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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]

Some cooperative games may have some players whose marginal contribution is zero but are indispensable to forming the coalition. However, the marginalism-based index allocates such players with zero payoffs. It is unreasonable and inconsistent with practical cases because the rest players cannot cooperate to make more payoffs without the participation of the players with no marginal contribution. This paper studies one such type of cooperative game called games with communication structure and introduces the α-Egalitarian Myerson value. This payoff index consolidates the Myerson value and the Equal Component Division value, which not only considers the marginal contribution of players but also regards egalitarianism. The main feature of this payoff index is to protect all players' payoffs. Three axiomatic systems are provided to show the rationality of the α-Egalitarian Myerson value. An application of the theoretical results in pharmaceutical supply chain management is offered to show the efficiency of the new payoff index. [ABSTRACT FROM AUTHOR]

This article is the first complete axiomatic presentation of the theory of cognition (epistemology). It presents the axioms of the theory of cognition, the definitions of the concepts and categories used in the text of the theory, and also provides detailed proofs of the propositions (theorems) arising from them. Based on this axiomatic system, evidencebased solutions to the problems (aporias) of the theory of cognition are proposed. This system of axiomatic epistemology can serve as a step in building a rigorous scientific theory of human cognition. The axioms of the proposed system follow the Aristotelian general understanding of the essence of human cognition. [ABSTRACT FROM AUTHOR]

In this paper, two important models for the finite hyperbolic plane (finite BolyaiLobachevsky plane) Bn,m will be given, the first model is when n = 3 and m = 3, while the second model is when n = 3 and m = 4. Also, two important models for the finite hyperbolic geometry (finite BolyaiLobachevsky geometry) are given, the first model is when each line contains either 4 or 3 distinct points and each point is on 6 distinct lines, while the second model is when each line contains either 3 or 2 distinct points and each point is on either 7 or 8 lines. All models are represented in a simple form, which help the readers and researchers to understand the different facts about the finite Bolyai-Lobachevsky plane and the finite Bolyai-Lobachevsky geometry. [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]

Axiomatic systems can be understood as subsets of syntactic systems. By a process of increasing abstraction, the notion of a syntactic system can become useful for understanding Meillassoux’s concept of hyper-Chaos.

It is known that a professional artist can enter the structure of any already created painting style, simulate it, or even independently create in it. Today, a painter can, for example, paint an impressionist, fauvist, cubist, etc., composition. The question that arises, however, is what does he have to know, understand, and master so that an existing painting style can “come to life” in a concrete painting? And, of course: what actually is the “existence” of style, as it appears to have already existed before a work of art, while on the other hand it does not factually reveal itself until the painting is realized? The hypothesis that the author will be defending on these pages is that painting artworks as “systems of organized perceptions” and painting styles as their generative matrices have an axiomatic nature and organization, that in their formalsemantic complexity they behave as specific axiomatic systems.

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]

The strategies, for performing the mathematical models of the walking robot to traverse an uneven terrain, are analyzed. These mathematical models are assumed that fulfilled the hypothesis emphasized by us on environment model. Our first mathematical characterization of the environment is derived from the property of separation between stable and unstable regions from the free parameters domain of the dynamical system, in the general case of the system depending on parameters. On a specific case, the reader can ad other axioms, analyzing the Godel theorem on axioms system. The mathematical modeling of the environment can be seen as a frontier notion and should be of interest for all mathematical approximation of the phenomena being described in the first section of the paper. Our study on modeling of the walking robot critical positions that can appear in your evolution is related in the second section of the paper. The study started with formulation of physical identification referred to critical position in particular case of improved mathematical model on walking robot leg model used by us. The leg model is compounded from two components leg namely the superior component leg as first component with one extremity attached to the body of the walking robot and other extremity jointed in "knee joint" to inferior component leg as second component leg. The inferior component leg is defined also through "base point" as another extremity of the component, in contact with terrain. The base point is assumed that traverses an ellipse arc trajectory. The geometrical identification of walking robot leg model critical position, where is changing the sense of the system movement and where the speed of the movement must be of zero value, imposed by the mathematical conditions of the environment, assure the possibility of physical identification for walking robot leg critical position. The algorithm on physical identification of the walking robot leg critical position through physical model and calling geometrical identification is described in the paper on our concrete case of walking robot leg mathematical model. The critical position is relevant for all the dynamic systems in the specialized literature, be it chemical, biological, economical and other system, were the mathematical study is similar. The principal way of research in the next time on identification of walking robot critical position is to perform an algorithm for physical identification of critical position on trajectory done and to apply the virtual result on real [ABSTRACT FROM AUTHOR]

In this paper, a connexive extension of the relevance logic R! was presented. It is defined by means of a natural deduction system, and a deductively equivalent axiomatic system is presented too. The goal of such an extension is to produce a logic with stronger connection between the antecedent and the consequent of an implication. [ABSTRACT FROM AUTHOR]

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Copyright of Phainomena is the property of Phenomenological Society of Ljubljana and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The identification of walking robot critical position is one of the most problems that arise for the general case of walking robots evolution on uneven terrain. Our study begins with identification of critical position for particular case of waking robot leg physical and mathematical model that consists from two components leg namely the superior component leg with one extremity jointed to the body of the walking robot and another extremity jointed to inferior component leg in "knee joint". The inferior component leg has "base point" as an extremity of the component, in contact with terrain. The base point describes in our model an ellipse arc. The geometrical identification of walking robot leg critical position, where the sense of movement is changing, is described in our previous study. The physical identification of the critical position, distinct of geometrical identification, is analyzed in the paper on our concrete case of walking robot leg mathematical model. The evolution of the walking robot leg is assumed that respects the environment mathematical model defined also by us. Some aspects referred to environment's mathematical model are described in the first part of the exposure. The new directions of research, opened by our study in this area, are emphasized. [ABSTRACT FROM AUTHOR]

The relationship between Reason and Religion is one of the most fundamental matters in the territory of Philosophy of Religion and philosophical epistemology. Theologians have considered especially religious aspects of it from many centuries ago and have presented different perspectives on this issue. In this paper, we intend to survey Motahari’s view about the Islamic Pillars or Principles, and also analyze possibility of putting these principles as axioms of an axiomatic (and maybe a deductive) system. Then, in further step, we examine the hypothesis that Motahari’s viewpoint of the principles of religion make a Rational Entrance for ancillaries and secondary articles of Islam. Furthermore, we are going to Show this entry is a rational position for the principles of religion that have a philosophical value. In addition; this entry specifies the relationship between reason and religion. Meanwhile, we will represent that its extern–religious prospect in philosophy of religion is independent of intra–religious prospect. Finally, based on this premises, we can derive only one compatible response to the question of relation between Reason and Religion. The response will be a Rational and cross religious one that would be the inter-subjective and defensive basis for dialogue among Religions.

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.

The Constitution is considered as an informal axiomatic system. The strategy proposed by the authors rests on the following propositions: (1) axioms are considered as contextual definitions of those concepts by means of which they are formulated; and (2) the main requirement for this type of system is internal consistency. The first proposition is necessary for considering the Constitution as an informal axiomatic system, while the second is sufficient, because the approach proposed, apart from consistency, must certainly consider the requirements for formal axiomatic systems, such as independence and completeness. The authors argue that the Constitution can be compared to axiomatic constructions in modern science in the sense that is given in the research on the logic and methodology of deductive sciences. This analogy is appropriate to the extent to which constitutional provisions are interpreted as the basic elements of the legal system, just as in the formal sciences axioms are regarded as basic principles that define the main features of the formal system. This means that the Constitution itself is seen as coherent, consistent discourse that contextually defines the meaning of the basic terms of the legal system. [ABSTRACT FROM AUTHOR]

Do other earthly forms of life evolved to the level of intelligent life? Cancer and resistance to antibiotics obliged to ask this question. Signs of intelligence are found at its simplest levels. We try to see if logic is used at these levels. Peter of Spain's suppositio materialis is applied to the chemical signals of cells. Dynamic Logic is used to understand these chemical communications. is used, instead of “language”. The development of life appears as the development of an axiomatic system. The rights of unborn humans and God's rights over His own creation appear as the most powerful arguments for conservationism. [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]

The article studies knowledge in multiagent systems where data available to the agents may have small errors. To reason about such uncertain knowledge, a formal semantics is introduced in which indistinguishability relations, commonly used in the semantics for epistemic logic S5, are replaced with metrics to capture how much two epistemic worlds are different from an agent's point of view. The main result is a logical system sound and complete with respect to the proposed semantics. [ABSTRACT FROM AUTHOR]

In this paper we study the axiomatic system proposed by Bourbaki for the Theory of Sets in the Éléments de Mathématique. We begin by examining the role played by the sign $$\uptau $$ in the framework of its formal logical theory and then we show that the system of axioms for set theory is equivalent to Zermelo-Fraenkel system with the axiom of choice but without the axiom of foundation. Moreover, we study Grothendieck's proposal of adding to Bourbaki's system the axiom of universes for the purpose of considering the theory of categories. In this regard, we make some historical and epistemological remarks that could explain the conservative attitude of the Group. [ABSTRACT FROM AUTHOR]

Meta-philosophically speaking, the philosophy of artificial intelligence (AI) is intended not only to explore the theoretical possibility of building “thinking machines,” but also to reveal philosophical implications of specific AI approaches. Wittgenstein’s comments on the analytic/empirical dichotomy may offer inspirations for AI in the second sense. According to his “river metaphor” in On Certainty, the analytic/empirical boundary should be delimited in a way sensitive to specific contexts of practical reasoning. His proposal seems to suggest that any cognitive modeling project needs to render the system context-sensitive by avoiding representing large amounts of truisms in its cognitive processes, otherwise neither representational compactness nor computational efficiency can be achieved. In this article, different AI approaches (like the Common Sense Law of Inertia approach, the Bayesian approach and the connectionist approach) will be critically evaluated under the afore-mentioned Wittgensteinian criteria, followed by the author’s own constructive suggestion on what AI needs to try to do in the near future. [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 present essay, named "Language authority at Witgenstein" aims to show the originality in Wittgenstein's thought and its contribution to the development of analytic approach in philosophy. Influenced by Frege, Wittgenstein assumes the existence of a logical space and elaborates the concept of logical form. Making a critique of the idea of demonstration present in the Russel's work Principia Mathematica, Wittgenstein said that the demonstration has no importance because all logical propositions valid are tautologies and the tautology not need of demonstration. Tautology is always true regardless of the true value of the proposition that a component. The whole logic is composed only of tautologies. It means that logic is not the work of man but is even the structure of world. Wittgenstein makes a difference between what can be said and what can be showed. Because of this propositions about the metaphysical subject and about logical space are propositions limit. They have more mystical value than epistemological value. Analysis of the sentence is just a scale that helps us reach the limit of enunciation. In second period of his creation, Wittgenstein is the author of theories of language games. Language is context dependent, while logic is independent speaker. If the linguistic sentence needs a language speaker, logical sentence, as timeless entity, is not required to be stated. Logical proposition relates to an absolute intelligence that creates and supports logical space [ABSTRACT FROM AUTHOR]

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]

The paper presents an axiomatic system for quantified propositional temporal logic (QPTL), which is propositional temporal logic equipped with quantification over propositions (Boolean variables). The advantages of this extended temporal logic is that its expressive power is strictly higher than that of the unquantified version (PTL) and is equal to that of S1S, as well as that of-automata. Another important application of QPTL is its use for formulating and verifying refinement relations between reactive systems. In fact, the completeness proof is based on the reduction of a QPTL formula into a Büchi automaton, and performing equivalence transformations on this automaton, formally justifying these transformations as a bi-directional refinement. [ABSTRACT FROM AUTHOR]

We study quasi-characterizing inference rules (this notion was introduced into consideration by A. Citkin (1977). The main result of our paper is a complete description of all self-admissible quasi-characterizing inference rules. It is shown that a quasi-characterizing rule is self-admissible iff the frame of the algebra generating this rule is not rigid. We also prove that self-admissible rules are always admissible in canonical, in a sense, logics S4 or IPC regarding the type of algebra generating rules. [ABSTRACT FROM AUTHOR]

For branching-time temporal logic based on an Ockhamist semantics, we explore a temporal language extended with two additional syntactic tools. For reference to the set of all possible futures at a moment of time we use syntactically designated “restricted variables” called fan-names. For reference to all possible futures alternative to the actual one we use a modification of a difference modality, localized to the set of all possible futures at the actual moment of time. We construct an axiomatic system for this extended branching-time logic and prove its soundness and completeness with respect to bundle tree semantics. Finally, we show how our axiomatic system can be extended with a variety of important additional operators, such as Since and Until, a global difference operator, operators for undivided and divided histories, reference pointers, etc. [ABSTRACT FROM AUTHOR]

Morris (1983) develops an axiom system for combining expert judgments by means of a processing rule. It is shown that the axioms are self-contradictory. [ABSTRACT FROM AUTHOR]

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]