Axiomatic Approach Research Articles

Zur Bedingung der Möglichkeit von Erfahrung. Eine modallogische Analyse

Abstract In Kantian philosophy, the term “condition of possibility” is central, but carries the following ambiguity. According to one reading, “condition of possibility” merely means “necessary condition”. However, it is demonstrated that a deeper interpretation of the term “possibility” proves to be more fruitful. This reading allows us to reconstruct an important background assumption of Kant: Every condition of the possibility of experience holds necessarily, provided that experience is possible. Or more generally: All conditions of the possibility hold necessarily as long as the conditioned is actually possible. This conclusion is understood through the axiomatic system S5. Therefore I argue by referencing the schematism chapter that Kant’s notion of modal terms can be formalized through S5.

Diversity Balance in Centralized Public School Admissions

Parental choice over public schools has become a major educational reform throughout the United States and the world. Most district policies are implemented via admission priorities. Diversity in admissions is a common policy goal. However, it necessitates the violation of some priorities. We develop an axiomatic theory for meeting diversity objectives with a reserves system. We axiomatize the trade-off between diversity and priorities. We characterize the solution that uniquely and optimally achieves the diversity objectives via reserves by minimizing priority violations. The choice rule corresponds to a simple and natural implementation of application orders in a reserves system.

Parametric dependence between random vectors via copula-based divergence measures

This article proposes copula-based dependence quantification between multiple groups of random variables of possibly different sizes via the family of Φ-divergences. An axiomatic framework for this purpose is provided, after which we focus on the absolutely continuous setting assuming copula densities exist. We consider parametric and semi-parametric frameworks, discuss estimation procedures, and report on asymptotic properties of the proposed estimators. In particular, we first concentrate on a Gaussian copula approach yielding explicit and attractive dependence coefficients for specific choices of Φ, which are more amenable for estimation. Next, general parametric copula families are considered, with special attention to nested Archimedean copulas, being a natural choice for dependence modelling of random vectors. The results are illustrated by means of examples. Simulations and a real-world application on financial data are provided as well.

On Some Weakened Forms of Transitivity in the Logic of Conditional Obligation

This paper examines the logic of conditional obligation, which originates from the works of Hansson, Lewis, and others. Some weakened forms of transitivity of the betterness relation are studied. These are quasi-transitivity, Suzumura consistency, acyclicity and the interval order condition. The first three do not change the logic. The axiomatic system is the same whether or not they are introduced. This holds true under a rule of interpretation in terms of maximality and strong maximality. The interval order condition gives rise to a new axiom. Depending on the rule of interpretation, this one changes. With the rule of maximality, one obtains the principle known as disjunctive rationality. With the rule of strong maximality, one obtains the Spohn axiom (also known as the principle of rational monotony, or Lewis’ axiom CV). A completeness theorem further substantiates these observations. For interval order, this yields the finite model property and decidability of the calculus.

Hypergraph p-Laplacians and Scale Spaces

The aim of this paper is to revisit the definition of differential operators on hypergraphs, which are a natural extension of graphs in systems based on interactions beyond pairs. In particular, we focus on the definition of Laplacian and p-Laplace operators for oriented and unoriented hypergraphs, their basic properties, variational structure, and their scale spaces. We illustrate that diffusion equations on hypergraphs are possible models for different applications such as information flow on social networks or image processing. Moreover, the spectral analysis and scale spaces induced by these operators provide a potential method to further analyze complex data and their multiscale structure. The quest for spectral analysis and suitable scale spaces on hypergraphs motivates in particular a definition of differential operators with trivial first eigenfunction and thus more interpretable second eigenfunctions. This property is not automatically satisfied in existing definitions of hypergraph p-Laplacians, and we hence provide a novel axiomatic approach that extends previous definitions and can be specialized to satisfy such (or other) desired properties.

An axiomatic model towards understanding value creation and appropriation in demand-driven markets

PurposeIn demand-driven markets, customer value, sometimes called perceived use value or consumer surplus, is defined by the customer rather than the firm. The value a firm can appropriate, its profits, is driven by the customer’s willingness to pay for the value they receive, adjusted by costs. This paper introduces a conceptual framework that helps understand value creation and appropriation in demand-driven markets and shows how to influence them through strategic decision-making.Design/methodology/approachThis paper uses an axiomatic approach combined with an extended analytical formulation of the jobs-to-be-done framework to contextualise demand-driven markets. It mathematically derives implications for managerial decision-making concerning selecting customer segments, optimising customer value creation and maximising firm value appropriation in a competitive environment.FindingsRooting strategic decision-making in the jobs-to-be-done framework allows distinguishing between what customers want to achieve (goal), what product attributes need to be satisfied (opportunity space/constraints) and what value creation criteria related to features are important (utility function). This paper shows that starting from a job-to-be-done, the problem of identifying which customer segments to serve, what product to offer and what price to charge, can be formulated as an optimisation problem that simultaneously (rather than sequentially) solves for the three decision variables, customer segments, product features and price, by maximising the value that a firm can appropriate, subject to maximising customer value creation and constrained by the competitive environment.Practical implicationsApplying the derived results to simultaneously deciding which customer segments to target, what product features to offer and what price to charge, given a set of competing products, allows managers to increase their chances of winning the competitive game.Originality/valueThis paper shows that starting from a job-to-be-done and simultaneously focusing on customers, product features, price and competitors enhances firm profitability. Strategic decision-making is formulated as an optimisation problem based on an axiomatic approach contextualising demand-driven markets.

Optimizing electrocoagulation for poultry slaughterhouse wastewater treatment: a fuzzy axiomatic design approach

White meat consumption is increasing day by day, and accordingly, there is an increase in the amount of wastewater resulting from the processes. Today, the reuse of wastewater has become a goal within the scope of the Green Deal. For this reason, wastewater treatment with high pollution and volume has gained importance. In this study, the fuzzy axiomatic design (FAD) method, one of the multi-criteria decision-making methods, has been used. With this method, coagulation, electrocoagulation (EC), dissolved air flotation (DAF), and anaerobic treatment alternatives preferred in poultry slaughterhouse wastewater (PSW) treatment were compared with each other and their information contents were calculated. The information content from the smallest to the largest is EC, DAF, coagulation, and anaerobic treatment, respectively. This treatment method was chosen because the smallest information content is in electrocoagulation. EC was applied to bloody PSW containing 1% blood by volume. The effectiveness of Fe and Al electrodes for PSW treatment in the batch EC reactor has been compared. The effective surface areas of 2 anodes and 2 cathodes connected bipolarly in the processes are 288 cm2. The electrolyte, pH, time, and current density effects on energy consumption were also investigated. The optimum conditions for Al and Fe electrodes were found to be 0.5 g·L−1 NaCl concentration, pH 5, 0.639 mA·cm−2 current density, and 5 min time. Under optimum conditions for the Fe electrode, COD, TOC, TN, and oil-grease removal efficiencies were determined as 76.3%, 71.8%, 70%, and 74%, respectively. Moreover, the highest COD, TOC, TN, and oil-grease removal efficiencies were achieved with an Al electrode (82.2%, 82.3%, 82.7%, and 78.9%, respectively). The experimental data were fit to a variety of isotherms and kinetic models to determine the characteristics of the EC. The results indicated that the pseudo-second-order equation provided the best fit for COD removal. Under optimum conditions, the operating cost was calculated as $3.39 and $3.09 for Al and Fe electrodes, respectively. In this study, the fuzzy axiomatic design method was used for the first time to select the most appropriate treatment method for PSW. In addition, blood, a major problem for the poultry slaughterhouse industry, was mixed with PSW at a ratio of 1% (v/v) and treated with EC for the first time with high removal efficiency. By treating PSW, which has a high pollution load, with electrocoagulation, the pollution load of the water to be given to secondary treatment has been greatly reduced.

Developing a Blockchain-Based Framework for Digital Archiving of BIM Using Axiomatic Design

Building information modeling (BIM) has been attracting increasing attention in the architecture, engineering, and construction (AEC) industry in recent years. The wide spread of BIM marks the transition from 2D and paper-based archiving to 3D and digital archiving of project information. However, the commonly used centralized managing approaches for BIM data have high risks of data loss and data tampering. With cryptographic algorithms and distributed databases, blockchain has the potential to address the limitations of data loss and trust in conventional BIM management methods. Therefore, this paper proposes a blockchain-based framework for digital archiving of BIM data. In this paper, the axiomatic design approach is utilized to design the archiving framework in order to systematically map the design parameters with the functional requirements and minimize the information contents. The proposed framework contains five modules, including the BIM module, building plan approval (BPA) module, building data simplification (BDS) module, distributed data storage (DDS) module, and digital document verification (DDV) module. Hyperledger Fabric is utilized to develop the blockchain system based on the proposed framework. In the end, a simple BIM model with 240 components and around 11,000 lines of content in the Industry Foundation Classes (IFC) file is taken as an illustrative example to validate the proposed blockchain approach. By storing the BIM model on to the developed blockchain, it is found that each transaction of a blockchain can store over 5000 lines of IFC contents with 0.09 s of uploading latency. The results show that the proposed blockchain-based approach can effectively and securely archive BIM data.

Probabilistic hesitant fuzzy multiple criteria decision-making with triangular norm based similarity and entropy measures

Existing probabilistic hesitant fuzzy set (PHFS) measures are constructed using two information measures: hesitancy and unwrapped probabilities. We argue that unifying these semantic terms in PHFS information theory is not logical. We introduce a new class of information measures for PHFSs, which address the logical wrapping of hesitant fuzzy sets (HFS) and probability. We propose several similarity measures for these sets that use the Triangular norm operator. We consider the relationship between measures of entropy and similarity and represent the axiomatic definition of PHFS entropy measures. Finally, we use case studies to demonstrate applications of these information measures. We describe two multiple-criteria decision-making algorithms. The last step is devoted to PHFS ranking procedures: one based on the score function of alternatives and the other based on the relative closeness of alternatives. This contribution describes new information measures and uses case studies to illustrate how they can be applied to decision-making processes.

Гильбертовская концепция «существования в математике» и ее моделирование формальной аксиоматической теорией Ф+∃, рассматривающей существование не как квантор, а как модальность (на англ.)

The subject-matter of investigation is Hilbert’s-principle consisting of two parts: (a) proclaiming equivalence-of-consistency-and-truth-in-mathematics; (b) proclaiming equivalence-of-consistency-and-existence-in‑mathematics. The target – explication and vindication of the principle. The scientific novelty: for reaching the goal, (1) a hitherto unknown logically formalized multimodal axiomatic epistemology-and-ontology-system called Ф+∃ has been constructed; (2) by means of Ф+∃ , a precise axiomatic definition of the notion “existence as modality” is submitted for the first time; (3) by means of artificial language of Ф+∃ , a precise formulation of the principle-of-equivalence-of-consistency-and-existence is given; (4) for the first time, the article presents formal deductive inferences (in formal-theory-Ф+∃ ) of such formulae which make up Hilbert’s principle (given an appropriate interpretation of these formulae).

Principles of Defragmentation Medicine

A number of features of the Medical Space have been analyzed and an attempt has been made to construct a General Axiomatic Theory of Medicine. It shows how to build a necessary and sufficient reference point for the Medical Space, necessary for the construction of the General Phenomenology of Medicine and the working Selection Rules common to all Medicine.

Minimal coverage of generalized typed inclusion dependencies in databases

The paper discusses the theory and algorithms necessary to construct a minimal covering of generalized typed inclusion dependencies. Traditionally, the construction of minimal covering is used for all types of dependencies in order to obtain a non-redundant and consistent database design. Generalized inclusion dependencies correspond to referential integrity constraints, when several main and several external relations are involved in one constraint, which corresponds to an ultragraph edge. In previous work, based on a study of the properties of dependencies, a system of axioms was presented with proof of consistency and completeness. In this work, the closures were studied for generalized typed inclusion dependencies. An algorithm for constructing closures has been developed and its correctness has been proven. The results obtained are further used to develop an algorithm for constructing a minimal covering. At the end of the article, examples are presented that demonstrate the operation of the algorithms.

Formation of fluvial xenolandscapes of Martian valleys and channels


 
 
 Contemporary concepts of Martian Valley formation and the current state of their study are examined. Three-dimensional modeling was conducted using the examples of two regions on Mars, the Lani Chaos Region and Kasei Vallis, to determine and map the main morphological features typical of Martian valleys as a basis for identifying xenolandscapes. The xenaxiomatic author’s concept was applied as a means of investigating xenolandscape diversity on the surface of Earth-like planets, in this case, Mars. The xenaxiomatic concept is the result of incorporating and utilizing traditional knowledge of the differentiation and application of axioms of cognition. Specialized for xenoplanetological use, this integrative cognitive tool is a variant of an axiomatic approach. The main essence of this approach, in the case of distinguishing xenolandscapes, lies in developing a unified scheme for searching for corresponding xenolandscape elements that are axiomatically elementary fragments of the planet’s surface, followed by their classification and xenolandscape interpretation. Scientific awareness has been achieved by filling it with all available information from various natural sciences related to xenoplanetology and subsequent exploratory xenolandscape interpretation and synthetic cartographic representation of characteristic, typical local xenolandscape formations on Mars (part of the Kasei Vallis valley). These depicted objects are extra-rank, meaning they have not yet been ranked in terms of xenolandscape formations but are uniformly formed due to the synergy of influences and interactions of different forces, yet genetically stemming from the same xenolandscape-forming factors of material and energy-field xenonature. A mechanism for the formation of modern Martian valleys is proposed through the influx of heat flow and impact events. Exploratory xenolandscape studies, with their positions verified by this conducted research in terms of theoretical, methodological, and methodical content, have become an unexpected benchmark for the effectiveness of similar theoretical and methodological components of classical landscape science, with which the research capabilities of landscape science can and should be compared.
 
 

A systems identification approach using Bayes factors to deconstruct the brain bases of emotion regulation.

Cognitive reappraisal is fundamental to cognitive therapies and everyday emotion regulation. Analyses using Bayes factors and an axiomatic systems identification approach identified four reappraisal-related components encompassing distributed neural activity patterns across two independent functional magnetic resonance imaging (fMRI) studies (n = 182 and n = 176): (1) an anterior prefrontal system selectively involved in cognitive reappraisal; (2) a fronto-parietal-insular system engaged by both reappraisal and emotion generation, demonstrating a general role in appraisal; (3) a largely subcortical system activated during negative emotion generation but unaffected by reappraisal, including amygdala, hypothalamus and periaqueductal gray; and (4) a posterior cortical system of negative emotion-related regions downregulated by reappraisal. These systems covaried with individual differences in reappraisal success and were differentially related to neurotransmitter binding maps, implicating cannabinoid and serotonin systems in reappraisal. These findings challenge 'limbic'-centric models of reappraisal and provide new systems-level targets for assessing and enhancing emotion regulation.

Maintaining the completion-time mechanism for Greening tasks scheduling on DVFS-enabled computing platforms

The key factor in reducing the consumed energy when dependent-tasks applications are scheduled on DVFS-enabled computing platforms is task execution time slots. The unique and axiomatic approach to reduce the energy consumption on such platforms involves scaling down the execution frequency of each task within its execution time slot, provided a suitable scaling-down frequency is available. Regrettably, scheduling algorithms often shrink task execution time slots due to minimizing task completion times. This paper presents BlueMoon, a mechanism that reschedules the application tasks to extend the execution time slot of each task while ensuring that the overall completion time of the application tasks remains unaffected. BlueMoon is implemented and tested on numerous schedules of application graphs. The experimental results, conducted through computer simulations, demonstrate that BlueMoon substantially extends the execution time slots of tasks when compared to other mechanisms.

Soft rough sets based on covering and their applications

Soft rough based on covering SRC\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\mathcal {S}RC$\\end{document} theory has become a useful and well-known area of research in theories of uncertainty. The present work follows up on this flourishing research topic. We introduce a new model of SRC\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\mathcal {S}RC$\\end{document} in a fusion of soft set theory SST\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\mathcal {S}ST$\\end{document} and rough set depending on covering CRS\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\mathcal {C}RS$\\end{document}. We put forth a definition of soft rough covering approximation space SCAS\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\mathcal {S}CAS$\\end{document} via neighborhood concept. Some axiomatic systems of our model of SRC\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\mathcal {S}RC$\\end{document} are discussed. We study the relationship between our model of SRC\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\mathcal {S}RC$\\end{document} and three other SRC\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\mathcal {S}RC$\\end{document}-models. An algorithm for reduction of the attributes of the information systems using SCAS\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\mathcal {S}CAS$\\end{document} is established. Based on the theoretical discussion, we set forth some applications of our model which will be helpful in decision making process via SRC\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\mathcal {S}RC$\\end{document} theory.

Mülahizələr hesabında deduksiya metodunun tətbiqinin elmi-nəzəri metodoloji problemləri

The issue of the emergence of formal axiomatic logical systems due to the emergence of logical antinomies in formal axiomatic systems, specifically the issue of developing formal logical axiomatics in the calculus of considerations was investigated in the considered research. At the same time, in order to determine the characteristics of the implementation of the logical-methodological principles and provisions of the deductive reasoning obviously, conceptual-logical foundations of the calculus of considerations was studied and the main propositions of the calculus of considerations and the analysis of the initial logical operations on them were given in the study. The basic laws of logic and the expression of one logical act with another one were also explained in the research work by giving the concepst of proportional form and tautology in the calculus of considerations. At the same time, main properties and the procedure of setting of the formal deductive theory in the calculus of considerations were studied in the article. In order to provide an adequate characterization of the conceptual and methodological bases of the calculus of considerations in the research work, the basic logical laws of the calculus of considerations developed by the German mathematician and thinker P. Hilbert were also given. In addition, the main principles and methodological provisions of the deductive method were investigated, and the rules of deriving new conclusions from the axioms were interpreted. At the end of the reviewed article, the main principles and methods of the formal axiomatic mathematical systems built on a deductive basis, specifically the calculus of considerations, were studied and a logical-methodological analysis of the calculus of considerations was carried out on this basis. In this framework, the syntactic and semantic analysis of formalized language in formal axiomatic logical systems was carried out separately, the constituent parts of those systems, including the construction scheme, were given.

A novel grade assessment method for cybersecurity situation of online retailing with decision makers’ bounded rationality

The online retailing cybersecurity situations grade assessment (GS) is a key issue in cybersecurity management, which can be regarded as a type of multi-attributes GS problems. However, traditional GS methods rarely discuss the boundary fuzziness and hesitation in the grade classification of attributes, as well as the monotony relation and interrelation between entropy fuzziness and intuitionism. A novel GS method with respect to decision makers’ bounded rationality is proposed. To get the method, the membership functions (MFs) and non-membership functions (NMFs) of attributes’ eigenvalue grade considering decision maker s’ bounded rationality and hesitation are proposed. An axiomatic definition of IF entropy on the basis of isentropic arcs is proposed, providing the formula of the monotony relation and interrelation between fuzziness and intuitionism. We, considering the reliability and the IF grade assessment method, propose the similarity of IF grade eigenvalue, which identifies grades reasonably and distinguishes the ranking of the same grade, and overcomes the defect that the maximum membership degree principle ignores the position differences of each grade assessment level.

A non-polynomial axiomatic framework to investigate the structural responses of CNT-reinforced beams: An analytical solution

A non-polynomial axiomatic framework to investigate the structural responses of CNT-reinforced beams: An analytical solution

Логический анализ данных и знаний без использования аксиоматического подхода

Logical analysis of data and knowledge is required not only in artificial intelligence systems, but also in mathematical proofs. This work shows the difficulties of logical analysis caused by the indisputable application of the formal axiomatic approach adopted at the turn of the XIX and XX centuries as the only theoretical basis of modern logic and the foundations of mathematics. In this approach, the main role is played by the axioms and methods of syntactic analysis, which underlie predicate calculus. Instead of set theory, we propose to use more simple algebra of sets as a theoretical basis of such a logic, for which the substantiation of the basic laws does not require axioms. A new approach to logical analysis based on the laws of set algebra is considered. Some advantages of this approach are shown, and a list of unresolved problems is provided.