Search results for "Axiom"
showing 10 items of 91 documents
A common extension of Arhangel'skii's Theorem and the Hajnal-Juhasz inequality
2019
AbstractWe present a result about $G_{\unicode[STIX]{x1D6FF}}$ covers of a Hausdorff space that implies various known cardinal inequalities, including the following two fundamental results in the theory of cardinal invariants in topology: $|X|\leqslant 2^{L(X)\unicode[STIX]{x1D712}(X)}$ (Arhangel’skiĭ) and $|X|\leqslant 2^{c(X)\unicode[STIX]{x1D712}(X)}$ (Hajnal–Juhász). This solves a question that goes back to Bell, Ginsburg and Woods’s 1978 paper (M. Bell, J.N. Ginsburg and R.G. Woods, Cardinal inequalities for topological spaces involving the weak Lindelöf number, Pacific J. Math. 79(1978), 37–45) and is mentioned in Hodel’s survey on Arhangel’skiĭ’s Theorem (R. Hodel, Arhangel’skii’s so…
Understanding the shortcomings of commodity-based technology in input-output models: an economic-circuit approach
2004
International audience; The Make-Use Model serves as a basis for most national accounting systems as the System of National Accounts (SNA) and is acknowledged as the most suitable model for interregional analysis. Two hypotheses are traditionally made featuring either industry-based technologies (IBT) or commodity-based technologies (CBT). While industry-based technologies can be easily interpreted in terms of a demand-driven economic circuit, it will be shown that: (1) commodity-based technologies cannot be interpreted as a demand-driven economic circuit because this involves computing the inverse of a matrix (the matrix of industry output proportions), which is either impossible or genera…
A Design Theory for Secure Information Systems Design Methods
2006
Many alternative methods for designing secure information systems (SIS) have been proposed to ensure system security. However, within all the literature on SIS methods, there exists little theoretically grounded work that addresses the fundamental requirements and goals of SIS design. This paper first uses design theory to develop a SIS design theory framework that defines six requirements for SIS design methods, and second, shows how known SIS design methods fail to satisfy these requirements. Third, the paper describes a SIS design method that does address these requirements and reports two empirical studies that demonstrate the validity of the proposed framework. peerReviewed
Horizontal inequity comparisons
1998
In this paper, we expound the idea that horizontal inequity (HI) in different tax systems be compared by transplanting the HI from one tax system into the other, as a mapping between its pre- and post-tax living standard distributions, and then applying known results to compare the extent of association present in the two joint distributions. We make this idea operational by means of axioms which, we show, lead to an implementable procedure based on the `copula'. Statistical inference procedures are discussed, and illustrative empirical exercises are undertaken for the UK, Canadian and Israeli tax and benefit systems.
Knowledge Representation in Extended Pawlak’s Information Systems: Algebraic Aspects
2002
The notion of an information system in Pawlak's sense is extended by introducing a certain ordering on the attribute set, which allows to treat some attributes as parts of others. With every extended information system S associated is the set K(S) of those pieces of information that, in a sense, admit a direct access in S. The algebraic structure of the "information space" K(S) is investigated, and it is shown, in what extent the structure of S can be restored from the structure of its information space. In particular, an intrinsic binary relation on K(S), interpreted as entailment, is isolated, and an axiomatic description of a knowledge revision operation based on it is proposed.
The Duality of Entropy/Extropy, and Completion of the Kullback Information Complex
2018
The refinement axiom for entropy has been provocative in providing foundations of information theory, recognised as thoughtworthy in the writings of both Shannon and Jaynes. A resolution to their concerns has been provided recently by the discovery that the entropy measure of a probability distribution has a dual measure, a complementary companion designated as &ldquo
Performability of Actions
2021
AbstractAction theory may be regarded as a theoretical foundation of AI, because it provides in a logically coherent way the principles of performing actions by agents. But, more importantly, action theory offers a formal ontology mainly based on set-theoretic constructs. This ontology isolates various types of actions as structured entities: atomic, sequential, compound, ordered, situational actions etc., and it is a solid and non-removable foundation of any rational activity. The paper is mainly concerned with a bunch of issues centered around the notion of performability of actions. It seems that the problem of performability of actions, though of basic importance for purely practical ap…
Leon Henkin the Reviewer
2014
In this chapter, we intend to look at Henkin’s reviews, a total of forty-six. The books and papers reviewed deal with a large variety of subjects that range from the algebraic treatment of logical systems to issues concerning the philosophy of mathematics and, not surprisingly—given his active work in mathematical education—one on the teaching of this subject. Most of them were published in The Journal of Symbolic Logic and only one in the Bulletin of the American Mathematical Society. We will start by sorting these works into subjects and continue by providing a brief summary of each of them in order to point out those aspects that are originally from Henkin, and what we take to be mistake…
Basic Mathematical Thinking
2016
Mathematics, from the Greek word “mathema”, is simply translated as science or expression of the knowledge.
Two Paths to Logical Consequence: Pieri and the Peano School
2021
This chapter1 has two main goals. First, it will explore the “negative” avenue leading from the concepts of independence and consistency to that of logical consequence.