Search

This paper focuses on games on augmenting systems with a coalition structure that can be seen as an extension of games with a coalition structure and games on augmenting systems. Considering the player payoffs, the quasi-Owen value is defined. To show the rationality of this payoff index, five representative axiomatic systems are established. The population monotonic allocation scheme (PMAS) and the core are introduced. Moreover, the relationships between the PMAS and quasi-Owen value as well as the core and quasi-Owen value are discussed. Finally, an illustrative example is given to show the concrete application of the new payoff indices. [ABSTRACT FROM AUTHOR]

In a recent paper on Hertz's Mechanics , Eisenthal claims that this mechanics is without mechanisms. He argues that the absence of mechanisms is a consequence of Hertz's philosophy of physics, presented in the introduction to this book. In the present paper, I will show that Hertz created four mechanisms. These mechanisms play a fundamental role in the deduction of the equations of motion. Some physicists used these mechanisms to create Hertzian mechanical models or to apply Hertz's mechanics to phenomena. • 'Mechanics without mechanisms' is an untenable thesis. • In Hertz's mechanics, there are four mechanisms. • Without these mechanisms, Hertz's axiomatic mechanics would be meaningless. • Some physicists used Hertz's mechanisms to apply his mechanics to phenomena. [ABSTRACT FROM AUTHOR]

Our aim is to critically analyse the approach to the notion of model by Alfred Tarski that Patrick Suppes integrates into his semanticist conception of scientific theories. Indeed, we will show how this notion is configured in Suppes (1960; 1970) from a formal review of the notion of model in Tarski (1936), focusing our analysis on three main axes: i) a critique of the static perspective of semanticism; ii) an analysis of the restrictive conditions and the language for the axiomatization of theories; and iii) the revision of the notions of 'axiomatic system', 'formal system' and 'axiomatic method'. [ABSTRACT FROM AUTHOR]

We significantly simplify the axiomatic system LCBA for fuzzy logic with a non-associative conjunction. [ABSTRACT FROM AUTHOR]

In this work, we combine features from Justification Logics and Logics of Plausibility-Based Beliefs to build a logic for Multi-Agent Systems where each agent can explicitly state his justification for believing in a given sentence. Our logic is a normal modal logic based on the standard Kripke semantics, where we provide a semantic definition for the evidence terms and define the notion of plausible evidence for an agent, based on plausibility relations in the model. As we deal with beliefs, justifications can be faulty and unreliable. In our logic, agents can disagree not only over whether a sentence is true or false, but also on whether some evidence is a valid justification for a sentence or not. After defining our logic and its semantics, we provide a strongly complete axiomatic system for it, show that it has the finite model property, analyze the complexity of its Model-Checking Problem and show that its Satisfiability Problem has the same complexity as the one from basic modal logics. Thus, this logic seems to be a good first step for the development of a dynamic logic that can model the processes of argumentation and debate in Multi-Agent Systems. [ABSTRACT FROM AUTHOR]

In this paper we introduce the operators of validation and invalidation of a proposition, and we extend the operator of S-denying a proposition, or an axiomatic system, from the geometric space to respectively any theory in any domain of knowledge, and show six examples in geometry, in mathematical analysis, and in topology. [ABSTRACT FROM AUTHOR]

In this paper we introduce the operators of validation and invalidation of a proposition, and we extend the operator of S-denying a proposition, or an axiomatic system, from the geometric space to respectively any theory in any domain of knowledge, and show six examples in geometry, in mathematical analysis, and in topology. [ABSTRACT FROM AUTHOR]

This is the third part of a trilogy. The first article is a critique of current empirical research and the second presents the bricoleur model of practice. Here, I try to describe parts of what follows from what we all know about being human because we are human. This knowledge may be partly inherited: that is, we may have an inborn disposition to understand other members of our species in certain ways. An axiomatic system consisting of nine axioms is presented and discussed. They are labelled as follows: Mentality, Intentionality, Reflectivity, Verbality, Learning, Responsibility, Morality, Feeling, and Vulnerability. The axioms are formulated partly in terms of Wierzbicka’s semantic primitives, assumed to be found in all human languages. The usefulness of the axioms is taken to be testable only by general consensus. [ABSTRACT FROM PUBLISHER]

Abstract: Applying classical association rule extraction framework on fuzzy datasets leads to an unmanageably highly sized association rule sets. Moreover, the discretization operation leads to information loss and constitutes a hamper towards an efficient exploitation of the mined knowledge. To overcome such a drawback, this paper proposes the extraction and the exploitation of compact and informative generic basis of fuzzy association rules. The presented approach relies on the extension, within the fuzzy context, of the notion of closure and Galois connection, that we introduce in this paper. In order to select without loss of information a generic subset of all fuzzy association rules, we define three fuzzy generic basis from which remaining (redundant) FARs are generated. This generic basis constitutes a compact nucleus of fuzzy association rules, from which it is possible to informatively derive all the remaining rules. In order to ensure a sound and complete derivation process, we introduce an axiomatic system allowing the complete derivation of all the redundant rules. The results obtained from experiments carried out on benchmark datasets are very encouraging. They highlight a very important reduction of the number of the extracted fuzzy association rules without information loss. [Copyright &y& Elsevier]

The extremely large number of association rules that can be drawn from – even reasonably sized datasets, bootstrapped the development of more acute techniques or methods to reduce the size of the reported rule sets. In this context, the battery of results provided by the Formal Concept Analysis (FCA) allowed one to define "irreducible" nuclei of association rule subset better known as generic bases. From such a condensed and reduced size set of association rules, it is possible to infer all association rules commonly via an adequate axiomatic system. In this paper, we introduce a novel informative generic basis of association rules, conveying two types of knowledge: "factual" and "implicative". We also present a valid and complete axiomatic system allowing one to infer the set of all association rules. Results of the experiments carried out on real-life datasets have shown important profits in terms of compactness of the introduced generic basis. [ABSTRACT FROM AUTHOR]

In this paper, I show the complementarity of foundationalism and coherentism with respect to any efficient system of beliefs by means of a distinction between two types of proposition drawn from an analogy with an axiomatic system. This distinction is based on the way a given proposition is acknowledged as true, either by declaration (F-proposition) or by preservation (C-proposition). Within such a perspective, i.e., epistemological complementarism, not only can one see how the usual opposition between foundationalism and coherentism is irrelevant, but furthermore one can appreciate the reciprocal relation between these two theories as they refer to two separate epistemological functions involved in the dynamics of constituting and expanding an epistemic system. [ABSTRACT FROM AUTHOR]

Abstract: The Swedish mathematician Torsten Brodén (1857–1931) wrote two articles on the foundations of Euclidean geometry. The first was published in 1890, almost a decade before Hilbert''s first attempt, and the second was published in 1912. Brodén''s philosophical view of the nature of geometry is discussed and his thoughts on axiomatic systems are described. His axiomatic system for Euclidean geometry from 1890 is considered in detail and compared with his later work on the foundations of geometry. The two continuity axioms given are compared to and proved to imply Hilbert''s two continuity axioms of 1903. [Copyright &y& Elsevier]

Aristotle's syllogistic is the first ever deductive system. After centuries, Aristotle's ideas are still interesting for logicians who develop Aristotle's work and draw inspiration from his results and even more from his methods. In the paper we discuss the essential elements of the Aristotelian system of syllogistic and Łukasiewicz's reconstruction of it based on the tools of modern formal logic. We pay special attention to the notion of completeness of a deductive system as discussed by both authors. We describe in detail how completeness can be defined and proved with the use of an axiomatic refutation system. Finally, we apply this methodology to different axiomatizations of syllogistic presented by Łukasiewicz, Lemmon and Shepherdson. [ABSTRACT FROM AUTHOR]