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1

Distributive atomic efect algebras

100%

Riečanová Z.

Demonstratio Mathematica

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2003

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tom Vol. 36, nr 2

247--259

EN

Motivated by the use of fuzzy or unsharp quantum logics as carriers of probability measures there have been recently introduced effect algebras (D-posets). We extend a result by Greechie, Foulis and Pulmannova of finite distributive effect algebras to all Archimedean atomic distributive effect algebras. We show that every such an effect algebra is join and meet dense in a complete effect algebra being a direct product of finite chains and distributive diamonds. This proves that every such effect algebra has a MacNeille completion being again a distributive effect algebra and both these effect algebras are continuous lattices. Moreover, we show that every faithful or (o)-continuous state (probability) on such an effect algebra is a valuation, hence a subadditive state. Its existence is also proved. Finally, we prove that every complete atomic distributive effect algebra E is a homomorphic image of a complete modular atomic ortholattice regarded as effect algebra and E is an MV-effect algebra (MV-algebra) if and only if it is a homomorphic image of a Boolean algebra regarded as effect algebra.

2

Monotone Valuations on the Space of Convex Functions

88%

Cavallina L. , Colesanti A.

Analysis and Geometry in Metric Spaces

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2015

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tom 3

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nr 1

EN

We consider the space Cn of convex functions u defined in Rn with values in R ∪ {∞}, which are lower semi-continuous and such that lim|x| } ∞ u(x) = ∞. We study the valuations defined on Cn which are invariant under the composition with rigid motions, monotone and verify a certain type of continuity. We prove integral representations formulas for such valuations which are, in addition, simple or homogeneous.

3

The Return to Values in Recent Sociological Theory

75%

Sztompka P.

Polish Sociological Review

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2007

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tom 159

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nr 3

247-261

EN

The author reviews two opposite traditional positions on the role of values and value judgements in sociological research and theory: treating values as a bias interfering in research, or treating values as ideology providing privileged access to knowledge. He traces the recent revival of the debate about valuations, focusing particularly on the claims of the so-called “public sociology.” Then the author’s own position is outlined based on the fundamental particularity of the social sciences as contrasted with the natural sciences. The old argument that values do not follow from facts is acknowledged as true in the sense of logical deduction, but in the social sciences we encounter different mechanism of implication, which may be called “sociological syllogism:” values may follow from facts, and facts may imply values because, on the one hand, people act on their axiological beliefs, and human actions constitute social facts, and on the other hand, social facts (e.g. about poverty, inequality, degradation, crime, terrorism) mobilize moral impulses and valuational commitments. In other words values shape meanings of human actions and resulting social facts, and the knowledge of facts acquires valuational meaning by mobilizing human axiological impulses. The strict separation of facts and values does not work in the social sciences; there is a two-directional link between the two. This opens the possibility for “sociological ethics” deriving normative standards of social life from the research results of sociology.

4

Safety Culture in Functional and Axiological Approach

75%

Skurjat K.

Security Dimensions: International & National Studies

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2021

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tom 35(35)

166-178

EN

It still remains an open problem as to which directions and methods are necessary to choose in the situations of risk, xenophobia, and intolerance, so as to settle disputes and resolve conflicts; it should be done in such a way as to have the desired social effects and to properly implement moral principles, including responsibility for the real future of one’s own, of one’s community, and of the whole human species. The author justifies the position that the processes of transformation of the social order should take a more remarkable account of the requirements of safety culture and praxeology recommendations.

5

Choosing what to protect when attacker resources and asset valuations are uncertain

63%

HAUSKEN K.

Operations Research and Decisions

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2014

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tom 24

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nr 3

23-44

EN

The situation has been modelled where the attacker’s resources are unknown to the defender. Protecting assets presupposes that the defender has some information on the attacker’s resource capabilities. An attacker targets one of two assets. The attacker’s resources and valuations of these assets are drawn probabilistically. We specify when the isoutility curves are upward sloping (the defender prefers to invest less in defense, thus leading to higher probabilities of success for attacks on both assets) or downward sloping (e.g. when one asset has a low value or high unit defense cost). This stands in contrast to earlier research and results from the uncertainty regarding the level of the attacker’s resources. We determine which asset the attacker targets depending on his type, unit attack costs, the contest intensity, and investment in defense. A two stage game is considered, where the defender moves first and the attacker moves second. When both assets are equivalent and are treated equivalently by both players, an interior equilibrium exists when the contest intensity is low, and a corner equilibrium with no defense exists when the contest intensity is large and the attacker holds large resources. Defense efforts are inverse U shaped in the attacker’s resources.

6

Choosing what to protect when attacker resources and asset valuations are uncertain

44%

Hausken K.

Operations Research and Decisions

|

2014

|

tom Vol. 24, No. 3

23--44

EN

The situation has been modelled where the attacker’s resources are unknown to the defender. Protecting assets presupposes that the defender has some information on the attacker’s resource capabilities. An attacker targets one of two assets. The attacker’s resources and valuations of these assets are drawn probabilistically. We specify when the isoutility curves are upward sloping (the defender prefers to invest less in defense, thus leading to higher probabilities of success for attacks on both assets) or downward sloping (e.g. when one asset has a low value or high unit defense cost). This stands in contrast to earlier research and results from the uncertainty regarding the level of the attacker’s resources. We determine which asset the attacker targets depending on his type, unit attack costs, the contest intensity, and investment in defense. A two stage game is considered, where the defender moves first and the attacker moves second. When both assets are equivalent and are treated equivalently by both players, an interior equilibrium exists when the contest intensity is low, and a corner equilibrium with no defense exists when the contest intensity is large and the attacker holds large resources. Defense efforts are inverse U shaped in the attacker’s resources.