Personal Structures: I. a Basis for Personal Structures

1963 ◽  
Vol 13 (1) ◽  
pp. 3-17 ◽  
Author(s):  
Maynard W. Shelly
Keyword(s):  
Boolean Algebras ◽  
The Real ◽  
Boolean Rings ◽  
Further Development ◽  
Psychological Experiments

Personal structures were defined as structures pairing judgments and sets of environmental states. It was shown how either the judgments or environmental sets of these structures could be treated both as Boolean algebras and as Boolean rings. It was shown that a basis for the personal structures always existed, and this basis made it possible uniquely to construct the remainder of the personal structure. Some discussion was presented concerning the usefulness of the concepts of personal structure and a basis for a personal structure. These discussions were, however, very preliminary, and the real usefulness of this approach rests upon developments in future papers, in particular the further development of the concept of uncertain judgment. It may be that this concept of an uncertain judgment will have to “absorb” much of the variability usually found in psychological experiments. In this connection it is to be noted that we have thus far not limited the concept of judgment to a single instant in time, nor even to a continuous interval in time, thus permitting the concept of uncertain judgment to include as factors, judgments made over a series of trials.

Hybrid argumentation systems for structured news reports

2001 ◽  
Vol 16 (4) ◽  
pp. 295-329 ◽  
Author(s):  
ANTHONY HUNTER
Keyword(s):  
Knowledge Management ◽  
Decision Support ◽  
Hybrid Systems ◽  
Real World ◽  
Hybrid Approach ◽  
Graphical Notation ◽  
The Real ◽  
News Reports ◽  
Further Development ◽  
Argumentation Systems

Numerous argumentation systems have been proposed in the literature. Yet there often appears to be a shortfall between proposed systems and possible applications. In other words, there seems to be a need for further development of proposals for argumentation systems before they can be used widely in decision-support or knowledge management. I believe that this shortfall can be bridged by taking a hybrid approach. Whilst formal foundations are vital, systems that incorporate some of the practical ideas found in some of the informal approaches may make the resulting hybrid systems more useful. In informal approaches, there is often an emphasis on using graphical notation with symbols that relate more closely to the real-world concepts to be modelled. There may also be the incorporation of an argument ontology oriented to the user domain. Furthermore, in informal approaches there can be greater consideration of how users interact with the models, such as allowing users to edit arguments and to weight influences on graphs representing arguments. In this paper, I discuss some of the features of argumentation, review some key formal argumentation systems, identify some of the strengths and weaknesses of these formal proposals and finally consider some ways to develop formal proposals to give hybrid argumentation systems. To focus my discussions, I will consider some applications, in particular an application in analysing structured news reports.

Yap Hian Poh. Postulational study of an axiom system of Boolean algebra. Majallah Tahunan 'Ilmu Pasti—Shu Hsüeh Nien K'an—Bulletin of Mathematical Society of Nanyang University (1960), pp. 94–110. - R. M. Dicker. A set of independent axioms for Boolean algebra. Proceedings of the London Mathematical Society, ser. 3 vol. 13 (1963), pp. 20–30. - P. J. van Albada. A self-dual system of axioms for Boolean algebra. Koninklijke Nederlandse Akademie van Wetenschappen, Proceedings, series A vol. 67 (1964), pp. 377–381; also Indagationes mathematicae, vol. 26 (1964), pp. 377–381. - Antonio Diego and Alberto Suárez. Two sets of axioms for Boolean algebras. Portugaliae mathematica, vol. 23 nos. 3–4 (for 1964, pub. 1965), pp. 139–145. (Reprinted from Notas de lógica matemática no. 16, Instituto de Matemática, Universidad Nacional del Sur, Bahía Blanca 1964, 13 pp.) - P. J. van Albada. Axiomatique des algèbres de Boole. Bulletin de la Société Mathématique de Belgique, vol. 18 (1966), pp. 260–272. - Lawrence J. Dickson. A short axiomatic system for Boolean algebra. Pi Mu Epsilon journal, vol. 4 no. 6 (1967), pp. 253–257. - Leroy J. Dickey. A shorter axiomatic system for Boolean algebra. Pi Mu Epsilon journal, vol. 4 no. 8 (1968), p. 336. - Chinthayamma . Independent postulate sets for Boolean algebra. Pi Mu Epsilon journal, vol. 4 no. 9 (1968), pp. 378–379. - Kiyoshi Iséki. A simple characterization of Boolean rings. Proceedings of the Japan Academy, vol. 44 (1968), pp. 923–924. - Sakiko Ôhashi. On definitions of Boolean rings and distributive lattices. Proceedings of the Japan Academy, vol. 44 (1968), pp. 1015–1017.

1973 ◽  
Vol 38 (4) ◽  
pp. 658-660
Author(s):  
Donald H. Potts
Keyword(s):  
Boolean Algebra ◽  
London Mathematical Society ◽  
Axiom System ◽  
Dual System ◽  
Boolean Algebras ◽  
Axiomatic System ◽  
Mathematical Society ◽  
Distributive Lattices ◽  
Boolean Rings

scholarly journals On Infinite Series of Sets

1954 ◽  
Vol 2 (2) ◽  
pp. 89-92
Author(s):  
David Ellis
Keyword(s):  
Infinite Series ◽  
Boolean Algebras ◽  
Real Field ◽  
The Real ◽  
Convergence Of Series

We continue our studies (2, 3, 4, 5) of the algebraic, geometric, and analytical similarities and contrasts between Boolean algebras and the real field. In this note we contrast the convergence of series in set algebras with that in the real field.

scholarly journals GEOLOGICAL AND ECONOMIC ASSESMENT OF THE PERSPECTIVE OF THE MINING IN LJUBIJA ORE REGION

2018 ◽  
Vol 1 (18) ◽  
Author(s):  
Ranko Cvijić ◽  
Aleksej Milošević ◽  
Miodrag Čelebić ◽  
Žarko Kovačević
Keyword(s):  
Production Process ◽  
Iron Ore ◽  
Potential Space ◽  
Geological Exploration ◽  
Exploration And Exploitation ◽  
The Real ◽  
Commercial Viability ◽  
The City ◽  
Further Development

The iron ore of the Ljubija ore region for decades has a very great impact on the overall socialreproduction in the area of the city of Prijedor, RS, BiH, which is clearly connected with theconstant renewal and intensification of the production process. We have systematic geologicalexplorations last over 135 years and exploitation with certain interruptions over 100 years.Existing resources/reserves should be optimally activated in order to achieve the commercial viability ofinvestment funds invested in them, but also those that have yet to be invested, and a certain expectednational benefit, and at the same time an intensive geological exploration of the potential space forfinding new reserves in terms of iron ore base.The paper attempts to assess the real justification of further geological exploration and exploitation inthis area and the strategy for further development of iron ore mining.

A Generalization of Certain Rings of A. L. Foster

1963 ◽  
Vol 6 (1) ◽  
pp. 55-60 ◽  
Author(s):  
Adil Yaqub
Keyword(s):  
Boolean Algebra ◽  
Boolean Algebras ◽  
Boolean Ring ◽  
Boolean Rings ◽  
Image Position

The concept of a Boolean ring, as a ring A in which every element is idempotent (i. e., a2 = a for all a in A), was first introduced by Stone [4]. Boolean algebras and Boolean rings, though historically and conceptually different, were shown by Stone to be equationally interdefinable. Indeed, let (A, +, x) be a Boolean ring with unit 1, and let (A, ∪, ∩, ') be a Boolean algebra, where ∩, ∪, ', denote "union", " intersection", and "complement". The equations which convert the Boolean ring into a Boolean algebra are:IConversely, the equations which convert the Boolean algebra into a Boolean ring are:II

scholarly journals Applying Neuroscience to Emergent Processes in Teams

2020 ◽  
pp. 109442812091551
Author(s):  
Danni Wang ◽  
David A. Waldman ◽  
Pierre A. Balthazard ◽  
Maja Stikic ◽  
Nicola M. Pless ◽  
...  
Keyword(s):  
Problem Solving ◽  
Real Time ◽  
Team Dynamics ◽  
Team Members ◽  
The Real ◽  
Research Questions ◽  
Quantitative Electroencephalogram ◽  
Further Development ◽  
Problem Solving Task ◽  
Over Time

In this article, we describe how neuroscience can be used in the study of team dynamics. Specifically, we point out methodological limitations in current team-based research and explain how quantitative electroencephalogram technology can be applied to the study of emergent processes in teams. In so doing, we describe how this technology and related analyses can explain emergent processes in teams through an example of the neural assessment of attention of team members who are engaged in a problem-solving task. Specifically, we demonstrate how the real-time, continuous neural signatures of team members’ attention in a problem-solving context emerges in teams over time. We then consider how further development of this technology might advance our understanding of the emergence of other team-based constructs and research questions.

On the Vitali–Hahn–Saks theorem

1981 ◽  
Vol 90 (1-2) ◽  
pp. 163-173 ◽  
Author(s):  
Aníbal Moltó
Keyword(s):  
Type Theorem ◽  
Boolean Algebras ◽  
Topological Spaces ◽  
Boolean Rings ◽  
Set Functions ◽  
Grothendieck Space

SynopsisIn this paper, a class of Boolean rings containing the class discussed in papers by Seever (1968) and Faires (1976), is defined in such a way that an extension of the classical Vitali–Hahn–Saks theorem holds for exhausting additive set functions. Some new compact topological spaces K for which C(K) is a Grothendieck space are constructed and a Nikodym type theorem is deduced from it. The Boolean algebras of Seever and Faires and those we study here are defined by ‘interpolation properties’ between disjoint sequences in the algebra. We give an example at the end of the paper that illustrates the difficulties arising when we try to find a larger class of Boolean algebras, defined in terms of such properties, for which the Vitali–Hanh–Saks theorem holds.

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