies on gout, diabetes, and housing demonstrate efficiency of MOEKA.

Explainable machine learning is important for increasing the confidence of domain experts in each model. However, simply using explainable methods is not enough. Explainable methods such as Decision Trees and Rule-Based models can be insufficient for certain datasets to provide satisfactory models. To solve this problem, Visual Knowledge Discovery (VKD) offers a solution through explainable, interactive, reversible lossless n-D visualizations using General Line Coordinates (GLC). Nevertheless, VKD and other visual methods suffer from occlusion when visualizing large amounts of data. This paper presents methods for both removing visual occlusion and limiting rule complexity and overfitting with hyperblocks at several levels. Hyperblocks create intrinsically explainable rules using meaningful numeric attributes. They allow finding and generalizing areas where data are similar, decreasing the occlusion in each hyperblock while creating less complex and more general rules. Major benefits from higher level hyperblocks include increased generalization, less complex rules, and increased user confidence in each classification.

Machine learning (ML) methods achieved remarkable success recently. However, the trust by domain experts for many new black-box models is quite low. Visualization is natural way to involve domain experts to the process of development of explainable models, which can mitigate the deficiencies of black-box models. It is typically easier for humans to understand and reason within visualizations of data and models. Recent Sequential Rule Generation (SRG) algorithms for categorical qualitative data, and a lossless visualization system in 3-D based on the Shifted Paired Coordinates (SPC-3D) allow producing ML models as (1) interpretable approximators of black-boxes or as (2) independent interpretable models with accuracy comparable with black boxes on the same data. However, SRG can generate a large set of rules that are difficult to analyze and visualize. This paper proposes a new algorithm to Join and Modify Rules (JMR), which creates a smaller set of rules with the same precision and coverage for a given set of rules. It is explored in the case studies, which show its efficiency along with SPC-3D visualization system for getting trustable models.

In the geological context, the analysis of multidimensional data is a very common task and requires visualization techniques for exploration. General Line Coordinates (GLC) is a technique especially intended for lossless representation among the various techniques available for the visualization of multidimensional data. In this study, the application of GLC for pattern analysis and identification in mineral datasets is investigated. Furthermore, we develop a web-based tool to explore the possibility of employing GLC to leverage these approaches to derive visual discovery rules for pattern recognition.

Insufficient amounts of available training data is a critical challenge for both development and deployment of artificial intelligence and machine learning (AI/ML) models. This paper proposes a unified approach to both synthetic data generation (SDG) and automated data labeling (ADL) with a unified SDG-ADL algorithm. SDG-ADL uses multidimensional (n-D) representations of data visualized losslessly with General Line Coordinates (GLCs), relying on reversible GLC properties to visualize n-D data in multiple GLCs. This paper demonstrates use of the new Circular Coordinates in Static and Dynamic forms, used with Parallel Coordinates and Shifted Paired Coordinates, since each GLC exemplifies unique data properties, such as inter-attribute n-D distributions and outlier detection. The approach is interactively implemented in computer software with the Dynamic Coordinates Visualization system (DCVis). Results with real data are demonstrated in case studies, evaluating impact on classifiers.

The expansion of the use of a machine learning (ML) technology in multiple domains heavily depends on acceptance of these models by end users and their abilities to understand the patterns discovered by machine learning algorithms. The simplicity and understandability of those patterns by the domain expert is critical for success of such ML explorations. This paper proposes a method for designing lossless compact and interpretable machine learning visual patterns to be easily captured and remembered by the domain experts due to their compactness and simplicity. This glyph approach is illustrated with a “bird” glyph. This glyph is a combination of Stick Figures and a type of General Line Coordinates known as Shifted Paired Coordinates. The efficiency of the approach is demonstrated on several benchmark machine learning data sets.

DV 2.0 is a no-code platform contributing to interpretable machine learning via Visual Knowledge Discovery in General Line Coordinates (GLC). GLC-Linear (GLC-L), a type of GLC, provides interactive tools to enhance the model creation process and create interpretable visualizations. DV 2.0 uses these techniques so end-users can directly involve themselves in the model creation pipeline. GLC-L visualizations are easily understood by end-users and allow for complex multidimensional relationships to be visualized. Additionally, using GLC-L allows both classification and regression models to be visualized with high degrees of accuracy. For classification, DV 2.0 also offers additional expansions of GLC-L such as GLC non-Linear (GLC-nL) and GLC Hyperblock Rules Linear (GLC-HBRL) to provide different interpretable non-linear classifiers for more complex data. DV 2.0 was tested on benchmark data from the UCI Machine Learning repository.

Understanding and visualizing principal components without losing multi-dimensional information has been a long-standing challenge until now. Here, we describe a novel lossless visual technique that overcomes such difficulties, General Line Coordinates-Principal Components Analysis (GLC-PCA)-an approach that provides much more information about individual cases than other methods, with improved structural readability and comprehensibility for PCA. Experimental case studies and comparisons with other works demonstrate this effect. A software system called MAVERICK implements it.

Interpretable interactive visual pattern discovery in lossless 3D visualization is a promising way to advance machine learning. It enables end users who are not data scientists to take control of the model development process as a self-service. It is conducted in 3D General Line Coordinates (GLC) visualization space, which preserves all n-D information in 3D. This paper presents a system which combines three types of GLC: Shifted Paired Coordinates (SPC), Shifted Tripled Coordinates (STC), and General Line Coordinates-Linear (GLC-L) for interactive visual pattern discovery. A transition from 2-D visualization to 3-D visualization allows for a more distinct visual pattern than in 2-D and it also allows for finding the best data viewing positions, which are not available in 2-D. It enables in-depth visual analysis of various class-specific data subsets comprehensible for end users in the original interpretable attributes. Controlling model overgeneralization by end users is an additional benefit of this approach.

Developing Machine Learning (ML) algorithms for heterogeneous/mixed data is a longstanding problem. Many ML algorithms are not applicable to mixed data, which include numeric and non-numeric data, text, graphs and so on to generate interpretable models. Another longstanding problem is developing algorithms for lossless visualization of multidimensional mixed data. The further progress in ML heavily depends on success interpretable ML algorithms for mixed data and lossless interpretable visualization of multidimensional data. The later allows developing interpretable ML models using visual knowledge discovery by end-users, who can bring valuable domain knowledge which is absent in the training data. The challenges for mixed data include: (1) generating numeric coding schemes for non-numeric attributes for numeric ML algorithms to provide accurate and interpretable ML models, (2) generating methods for lossless visualization of n-D non-numeric data and visual rule discovery in these visualizations. This paper presents a classification of mixed data types, analyzes their importance for ML and present the developed experimental toolkit to deal with mixed data. It combines the Data Types Editor, VisCanvas data visualization and rule discovery system which is available on GitHub.

This paper contributes to interpretable machine learning via visual knowledge discovery in general line coordinates (GLC). The concepts of hyperblocks as interpretable dataset units and general line coordinates are combined to create a visual self-service machine learning model. Dynamic Scaffolding Coordinates as lossless multidimensional coordinate systems are proposed, and their applications as visual models is shown. DSC1 and DSC2 can map multiple dataset attributes to a single two-dimensional (X, Y) Cartesian plane using a graph construction algorithm. The hyperblock analysis was used to determine visually appealing dataset attribute orders and to reduce line occlusion. It is shown that hyperblocks can generalize decision tree rules and a series of DSC1 or DSC2 plots can visualize a decision tree. The DSC1 and DSC2 plots were tested on benchmark datasets from the UCI ML repository. They allowed for visual classification of data. Additionally, areas of hyperblock impurity were discovered and used to establish dataset splits that highlight the upper estimate of worst-case model accuracy to guide model selection for high-risk decision-making. Major benefits of DSC1 and DSC2 is their highly interpretable nature. They allow domain experts to control or establish new machine learning models through visual pattern discovery.

Visualization of Machine Learning (ML) models is an important part of the ML process to enhance the interpretability and prediction accuracy of the ML models. This paper proposes a new method SPC-DT to visualize the Decision Tree (DT) as interpretable models. These methods use a version of General Line Coordinates called Shifted Paired Coordinates (SPC). In SPC, each n-D point is visualized in a set of shifted pairs of 2-D Cartesian coordinates as a directed graph. The new method expands and complements the capabilities of existing methods, to visualize DT models. It shows: (1) relations between attributes, (2) individual cases relative to the DT structure, (3) data flow in the DT, (4) how tight each split is to thresholds in the DT nodes, and (5) the density of cases in parts of the n-D space. This information is important for domain experts for evaluating and improving the DT models, including avoiding overgeneralization and overfitting of models, along with their performance. The benefits of the methods are demonstrated in the case studies, using three standard benchmarks.

This paper contributes to interpretable machine learning via visual knowledge discovery in parallel coordinates. The concepts of hypercubes and hyper-blocks are used as easily understandable by end-users in the visual form in parallel coordinates. The Hyper algorithm for classification with mixed and pure hyper-blocks (HBs) is proposed to discover hyper-blocks interactively and automatically in individual, multiple, overlapping, and non-overlapping setting. The combination of hyper-blocks with linguistic description of visual patterns is presented too. It is shown that Hyper models generalize decision trees. The Hyper algorithm was tested on the benchmark data from UCI ML repository. It allowed discovering pure and mixed HBs with all data and then with 10-fold cross validation. The links between hyper-blocks, dimension reduction and visualization are established. Major benefits of hyper-block technology and the Hyper algorithm are in their ability to discover and observe hyperblocks by end-users including side by side visualizations making patterns visible for all classes. Another advantage of sets of HBs relative to the decision trees is the ability to avoid both data overgeneralization and overfitting.

This paper proposed a new methodology for machine learning in 2-dimensional space (2-D ML) in inline coordinates. It is a full machine learning approach that does not require to deal with n-dimensional data in n-dimensional space. It allows discovering n-D patterns in 2-D space without loss of n-D information using graph representations of n-D data in 2-D. Specifically, it can be done with the inline based coordinates in different modifications, including static and dynamic ones. The classification and regression algorithms based on these inline coordinates were introduced. A successful case study based on a benchmark data demonstrated the feasibility of the approach. This approach helps to consolidate further a whole new area of full 2-D machine learning as a promising ML methodology. It has advantages of abilities to involve actively the end-users into the discovering of models and their justification. Another advantage is providing interpretable ML models.

Transforming non-image Machine Learning (ML) problems into the image recognition problems, opens an opportunity to solve these problems, by powerful deep learning algorithms. This paper proposes a new CPC-R algorithm, which converts non-image data into images, by visualizing non-image data. Then several deep learning CNN algorithms are exploited to solve the learning problems. The CPC-R algorithm preserves high-dimensional information in 2-D. It splits the attributes of an n-D point into pairs of its values and visualizes pairs as 2-D points, in the same 2-D Cartesian coordinates. Next, it maps pairs to grey scale or color intensity values to encode the order of pairs producing a heatmap. This paper reports the results of computational experiments with CPC-R for different CNN architectures, and methods to optimize the CPC-R images. These results show that the combined CPC-R and deep learning CNN algorithms can solve non-image ML problems, at the state-of-the-art level of accuracy for the benchmark datasets.

Data with more than two or three dimensions are difficult for humans to conceptualize and facilitate knowledge discovery. Novel Elliptic Paired Coordinates (EPCs) allow for multidimensional data to be represented in 2-D without loss of multidimensional information. In addition, EPC halves the required visual elements in the graph in comparison with parallel and radial coordinates. This research explores the effectiveness of constructing predictive machine learning models interactively using EPC visualizations. For this research EllipseVis, an interactive software system, was developed to process high-dimensional datasets, create corresponding EPC visualizations, and build predictive classification models based on dominance rules. The EllipseVis system allows both interactive and automatic discovery of areas that are located with a high percentage of single-class dominance. The experiments using it on benchmark datasets suggest EPC approach is a promising method for discovering predictive models with high coverage and precision that could be useful in many fields allowing for visually appealing dominance rules to be easily interpreted in the application domains.

Although machine learning algorithms are progressively used in an expansive range of domains, the effective machine learning classifiers are often black-boxed, non-comprehensive to the end users and beyond their abilities to develop models themselves. To overcome this challenge, data visualization combined with self-service or democratized machine learning is proposed in the form of the Iterative Logical Classifier (ILC) algorithm with an added advantage of outperforming the accuracies of black-box machine learning classifiers on benchmark datasets. The algorithm is based on the concept of Shifted Paired Coordinates that allow 2-D visualization of n-D data without loss of n-D information.

Intelligible machine learning and knowledge discovery are important for modeling individual and social behavior, user activity, link prediction, community detection, crowd-generated data, and others. The role of the interpretable method in web search and mining activities is also very significant to enhance clustering, classification, data summarization, knowledge acquisition, opinion and sentiment mining, web traffic analysis, and web recommender systems. Deep learning success in accuracy of prediction and its failure in explanation of the produced models without special interpretation efforts motivated the surge of efforts to make Machine Learning (ML) models more intelligible and understandable. The prominence of visual methods in getting appealing explanations of ML models motivated the growth of deep visualization, and visual knowledge discovery. This tutorial covers the state-of-the-art research, development, and applications in the area of Intelligible Knowledge Discovery, and Machine Learning boosted by Visual Means.

This tutorial covers the state-of-the-art research, development, and applications in the KDD area of interpretable knowledge discovery reinforced by visual methods to stimulate and facilitate future work. It serves the KDD mission and objectives of gaining insight from the data. The topic is interdisciplinary bridging of scientific research and applied communities in KDD, Visual Analytics, Information Visualization, and HCI. This is a novel and fast growing area with significant applications, and potential. First, in KDD, these studies have grown under the name of visual data mining. The recent growth under the names of deep visualization, and visual knowledge discovery, is motivated considerably by deep learning success in accuracy of prediction and its failure in explanation of the produced models without special interpretation efforts. In the areas of Visual Analytics, Information Visualization, and HCI, the increasing trend toward machine learning tasks, including deep learning, is also apparent. This tutorial reviews progress in these areas with a comparative analysis of what each area brings to the joint table. The comparison includes the approaches: (1) to visualize Machine Learning (ML) models produced by the analytical ML methods, (2) to discover ML models by visual means, (3) to explain deep and other ML models by visual means, (4) to discover visual ML models assisted by analytical ML algorithms, (5) to discover analytical ML models assisted by visual means. The presenter will use multiple relevant publications including his books: "Visual and Spatial Analysis: Advances in Visual Data Mining, Reasoning, and Problem Solving" (Springer, 2005), and "Visual Knowledge Discovery and Machine Learning" (Springer, 2018). The target audience of this tutorial consists of KDD researchers, graduate students, and practitioners with the basic knowledge of machine learning.

Developing more efficient automated methods for interpretable machine learning (ML) is an important and longterm machine-learning goal. Recent studies show that unintelligible "black" box models, such as Deep Learning Neural Networks, often outperform more interpretable "grey" or "white" box models such as Decision Trees, Bayesian networks, Logic Relational models and others. Being forced to choose between accuracy and interpretability, however, is a major obstacle in the wider adoption of ML in healthcare and other domains where decisions requires both facets. Due to human perceptual limitations in analyzing complex multidimensional relations in ML, complex ML must be "degraded" to the level of human understanding, thereby also degrading model accuracy. To address this challenge, this paper presents the Dominance Classifier and Predictor (DCP) algorithm, capable of automating the process of discovering human-understandable machine learning models that are simple and visualizable. The success of DCP is shown on the benchmark Wisconsin Breast Cancer dataset with the higher accuracy than the accuracy known for other interpretable methods on these data. Furthermore, the DCP algorithm shortens the accuracy gap between interpretable and non-interpretable models on these data. The DCP explanation includes both interpretable mathematical and visual forms. Such an approach opens a new opportunity for producing more accurate and domain-explainable ML models.

The Big data challenge includes dealing with a big number of heterogeneous and multidimensional datasets of all possible sizes not only with data of big size. As a result a huge number of Machine Learning (ML) tasks, which must be solved dramatically exceeds the number of data scientists who can solve these tasks. Next many ML tasks require critical input from subject matter experts (SME) and end users/decision makers who are not ML experts. A set of tools that we call a “virtual data scientist” is needed to assist SMEs and end users to construct ML models for their tasks to meet this Big data challenge with a minimal contribution from data scientists. This paper describes our vision of such a “virtual data scientist” based on the visual approach with collocated and shifted paired coordinates. The approach is illustrated with real world data and ML tasks, as well as simulated data.

The focus of this paper is to clarify the concepts of solutions of linear equations in interval, probabilistic, and fuzzy sets setting for real world tasks. There is a fundamental difference between formal definitions of the solutions and physically meaningful concepts of solution in applied tasks, when equations have uncertain components. For instance, a formal definition of the solution in terms of Moore interval analysis can be completely irrelevant for solving a real world task. We show that formal definitions must follow a meaningful concept of the solution in the real world. The paper proposed several formalized definitions of the concept of solution for the linear equations with uncertain components in the interval, probability and fuzzy set terms that can be interpreted in the real world tasks.

Fundamental challenges and goals of the cognitive algorithms are moving super-intelligent machines and super-intelligent humans from dreams to reality. This paper is devoted to a technical way to reach some specific aspects of super-intelligence that are beyond the current human cognitive abilities. Specifically the proposed technique is to overcome inabilities to analyze a large amount of abstract numeric high-dimensional data and finding complex patterns in these data with a naked eye. Discovering patterns in multidimensional data using visual means is a long-standing problem in multiple fields and Data Science and Modeling in general. The major challenge is that we cannot see n-D data by a naked eye and need visualization tools to represent n-D data in 2-D losslessly. The number of available lossless methods is quite limited. The objective of this paper is expanding the class of such lossless methods, by proposing a new concept of Generalized Shifted Collocated Paired Coordinates. The paper shows the advantages of proposed lossless technique by proving mathematical properties and by demonstration on real data.

The number of platforms and sensors with the best capabilities often is limited in the stressing tasking environment relative to the sensing needs. This is the case for Overhead Persistent InfraRed (OPIR) sensors. Sensor assets differ significantly in number, location, and capability over time. Planning for engagements prior to actual tasking sensors involves these factors. This paper proposes a new sensor tasking methodology and optimization models for both long-time planning and real-time Sensor Resource Management (SRM). It is based on the rigorous and adaptive mathematical formulation of the problem and the use of Computational Intelligence techniques such as genetic algorithms and dynamic logic to find a solution.

The issues of Interpretable Fuzzy Systems (IFS) spin from the fundamental definitions of the concept of IFS to practical design of such systems. This paper addresses the current issues of formalization of the concept of interpretability, its dimensions, evaluations and design of interpretable Fuzzy Systems, including fuzzy control systems. T-norms and T-conorms are in the core of Fuzzy Systems, therefore we consider the following questions about them. Where is the adequate sphere for T-norms in IFS to be interpretable operations? How to modify the T-norms to satisfy the IFS requirements? What are the alternatives to T-norms and t-conorms in IFS? This analysis of T-norms is done in the context of their interpretation as measurements. We show that the approach used in the representative measurement theory is a source of the interpretability definition, which is in line with Tarsky's definition of interpretability. This approach is used to define a concept of the interpretable fuzzy operations. Next, it is shown that an adequate scope for scalar T-norms is to be compact approximations of 2-D lattice operations. Such lattice operations are an alternative to T-norms and T-conorms in IFS because they have better interpretability. It is shown that such popular T-norms as the minimum and the product operations are similar as approximations of the Pareto optimal set, but quite different in representation of the lattice structure, where the product is preferable because it distorts the lattice structure less.

Boolean and discrete networks play an important role in many domains such as cellular automata. This paper generalizes that concept of Boolean networks for complex situations with multiple agents acting under uncertainty. This paper creates a logic network using a concept of the Agent-based Uncertainty Theory (AUT). The AUT is based on complex fusion of crisp (non-fuzzy) conflicting judgments of agents. It provides a uniform representation and an operational empirical interpretation for several uncertainty theories such as rough set theory, fuzzy sets theory, evidence theory, and probability theory. The AUT models conflicting evaluations that are fused in the same evaluation context. An AUT network extend the traditional inferential process by using a set of logic matrices obtained from AUT logic evaluation samples connected in a network. This network computes transformations of AUT logic vectors and gives logic rules for uncertainty situation. The AUT logic network is a generalization of the Boolean network. A Boolean network consists of a set of Boolean variables whose states are determined by other variables in the network An AUT logic network consists of a set of agents presented as vector variables whose states or logic vector evaluations are determined by other variables in the network.

The purpose of this paper is to develop further the main concepts of Phenomena Dynamic Logic (P-DL) and Cognitive Dynamic Logic (C-DL), presented in the previous paper. The specific character of these logics is in matching vagueness or fuzziness of similarity measures to the uncertainty of models. These logics are based on the following fundamental notions: generality relation, uncertainty relation, simplicity relation, similarity maximization problem with empirical content and enhancement (learning) operator. We develop these notions in terms of logic and probability and developed a Probabilistic Dynamic Logic of Phenomena and Cognition (P-DL-PC) that relates to the scope of probabilistic models of brain. In our research the effectiveness of suggested formalization is demonstrated by approximation of the expert model of breast cancer diagnostic decisions. The P-DL-PC logic was previously successfully applied to solving many practical tasks and also for modelling of some cognitive processes.

Modeling of complex phenomena such as the mind presents tremendous computational complexity challenges. The Neural Modeling Fields (NMF) theory and Dynamic Logic of Phenomena (DLP) address these challenges in a non-traditional way. The main idea behind their success is matching the levels of uncertainty of the problem/model and the levels of uncertainty of the evaluation criterion used to identify the model. When a model becomes more certain then the evaluation criterion is also adjusted dynamically to match the adjusted model. This process mimics processes of the mind and natural evolution at the neural level. This paper describes the generalization of DLP for data fusion and mining of heterogeneous spatial objects in cyber-physical space.

This paper models neural uncertainty using a concept of the agent-based uncertainty theory (AUT). The AUT is based on complex fusion of crisp (non-fuzzy) conflicting judgments of agents. It provides a uniform representation and an operational empirical interpretation for several uncertainty theories such as rough set theory, fuzzy sets theory, evidence theory, and probability theory. The AUT models conflicting evaluations that are fused in the same evaluation context. This paper shows that the neural fusion at the synapse can be modeled by the AUT. The neuron is modeled as an operator that transforms classical logic expressions into many-valued logic expressions. The new neural network has neurons at two layers. The first-layer agents implement the classical logic operations, but at the second level, neurons or nagents (neuron agents) compute the same logic expression with different results for different agent inputs. The motivation for such neural network is to provide high flexibility and logic adaptation of the neural model.

Modeling of complex phenomena such as the mind presents tremendous computational complexity challenges. The neural modeling fields theory (NMF) addresses these challenges in a non-traditional way. The main idea behind success of NMF is matching the levels of uncertainty of the problem/model and the levels of uncertainty of the evaluation criterion used to identify the model. When a model becomes more certain then the evaluation criterion is also adjusted dynamically to match the adjusted model. This process is called dynamic logic (DL) of model construction, which mimics processes of the mind and natural evolution. This paper provides a formal description of phenomena dynamic logic (P-DL) and outlines its extension to the cognitive dynamic logic (C-DL). P-DL is presented with its syntactic, reasoning, and semantic parts. Computational complexity issues that motivate this paper are presented using an example of polynomial models.

In neural network modeling, the goal often is to get a most specific crisp output (e.g., binary classification of objects) from neuron inputs that have multiple possible values. In this paper, we change the viewpoint and assume that the neuron is an operator that transforms binary classical logic input to the many valued logic output, e.g., changes crisp sets into fuzzy sets. In this interpretation, the neural network is composed of agents or neurons, which work to implement uncertainty calculus and many valued logics from crisp perceptual input. This idea is closely related to the dynamic logic approach and recent cognitive science experimental discoveries. According to this model having crisp perceptual input, brain (1) produces a less certain representation, (2) processes input at this uncertainty level of representation, (3) converts results to the next more certain level of information representation, (4) processes this information and (5) repeats these steps several times until the acceptable level of certainty is reached. To build such model we rely not on the binary logic but on the logic of the uncertainty to obtain the high flexibility and logic adaptation of the described process. This paper presents a concept of the agent-based uncertainty theory (AUT) based on complex fusion of crisp conflicting judgments of agents Communication among agents is modeled by the fusion process in the neural elaboration.