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The importance of intuitionistic temporal logics in Computer Science and Artificial Intelligence has become increasingly clear in the last few years. From the proof-theory point of view, intuitionistic temporal logics have made it possible to extend functional languages with new features via type theory, while from its semantical perspective several logics for reasoning about dynamical systems and several semantics for logic programming have their roots in this framework. In this paper we consider several axiomatic systems for intuitionistic linear temporal logic and show that each of these systems is sound for a class of structures based either on Kripke frames or on dynamic topological systems. Our topological semantics features a new interpretation for the `henceforth' modality that is a natural intuitionistic variant of the classical one. Using the soundness results, we show that the seven logics obtained from the axiomatic systems are distinct., Comment: Under consideration in Theory and Practice of Logic Programming (TPLP). arXiv admin note: text overlap with arXiv:1803.05077

Resiliency for older people represents the capacity to return to equilibrium when difficulties arise and was found as integral predictor of their health status. This study aims to develop a theory that attempts to explain the older adults’ resiliency perspectives during crisis and how it has affected their well-being and quality of life as population group. Deductive theory generation using axiomatic approach was adopted resulting to five axioms that served as basis for the generation of three propositions such as: (1) An older person’s health needs have tendencies to develop into a health threat, (2) when the threat is perceived, older persons developed a sense of internal control and adaptation to the changes it creates known as internal resiliency, and (3) internal resiliency can influence the quality of life in old age. The evolved theory suggests that in times of crisis (e.g., COVID-19 pandemic), health needs develop into a health threat that compels older persons to develop internal resiliency in order to preserve their integrity, wellbeing and quality of life. This study widens the nursing perspectives in addressing older persons’ resiliency by the unique condition at which older clients are placed affecting both the pathological nature of the illness as well as the preventive interventions which the society is forced to implement.

The purpose of this paper is to propose an axiomatic characterization of ecological footprint indices. Using an axiomatic approach, we define a set of axioms representing the properties considered ...

Axiomatic Theories and Improving the Relevance of Information Systems Research This paper examines the fact that a significant number of empirical information systems (IS) studies engage in confirmative testing of self-evident axiomatic theories without yielding highly relevant knowledge for the IS community. The authors conduct both a horizontal analysis of 72 representative IS theories and an in-depth vertical analysis of 3 well-known theories (i.e., technology acceptance model, diffusion of innovation theory, and institutional theory) in order to measure how pervasive such testing of axiomatic theories is. The authors discovered that more than 60% of 666 hypotheses from the horizontal analysis could be regarded as axiomatic theory elements. In the vertical analysis, 68.1% of 1,301 hypotheses from 148 articles were axiomatic. Based on these findings, the authors propose four complementary IS research approaches: (1) identifying disconfirming boundary conditions, (2) measuring the relative importance of axiomatic causal factors, (3) measuring the stage of progression toward visionary goals when the nature of the axiomatic theory can be extended to future visions, and (4) engaging in the conceptual design of visionary axiomatic goals. They argue that these complementary IS research approaches can enhance the relevance of IS research outcomes without sacrificing methodological rigor.

Genuine Paraconsistent logics $$\mathbf {L3A}$$ and $$\mathbf {L3B}$$ were defined in 2016 by Beziau et al, including only three logical connectives, namely, negation disjunction and conjunction. Afterwards in 2017 Hernandez-Tello et al, provide implications for both logics and define the logics $$\mathbf {L3A_G}$$ and $$\mathbf {L3B_G}$$ . In this work we continue the study of these logics, providing sound and complete Hilbert-type axiomatic systems for each logic. We prove among other properties that $$\mathbf {L3A_G}$$ and $$\mathbf {L3B_G}$$ satisfy a restricted version of the Substitution Theorem, and that both of them are maximal with respect to Classical Propositional Logic. To conclude we make some comparisons between $$\mathbf {L3A_G}$$ and $$\mathbf {L3B_G}$$ and among other logics, for instance $${\mathbf {Int}}$$ and some $${\mathbf {LFI}}$$ s.

In this paper, we analyse the various meanings of probability and its different applications, and we focus especially on the classical, the frequentist, and the subjectivist view. We describe the different problems of how probability can be measured in each of the approaches, and how each of them can be well justified by a mathematical theory. We analyse the foundations of probability, where the scientific analysis of the theory that allows for a frequentist interpretation leads to unsolvable problems. Kolmogorov’s axiomatic theory does not suffice to establish statistical inference without further definitions and principles. Finally, we show how statistical inference essentially determines the meaning of probability and a shift emerges from purely objectivist views to a complementary conception of probability with frequentist and subjectivist constituents. For didactical purpose, the result of the present analyses explains basic problems of teaching, originating from a biased focus on frequentist aspects of probability. It also indicates a high priority for the design of suitable learning paths to a complementary conception of probability. In the applications, modellers use information in a pragmatic way processing this information regardless of its connotation into formal mathematical models, which are always thought as essentially wrong but useful.

A model is proposed to allocate Formula One World Championship prize money among the constructors. The methodology is based on pairwise comparison matrices, allows for the use of any weighting method, and makes possible to tune the level of inequality. We introduce an axiom called scale invariance, which requires the ranking of the teams to be independent of the parameter controlling inequality. The eigenvector method is revealed to violate this condition in our dataset, while the row geometric mean method always satisfies it. The revenue allocation is not influenced by the arbitrary valuation given to the race prizes in the official points scoring system of Formula One and takes the intensity of pairwise preferences into account, contrary to the standard Condorcet method. Our approach can be used to share revenues among groups when group members are ranked several times., Comment: 19 pages, 3 figures, 6 tables

We propose an axiomatic approach which economically underpins the representation of dynamic intertemporal decisions in terms of a utility function, which randomly reacts to the information available to the decision maker throughout time. Our construction is iterative and based on time dependent preference connections, whose characterization is inspired by the original intuition given by Debreu’s State Dependent Utilities (1960).

For a completely distributive De Morgan algebra L, we develop a general framework of L-fuzzy rough sets. Said precisely, we introduce a pair of L-fuzzy approximation operators, called upper and lower L-fuzzifying approximation operators derived from general L-fuzzifying neighborhood systems. It is shown that the proposed approximation operators are a common extension of the L-fuzzifying approximation operators derived from L-fuzzy relations (INS 2019) and the approximation operators derived from general neighborhood systems (KBS 2014). Furthermore, we investigate the unary, serial, reflexive, transitive and symmetric conditions in general L-fuzzifying neighborhood systems, and then study the associated approximation operators from both a constructive method and an axiomatic method. Particularly, for transitivity (resp., symmetry), we give two interpretations, one is an appropriate generalization of transitivity (resp., symmetry) for L-fuzzy relations, and the other is a suitable extension of transitivity (resp., symmetry) for general neighborhood systems. In addition, for some special L-fuzzifying approximation operators, we use single axiom to characterize them, respectively. At last, the proposed approximation operators are applied in the research of incomplete information system, and a three-way decision model based on them is established. To exhibit the effectiveness of the model, a practical example is presented.

This is an expository paper on tensor products where the standard approaches for constructing concrete instances of algebraic tensor products of linear spaces, via quotient spaces or via linear maps of bilinear maps, are reviewed by reducing them to different but isomorphic interpretations of an abstract notion, viz. the universal property, which is based on a pair of axioms.

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.

We provide a complete taxonomic characterization of robust hierarchical clustering methods for directed networks following an axiomatic approach. We begin by introducing three practical properties associated with the notion of robustness in hierarchical clustering: linear scale preservation, stability, and excisiveness. Linear scale preservation enforces imperviousness to change in units of measure whereas stability ensures that a bounded perturbation in the input network entails a bounded perturbation in the clustering output. Excisiveness refers to the local consistency of the clustering outcome. Algorithmically, excisiveness implies that we can reduce computational complexity by only clustering a subset of our data while theoretically guaranteeing that the same hierarchical outcome would be observed when clustering the whole dataset. In parallel to these three properties, we introduce the concept of representability, a generative model for describing clustering methods through the specification of their action on a collection of networks. Our main result is to leverage this generative model to give a precise characterization of all robust -- i.e., excisive, linear scale preserving, and stable -- hierarchical clustering methods for directed networks. We also address the implementation of our methods and describe an application to real data., arXiv admin note: substantial text overlap with arXiv:1607.06339

The general purpose of the research—systematical clarifying and explicating the too vague proper philosophical concepts of space, void, matter, motion, inertia, for making a logical harmony between them and the corresponding notions of proper physics. The special purpose of the research—invention (construction) of a formal inference of the well-known Newton’s first law of mechanics within a logically formalized axiomatic epistemology system from a set of precisely defined presumptions. For realizing this aim the following work has been done: a two-valued algebraic system of metaphysics as formal axiology has been applied to philosophical epistemology and philosophy of nature; a formal axiomatic theory called Sigma has been applied to physics for realizing the above-indicated special purpose of the research. Thus, constructing a discrete mathematical model of relationship between universal epistemology and philosophy of physics has been done. Research results: The main hitherto not published significantly new nontrivial scientific result of applied investigations presented in this article is a formal inference of the well-known Newton’s first law of mechanics within the formal axiomatic epistemology system Sigma from conjunction of the formal-axiological analog of the proper-law-of-mechanics (which analog is the formal-axiological law of two-valued algebra of metaphysics) and the assumption of a-priori-ness of knowledge. For obtaining this main research result, a set of accessory nontrivial novelties has been used, for instance; a precise algorithmic definition is given for the notion “law of metaphysics” in the algebraic system of metaphysics as formal axiology; a formal-axiological equivalence in the algebraic system is defined precisely. Precise tabular definitions are given for relevant evaluation-functions determined by evaluation-arguments, for example; “movement of (what, whom) x”; “speed of x”; “vector of x”; “velocity of x”; “magnitude of x”; “finiteness (definiteness) of x”; “dynamical closed-ness (isolated-ness) of x”; “constant-ness, immutability, conservation of x”.

The Borda rule, originally defined on profiles of individual preferences modelled as linear orders over the set of alternatives, is one of the most important voting rules. But voting rules often need to be used on preferences of a different format as well, such as top-truncated orders, where agents rank just their most preferred alternatives. What is the right generalisation of the Borda rule to such richer models of preference? Several suggestions have been made in the literature, typically considering specific contexts where the rule is to be applied. In this work, taking an axiomatic perspective, we conduct a principled analysis of the different options for defining the Borda rule on top-truncated preferences.

This paper proposes a new method for solving the problem of multicriteria optimization of a numerical vector function on a fuzzy set. The membership function of a fuzzy feasible set is joined to the original set of criteria that allows the original problem of multi-criteria optimization to be treated as the task of finding a suitable compromise (Pareto-optimal) solution with respect to an extended set of criteria. It is assumed that in a search for the “best” compromise solution there is only fuzzy information about the preferences of decision maker in the form of information quanta. At the first stage of the proposed method, the search for a compromise is made on the basis of an axiomatic approach, with which the Pareto set is reduced. The result of the reduction is a fuzzy set with a membership function, which is determined on the basis of the used fuzzy information. At the second stage, the obtained membership function is added to the extended set of criteria, after which the scalarization procedure based on the idea of goal programming is used to solve the formed multicriteria problem.

Historically, our theme is situated within the triangle of three of Kant's students: Hegel (1770-1831), Bolzano (1781-1848) and Peirce (1839-1914). All three wanted to change Kant's strict separation of philosophy and science by developing a new conception of logic. Bolzano inaugurated the so-called linguistic turn of philosophy which became the guiding principle of all analytical philosophy (Dummett, 2014) and he opposed Hegel’s unity of concept and object of knowledge. Charles Peirce took a middle position, a position that is expressed in his so-called Pragmatic Maxim (Peirce, CP 5.3). Taken together we might say that a universal principle of complementarity of meaning and reference, or of meaning and information (in the sense of Shannon) finds its origin in Post-Kantian philosophy. We encounter here the very same approach of principled thinking endorsed by Einstein in physics (special theory of relativity) or by the formal axiomatic approach in mathematics (Hilbert)! Key Words: Bolzano, Hegel, Peirce; Complementarity of sense and reference; Geometry from Euclid to Einstein; Hilbert. Historicamente, nosso tema se situa dentro do triângulo de três alunos de Kant: Hegel (1770-1831), Bolzano (1781-1848) e Peirce (1839-1914). Todos os três queriam mudar a separação estrita de Kant entre filosofia e ciência, desenvolvendo uma nova concepção de lógica. Bolzano inaugurou a chamada virada linguística da filosofia, que se tornou o princípio orientador de toda filosofia analítica (Dummett, 2014) e se opôs à unidade de conceito e objeto de conhecimento de Hegel. Charles Peirce assumiu uma posição intermediária, posição que se expressa em sua assim chamada Máxima Pragmática (Peirce, CP 5.3). Tomados em conjunto, podemos dizer que um princípio universal de complementaridade de significado e referência, ou de significado e informação (no sentido de Shannon) encontra sua origem na filosofia pós-kantiana. Encontramos aqui a mesma abordagem do pensamento baseado em princípios endossada por Einstein na física (teoria da relatividade especial) ou pela abordagem axiomática formal na matemática (Hilbert)! Palavras-chave: Bolzano, Hegel, Peirce; Complementaridade de sentido e referência; Geometria de Euclides a Einstein; Hilbert.

This paper shows the importance of applying a certain approach to the history and philosophy of mathematical practice to the study of Zygmunt Janiszewski's contribution to the topological foundations of Continuum theory. In the first part, a biography of Janiszewski is presented. It emphasizes his role as one of the founders of the Polish School of Mathematics, and the social, political and military facets in which his intellectual character was revealed, as well as the values that guided his academic and scientific life. Kitcher's view of mathematical practice is then adopted to examine the philosophical conceptions and epistemological style of Janiszewski in relation to the construction of the formal axiomatic system of knowledge about the continua. Finally, it is shown the convenience of differentiating in Kitcher's approach, the methods, procedures, techniques and strategies of practice, and the aesthetic values of mathematics. Keywords: Zygmunt Janiszewski; Continuum theory; Philosophy of mathematical practice; Polish school of mathematics. Este artigo mostra a importância de aplicar uma certa abordagem da história e da filosofia da prática matemática ao estudo da contribuição de Zygmunt Janiszewski para os fundamentos topológicos da Teoria do continuum. Na primeira parte, é apresentada uma biografia de Janiszewski. Ela enfatiza seu papel como um dos fundadores da Escola de Matemática da Polônia, e as facetas sociais, políticas e militares nas quais seu caráter intelectual foi revelado, assim como os valores que guiaram sua vida acadêmica e científica. A visão de Kitcher sobre a prática matemática é então adotada para examinar as concepções filosóficas e o estilo epistemológico de Janiszewski em relação à construção do sistema axiomático formal de conhecimento sobre o contínuo. Finalmente, mostra-se a conveniência de diferenciar na abordagem de Kitcher, os métodos, procedimentos, técnicas e estratégias da prática, e os valores estéticos da matemática. Palavras-chave: Zygmunt Janiszewski; Teoria do Continuum; Filosofia da prática matemática; Escola de Matemática da Polônia.