Search results for "Axiom"

Geometry and “Metaphysics of Space” in Gauss and Riemann

1994

Gauss’s research on the principles of geometry and the axiom of parallels have been the subject of study for long time (e.g. Stackel 1933) which has shed light once and for all on his role in the early history of non-Euclidean geometry. It is therefore unnecessary to go through it all over again; what is more interesting here is to examine the development of Gauss’s ideas from another standpoint which emerges from the first testimony of his reflections on a subject that mathematicians had examined in vain right from antiquity: i.e. the possibility of proving the proposition that Euclid had taken as an axiom and formulated in the following terms: “That, if a straight line falling on two stra…

Science and logic

2009

Generalized Rough Sets in Contextual Spaces

1997

This paper presents a generalization of Pawlak’s conception of rough sets [6] and [7]. It is more general than Pawlak’s solution of the problem of the definability of sets, the knowledge of which is incomplete and vague. The authors’ conception is based on conception of contextual space [4], which was inspired by Ziarko’s approach [12] to rough sets. Rough sets introduced by Pawlak [6] are particular cases of contextual rough sets defined in the contextual approximation space. This space is defined axiomatically by means of so called context relations. Every contextual rough set determined by set X can be determined by the union of the lower approximation of X and a subset of the boundary o…

Fundamentals of a Generalized Measure Theory

1999

In this chapter, we try to present a coherent survey on some recent attempts in building a theory of generalized measures. Our main goal is to emphasize a minimal set of axioms both for the measures and their domains, and still to be able to prove significant results. Therefore we start with fairly general structures and enrich them with additional properties only if necessary.

Comparative Reasoning for Intelligent Agents

2023

We demonstrate new comparative reasoning abilities of NARS, a formal model of intelligence, which enable the asymmetric comparison of perceivable quantifiable attributes of objects using rela- tions. These new abilities are implemented by extending NAL with addi- tional inference rules. We demonstrate the new capabilities in a bottle- picking experiment on a mobile robot running ONA, an implementation of NARS.

A value for multichoice games

2000

Abstract A multichoice game is a generalization of a cooperative TU game in which each player has several activity levels. We study the solution for these games proposed by Van Den Nouweland et al. (1995) [Van Den Nouweland, A., Potters, J., Tijs, S., Zarzuelo, J.M., 1995. Cores and related solution concepts for multi-choice games. ZOR-Mathematical Methods of Operations Research 41, 289–311]. We show that this solution applied to the discrete cost sharing model coincides with the Aumann-Shapley method proposed by Moulin (1995) [Moulin, H., 1995. On additive methods to share joint costs. The Japanese Economic Review 46, 303–332]. Also, we show that the Aumann-Shapley value for continuum game…

Towards Axiomatic Basis of Inductive Inference

2001

The language for the formulation of the interesting statements is, of course, most important. We use first order predicate logic. Our main achievement in this paper is an axiom system which we believe to be more powerful than any other natural general purpose discovery axiom system. We prove soundness of this axiom system in this paper. Additionally we prove that if we remove some of the requirements used in our axiom system, the system becomes not sound. We characterize the complexity of the quantifier prefix which guaranties provability of a true formula via our system. We prove also that if a true formula contains only monadic predicates, our axiom system is capable to prove this formula…

A Neo2 bayesian foundation of the maxmin value for two-person zero-sum games

1994

A joint derivation of utility and value for two-person zero-sum games is obtained using a decision theoretic approach. Acts map states to consequences. The latter are lotteries over prizes, and the set of states is a product of two finite sets (m rows andn columns). Preferences over acts are complete, transitive, continuous, monotonie and certainty-independent (Gilboa and Schmeidler (1989)), and satisfy a new axiom which we introduce. These axioms are shown to characterize preferences such that (i) the induced preferences on consequences are represented by a von Neumann-Morgenstern utility function, and (ii) each act is ranked according to the maxmin value of the correspondingm × n utility …

Weighted weak semivalues

2000

We introduce two new value solutions: weak semivalues and weighted weak semivalues. They are subfamilies of probabilistic values, and they appear by adding the axioms of balanced contributions and weighted balanced contributions respectively. We show that the effect of the introduction of these axioms is the appearance of consistency in the beliefs of players about the game.

Towards a more dynamic stakeholder model: acknowledging multiple issue arenas

2010

PurposeThe purpose of this paper is to suggest that corporate communications is becoming less predictable as interaction with stakeholders is moving from organizational control toward “issue arenas”, places of interaction where an issue is discussed by stakeholders and organizations both online and within the traditional media. The role of corporate communications and public relations (PR) is broadening beyond the traditional relationship management to issue arena monitoring.Design/methodology/approachThe paper takes a theoretical approach with six axioms suggested.FindingsSeveral central theories of corporate communications are combined with issues management and stakeholder theory to argu…