Axiomatic Approach Research Articles

О некоторых моделях альтруистического поведения

The paper surveys several recent approaches to studying, modeling, and interpreting altruistic behavior. In the first section we describe a modification of the system of axioms of classical rational choice theory taking into consideration moral reference points. We study the moral monotonicity axiom, compare the predictions of the standard and the modified system of axioms, and describe series of experiments contradicting the standard system, but agreeing with the modified one. In the second section we discuss the approach of J. Roemer who suggested to consider Kantian optimization in place of the standard Nash one. It is well known that Nash equilibria are not necessarily optimal. It happens, as, for example, in the tragedy of the commons, that all the participants would benefit from choosing a different, non-Nash equilibrium, and in this section we consider mechanisms allowing to realize an optimal choice. In the third section we consider a model in which different parenting styles (based on altruism and paternalism) emerge as equilibrium outcomes and are affected by both parental preferences and the socioeconomic environment. We discuss statistical and experimental data showing historical development of parental styles and allowing to check various predictions of the model.

Converting disease maps into heavyweight ontologies: general methodology and application to Alzheimer's disease.

Omics technologies offer great promises for improving our understanding of diseases. The integration and interpretation of such data pose major challenges, calling for adequate knowledge models. Disease maps provide curated knowledge about disorders' pathophysiology at the molecular level adapted to omics measurements. However, the expressiveness of disease maps could be increased to help in avoiding ambiguities and misinterpretations and to reinforce their interoperability with other knowledge resources. Ontology is an adequate framework to overcome this limitation, through their axiomatic definitions and logical reasoning properties. We introduce the Disease Map Ontology (DMO), an ontological upper model based on systems biology terms. We then propose to apply DMO to Alzheimer's disease (AD). Specifically, we use it to drive the conversion of AlzPathway, a disease map devoted to AD, into a formal ontology: Alzheimer DMO. We demonstrate that it allows one to deal with issues related to redundancy, naming, consistency, process classification and pathway relationships. Furthermore, we show that it can store and manage multi-omics data. Finally, we expand the model using elements from other resources, such as clinical features contained in the AD Ontology, resulting in an enriched model called ADMO-plus. The current versions of DMO, ADMO and ADMO-plus are freely available at http://bioportal.bioontology.org/ontologies/ADMO.

Gradual type theory

AbstractGradually typed languages are designed to support both dynamically typed and statically typed programming styles while preserving the benefits of each. Sound gradually typed languages dynamically check types at runtime at the boundary between statically typed and dynamically typed modules. However, there is much disagreement in the gradual typing literature over how to enforce complex types such as tuples, lists, functions and objects. In this paper, we propose a new perspective on the design of runtime gradual type enforcement: runtime type casts exist precisely to ensure the correctness of certain type-based refactorings and optimizations. For instance, for simple types, a language designer might desire that beta-eta equality is valid. We show that this perspective is useful by demonstrating that a cast semantics can be derived from beta-eta equality. We do this by providing an axiomatic account program equivalence in a gradual cast calculus in a logic we callgradual type theory(GTT). Based on Levy’s call-by-push-value, GTT allows us to axiomatize both call-by-value and call-by-name gradual languages. We then show that we can derive the behavior of casts for simple types from the corresponding eta equality principle and the assumption that the language satisfies a property calledgraduality, also known as the dynamic gradual guarantee. Since we can derive the semantics from the assumption of eta equality, we also receive a useful contrapositive: any observably different cast semantics that satisfies gradualitymustviolate the eta equality. We show the consistency and applicability of our axiomatic theory by proving that a contract-based implementation using the lazy cast semantics gives a logical relations model of our type theory, where equivalence in GTT implies contextual equivalence of the programs. Since GTT also axiomatizes the dynamic gradual guarantee, our model also establishes this central theorem of gradual typing. The model is parameterized by the implementation of the dynamic types, and so gives a family of implementations that validate type-based optimization and the gradual guarantee.

Justified Representation for Perpetual Voting

We study the social choice setting of perpetual voting where, based on voter preferences, decisions have to be taken over a finite horizon of consecutive points in time (e.g, days). We consider two complementary settings: a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Static</i> setting, in which voter preferences remain static over time, and a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Dynamic</i> setting, in which voter preferences may change over time. We adapt the well-established Justified Representation and Proportional Justified Representation axioms, commonly used in the social choice literature, to perpetual voting, resulting in two axiomatic variants for the static setting and four variants for the dynamic setting. We show that all of the axioms are always satisfiable, and that simple preference aggregation methods can be used to satisfy the axioms in both cases. We then conduct a large human study ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N=190$ </tex-math></inline-formula> ) aimed at identifying what potential voters (i.e., ordinary people) deem as desirable outcomes in simple perpetual voting settings. Our results show that approximately half of our participants consider different interpretations of fairness that correspond to our axiomatic framework. Taken jointly, our results can be used to help the research community identify appropriate aggregation methods to use in practice.

Induction, Axiomatic System, Theory and Reality

Induction, Axiomatic System, Theory and Reality

Retracted] A Formal Verification Method of Compilation Based on C Safety Subset

With the rapid increase in the number of wireless terminals and the openness of wireless networks, the security of wireless communication is facing serious challenges. The safety and security of computer communication have always been a research hotspot, especially the wireless communication that still has a more complex architecture which leads to more safety problems in the communication system development. In recent years, more and more wireless communication systems are applied in the safety‐critical field which tends to need high safety guarantees. A compiler is an important tool for system development, and its safety and reliability have an important impact on the development of safety‐critical software. As the strictest method, formal verification methods have been widely paid attention to in compiler verification, but the current formal verification methods have some problems, such as high proof complexity, weak verification ability, and low algorithm efficiency. In this paper, a compiler formal verification method based on safety C subsets is proposed. By abstracting the concept of C grammar units from safety C subsets, the formal verification of the compiler is transformed into the verification of limited C grammar units. In this paper, an axiom system of first‐order logic and special axioms are introduced. On this axiom system, the semantic consistency verification of C grammar unit and target code pattern is completed by means of theorem proving, and the formal verification of the compiler is completed.

Usage of Autonomous Mobile Robots Outdoors - an Axiomatic Design Approach

Industry 4.0, growing material supply chains, and changing logistics structures require flexible material flow solutions. As a result of this development, the usage of autonomous mobile robots (AMRs) is increasing significantly. Although there has been much research undertaken on the design of indoor AMRs, there is a lack of research regarding outdoor systems. Weather and road conditions are still challenging for sensors and actuators. Furthermore, requirements regarding the system, which must be known and met beforehand to guarantee industrial applicability, are yet to be sufficiently determined. This paper aims to close this gap and identify functional requirements through Axiomatic Design, which is used to develop design guidelines for practitioners. Starting with a systematic literature review and semi-structured interviews, the authors gather basic customer requirements. These customer requirements will then be analyzed to define functional requirements. Through a mapping and top-down decomposition process, the research team deduces design solutions for using outdoor AMRs. These requirements and solutions will be transformed into guidelines, which help system designers to improve the implementation of AMRs on the factory premises.

The Chalmers Trilemma Re-examined

The Continuum Hypothesis seems to be a counterexample to David Chalmers’s A Priori Scrutability thesis, according to which there is a compact class of truths (the scrutability base) from which all truths are a priori scrutable. Chalmers’s three-part answer to this problem (which I call the “Chalmers trilemma”) runs as follows: either the Continuum Hypothesis is indeterminate; or adding a new axiom will settle the issue; or, if these two options do not work, we should add the Continuum Hypothesis (or its negation) to the scrutability base. I argue that Chalmers’s answer is unsatisfactory: the first horn of the trilemma can be interpreted in several ways, and either it departs from common mathematical practice and rests on weak analogies, or it shares the same problems with two other horns; the second horn does not provide good reasons to believe that from a fixed system of axioms all truths about our world are scrutable; the third horn of the trilemma renders Chalmers’s project empty.

Interface modeling algorithms for dispatch control

The article offers mathematical tools for programming dispatcher tasks on programmable logic matrices, which allow to obtain closed axiomatic models of the dispatcher’s professional activity in the course of the dispatcher’s dialogue with the computer and implement it in the form of optimal combinational logic schemes with pairwise alternative outputs. These tools implement a user-friendly interface for modeling a logically complete consistent system of axioms written in the production language in a tabular form that resembles decision tables with a limited input. The modeling dialog completely frees the dispatcher from the need to know the properties of axiomatic models and requires only professional skills of dispatcher management. Its function in this dialogue is only to specify the desired action in a specific situation that occurs during the object management process. Such situations are constantly formed during the field work in crop production. Sudden failure of power units, two or three-day period of adverse weather increases the risk of violation of agricultural deadlines. This requires prompt decision - making on re-completing units, changing the plan of mechanized work. The search of all possible situations and obtaining on their basis an optimal set of consistent products closing the axiomatic model is provided exclusively by the interface software, which is developed using algorithms for negating and minimizing disjunctive normal forms of logical functions and includes software tools for modeling logically complete consistent decision tables and optimizing them in order to obtain optimal combinational logical devices with their subsequent hardware implementation in the form of microchips. In addition, these software tools are offered as one of the tools for software implementation of branched algorithms with high complexity indicators according to M. V. Arapov in the automated design of control systems for various purposes.

The Method of the Kernel of the Evolution Equation in the Theory of Gravity

Covariant perturbation theory allows one to calculate the nonlocal kernel of the evolution equation on a spin Riemannian manifold. The proposed axiomatic definition of effective action introduces a universal scale parameter with the dimension of the square of the distance into the dimensionless mathematical theory. It is shown that this purely geometric result has the physical meaning of the action of field theory, including gravity. The two lowest tensor orders of this covariant functional are independent of the type of the spin group and are local; they reproduce the action of general relativity with a cosmological constant. The modern value of the universal distance scale can be determined by the measured Hubble constant. This scale parameter, considered a physical variable, makes it possible to construct the cosmological theory axiomatically.

Spaces of algebraic measure trees and triangulations of the circle

In this paper we present with algebraic trees a novel notion of (continuum) trees which generalizes countable graph-theoretic trees to (potentially) uncountable structures. For that purpose we focus on the tree structure given by the branch point map which assigns to each triple of points their branch point. We give an axiomatic definition of algebraic trees, define a natural topology, and equip them with a probability measure on the Borel-$\sigma$-field.Under an order-separability condition, algebraic (measure) trees can be considered as tree structure equivalence classes of metric (measure) trees (i.e.\ subtrees of R-trees). Using Gromov-weak convergence (i.e.\ sample distance convergence) of the particular representatives given by the metric arising from the distribution of branch points, we define a metrizable topology on the space of equivalence classes of algebraic measure trees. In many applications, binary trees are of particular interest. We introduce on that subspace with the sample shape and the sample subtree mass convergence two additional, natural topologies. Relying on the connection to triangulations of the circle, we show that all three topologies are actually the same, and the space of binary algebraic measure trees is compact. To this end, we provide a formal definition of triangulations of the circle, and show that the coding map which sends a triangulation to an algebraic measure tree is a continuous surjection onto the subspace of binary algebraic non-atomic measure trees.

Q-Rung Orthopair Fuzzy Modified Dissimilarity Measure Based Robust VIKOR Method and its Applications in Mass Vaccination Campaigns in the Context of COVID-19

A new inclusion called total inclusion relation has improved the existing dissimilarity measure for q-rung orthopair fuzzy sets (qROFSs). For qROFSs, the modified axiomatic definition of dissimilarity measure is proposed. The modified Hamming and Euclidean dissimilarity measures are defined. An algorithmic procedure for a robust VIKOR method based on modified dissimilarity measures is established. The application of the robust VIKOR method in Mass Vaccination Campaigns (MVCs) in the COVID-19 situation is given.

An Axiomatic Approach to Gröbner Basis Theory by Examining Several Reduction Principles

Several variants of the classical theory of Grobner bases can be found in the literature. They come, depending on the structure they operate on, with their own specific peculiarity. Setting up an expedient reduction concept depends on the arithmetic equipment that is provided by the structure in question. Often it is necessary to introduce a term order that can be used for determining the orientation of the reduction, the choice of which might be a delicate task. But there are other situations where a different type of structure might give the appropriate basis for formulating adequate rewrite rules. In this paper we have tried to find a unified concept for dealing with such situations. We develop a global theory of Grobner bases for modules over a large class of rings. The method is axiomatic in that we demand properties that should be satisfied by a reduction process. Reduction concepts obeying the principles formulated in the axioms are then guaranteed to terminate. The class of rings we consider is large enough to subsume interesting candidates. Among others this class contains rings of differential operators, Ore-algebras and rings of difference-differential operators. The theory is general enough to embrace the well-known classical Grobner basis concepts of commutative algebra as well as several modern approaches for modules over relevant noncommutative rings. We start with introducing the appropriate axioms step by step, derive consequences from them and end up with the Buchberger Algorithm, that makes it possible to compute a Grobner basis. At the end of the paper we provide a few examples to illustrate the abstract concepts in concrete situations.

Assignments with Ethical Concerns

This study investigates an axiomatic approach to in-kind assignment problems with a single-unit demand such as triage. We consider multiple ethical criteria regarding which agents should be assigned that conflict with one another. To make compromises between criteria, we introduce two methods for configuring social choice rules that map from various problems to agents who are assigned slots: the method of procedure and the method of aggregation. From inter-problem regularities, we demonstrate characterization results, implying that the method of procedure emphasizes consistent respect for individual criteria across problems, whereas the method of aggregation emphasizes consistent respect for individual agents across problems. These methods are incompatible because only ethical dictatorships are induced by both methods. We show that the method of aggregation is superior when we can utilize detailed information about ethical concerns such as cardinality and comparability, while the method of procedure is superior when there are severe informational limitations.

Teaching Axiomatic Design for a Long-Term Sustainable Introduction of Industry 4.0 in SMEs

This work shows how to teach axiomatic design (AD) of manufacturing processes and systems in small and medium enterprises (SMEs) to achieve long-term sustainability in the introduction of Industry 4.0. This is about how to develop profitable and ethical design solutions by exploiting emerging technologies, especially for companies with limited resources. Suh’s axiomatic approach to design selects the best solution among plausible candidates early in the design process so that resources can be focused most effectively. It is important that engineers know how to develop ethical design solutions efficiently and effectively. Sustainability rests on three pillars, economic, ecological and social. Therefore, ethical design can be achieved, with responsible use of natural resources and protection of the environment, meeting the needs of people and society as well as profitability to ensure long-term prosperity for all. Literature on Industry 4.0 shows several approaches on how Industry 4.0 can be sustainable and human-centered. However, few works focus on SMEs and there is little on teaching. Here, AD is used to create a program for teaching how to apply AD to design problems in the context of Industry 4.0 for SMEs. AD theory states that the best design solutions are those that, 1- maintain the independence of the functional elements, and 2- minimize the information content, i.e., maximize the probability of success. In AD, needs of customers and other stake holders are considered first, so that the right problems are addressed. Then top-down, parallel, functional-physical decompositions, are followed by physical integrations, all guided by Suh’s axioms to select the right solutions. In order to test new technologies in a practice-oriented way in advance of introduction for SMEs, learning factory laboratories are used.

Formal Inferring the Law of Conservation of Energy from Assuming A-Priori-ness of Knowledge in a Formal Axiomatic Epistemology System Sigma

The research purpose is invention (construction) of a formal logical inference of the Law of Conservation of Energy within a logically formalized axiomatic epistemology-and-axiology theory Sigma from a precisely defined assumption of a-priori-ness of knowledge. For realizing this aim, the following work has been done: 1) a two-valued algebraic system of formal axiology has been defined precisely and applied to proper-philosophy of physics, namely, to an almost unknown (not-recognized) formal-axiological aspect of the physical law of conservation of energy; 2) the formal axiomatic epistemology-and-axiology theory Sigma has been defined precisely and applied to proper-physics for realizing the above-indicated purpose. Thus, a discrete mathematical model of relationship between philosophy of physics and universal epistemology united with formal axiology has been constructed. Results: 1) By accurate computing relevant compositions of evaluation-functions within the discrete mathematical model, it is demonstrated that a formal-axiological analog of the great conservation law of proper physics is a formal-axiological law of two-valued algebra of metaphysics. (A precise algorithmic definition of the unhabitual (not-well-known) notion “formal-axiological law of algebra of metaphysics” is given.) 2) The hitherto never published significantly new nontrivial scientific result of investigation presented in this article is a formal logical inference of the law of conservation of energy within the formal axiomatic theory Sigma from conjunction of the formal-axiological analog of the law of conservation of energy and the assumption of a-priori-ness of knowledge.

Neurorehabilitation: Sanogenetic and pathogenetic foundations of innovative directions

The processes of sanogenesis and pathogenesis in patients with acute cerebrovascular accident occur simultaneously, starting with the acute period of stroke. In most cases, this is a single process viewed from different perspectives. Modern innovative areas of neurorehabilitation include the use of drug therapy, rehabilitation measures and mechanisms of sanogenesis and self-healing, which can be influenced by the methods used in the course of restoring the health of neurological patients. The organizational model of modern neurorehabilitation is based on an interdisciplinary multistage approach. The analysis of the relationship between patho‑ and sanogenetic reactions is important for the development of this organizational model. Exogenous therapeutic and rehabilitation measures form a single complex with endogenous factors of sanogenesis. These measures achieve the maximum effect only with the conscious active participation of the patient in the recovery process. The theoretical basis of the research is the concept of the theory of functional systems by P. K. Anokhin and the axiomatic theory of human health. The integration of these approaches is considered as the most general self-acting self-healing mechanism, concretized in the form of the concept of sanogenesis. Mechanisms for maintaining homeostasis are activated at all levels when a damaging factor occurs. Pathogenesis develops, becoming an integral part of the processes of sanogenesis.

A Framework for Measures of Risk under Uncertainty

A risk analyst assesses potential financial losses based on multiple sources of information. Often, the assessment does not only depend on the specification of the loss random variable, but also various economic scenarios. Motivated by this observation, we design a unified axiomatic framework for risk evaluation principles which quantifies jointly a loss random variable and a set of plausible probabilities. We call such an evaluation principle a generalized risk measure. We present a series of relevant theoretical results. The worst-case, coherent, and robust generalized risk measures are characterized via different sets of intuitive axioms. We establish the equivalence between a few natural forms of law invariance in our framework, and the technical subtlety therein reveals a sharp contrast between our framework and the traditional one. Moreover, coherence and strong law invariance are derived from a combination of other conditions, which provides additional support for coherent risk measures such as Expected Shortfall over Value-at-Risk, a relevant issue for risk management practice.

Relative differential cohomology and generalized Cheeger–Simons characters

We provide a suitable axiomatic framework for differential cohomology in the relative case and we deduce the corresponding long exact sequences. We also construct the relative version of the generalized Cheeger-Simons characters and we define the integration map when the fibre has a boundary.

Some New Properties of &amp;lt;i&amp;gt;W&amp;lt;sub&amp;gt;d&amp;lt;/sub&amp;gt;&amp;lt;/i&amp;gt;-fuzzy Implication Algebras

Implication is an important logical connective in practically every propositional logic. In 1987, the so-called Fuzzy implication algebras were introduced by Wu Wangming, then various interesting properties of FI-algebras and some subalgebra of Fuzzy implication algebra, such as regular FI-algebras, commutative FI-algebras, Wd- FI-algebras, and other kinds of FI- algebras were reported. The main aim of this article is to study Wd-fuzzy implication algebras which are subalgebra of fuzzy implication algebras. We showed that Wd-fuzzy implication algebras are regular fuzzy implication algebras, but the inverse is not true. The relations between Wd-fuzzy implication algebras and other fuzzy algebras are discussed. Properties and axiomatic systems for Wd-fuzzy implication algebras are investigated. Furthermore, a few new results on Wd-fuzzy implication algebras has been added.