The universal theory of the free pseudo-Boolean algebra 𝐹_{𝜔}(𝐻) in the signature extended by constants for free generators

1992 ◽  
pp. 645-656
Author(s):  
V. V. Rybakov
Keyword(s):  
Boolean Algebra ◽  
Universal Theory ◽  
Free Generators

scholarly journals De Morgan Functions and Free De Morgan Algebras

2014 ◽  
Vol 47 (2) ◽  
Author(s):  
Yu. M. Movsisyan ◽  
V. A. Aslanyan ◽  
Alex Manoogian
Keyword(s):  
Boolean Algebra ◽  
Distributive Lattice ◽  
Boolean Functions ◽  
Bounded Lattice ◽  
De Morgan Algebra ◽  
Bounded Distributive Lattice ◽  
Monotone Boolean Functions ◽  
Free Generators ◽  
De Morgan Algebras

AbstractIt is commonly known that the free Boolean algebra on n free generators is isomorphic to the Boolean algebra of Boolean functions of n variables. The free bounded distributive lattice on n free generators is isomorphic to the bounded lattice of monotone Boolean functions of n variables. In this paper, we introduce the concept of De Morgan function and prove that the free De Morgan algebra on n free generators is isomorphic to the De Morgan algebra of De Morgan functions of n variables. This is a solution of the problem suggested by B. I. Plotkin.

Hierarchies of Boolean algebras

1970 ◽  
Vol 35 (3) ◽  
pp. 365-374 ◽  
Author(s):  
Lawrence Feiner
Keyword(s):  
Number Theory ◽  
Standard Model ◽  
Boolean Algebra ◽  
Boolean Algebras ◽  
Natural Numbers ◽  
Recursive Structure ◽  
The Standard Model ◽  
Free Generators ◽  
Basic Facts

A denumerable structure is said to be recursive iff its universe is a recursive subset of the natural numbers and its relations and operations are recursive. For example, the standard model of number theory is recursive. A structure is said to be recursively presentable iff it is isomorphic to a recursive structure. For example, a Boolean algebra generated by ℵ0 free generators is easily seen to be recursively presentable. (For basic facts concerning Boolean algebras, the reader is referred to R. Sikorski [9] and A. Tarski and A. Mostowski [10].)

Synthesis of Antennas on the Base of the Boolean Algebra Transformations and the Atomic Functions Theory

2005 ◽  
Vol 64 (9) ◽  
pp. 699-712
Author(s):  
Victor Filippovich Kravchenko ◽  
Miklhail Alekseevich Basarab
Keyword(s):  
Boolean Algebra

Synergetic Theory of Document in Evolution of Document Science

2018 ◽  
pp. 1060-1068
Author(s):  
Galina A. Dvoenosova ◽  
Keyword(s):  
Social Role ◽  
Scientific Study ◽  
Self Organization ◽  
Universal Theory ◽  
Social Self ◽  
Social Goal ◽  
The Social ◽  
Synergetic Theory ◽  
First Time

The article assesses synergetic theory of document as a new development in document science. In information society the social role of document grows, as information involves all members of society in the process of documentation. The transformation of document under the influence of modern information technologies increases its interest to representatives of different sciences. Interdisciplinary nature of document as an object of research leads to an ambiguous interpretation of its nature and social role. The article expresses and contends the author's views on this issue. In her opinion, social role of document is incidental to its being a main social tool regulating the life of civilized society. Thus, the study aims to create a scientific theory of document, explaining its nature and social role as a tool of social (goal-oriented) action and social self-organization. Substantiation of this idea is based on application of synergetics (i.e., universal theory of self-organization) to scientific study of document. In the synergetic paradigm, social and historical development is seen as the change of phases of chaos and order, and document is considered a main tool that regulates social relations. Unlike other theories of document, synergetic theory studies document not as a carrier and means of information transfer, but as a unique social phenomenon and universal social tool. For the first time, the study of document steps out of traditional frameworks of office, archive, and library. The document is placed on the scales with society as a global social system with its functional subsystems of politics, economy, culture, and personality. For the first time, the methods of social sciences and modern sociological theories are applied to scientific study of document. This methodology provided a basis for theoretical vindication of nature and social role of document as a tool of social (goal-oriented) action and social self-organization. The study frames a synergetic theory of document with methodological foundations and basic concepts, synergetic model of document, laws of development and effectiveness of document in the social continuum. At the present stage of development of science, it can be considered the highest form of theoretical knowledge of document and its scientific explanatory theory.

An Outline of a Theory of Propositional Vagueness

2018 ◽  
Author(s):  
Andrew Bacon
Keyword(s):  
Boolean Algebra ◽  
Total Evidence ◽  
Coarse Grained ◽  
Atomic Boolean Algebra

This chapter presents a series questions in the philosophy of vagueness that will constitute the primary subjects of this book. The stance this book takes on these questions is outlined, and some preliminary ramifications are explored. These include the idea that (i) propositional vagueness is more fundamental than linguistic vagueness; (ii) propositions are not themselves sentence-like; they are coarse grained, and form a complete atomic Boolean algebra; (iii) vague propositions are, moreover, not simply linguistic constructions either such as sets of world-precisification pairs; and (iv) propositional vagueness is to be understood by its role in thought. Specific theses relating to the last idea include the thesis that one’s total evidence can be vague, and that there are vague propositions occupying every evidential role, that disagreements about the vague ultimately boil down to disagreements in the precise, and that one should not care intrinsically about vague matters.

scholarly journals Assessing the Risk of Democratic Reversal in the United States: A Reply to Kurt Weyland

2021 ◽  
pp. 1-6
Author(s):  
Matias López ◽  
Juan Pablo Luna
Keyword(s):  
United States ◽  
Comparative Analysis ◽  
Boolean Algebra ◽  
Qualitative Comparative Analysis ◽  
The United States ◽  
American Democracy ◽  
Institutional Dynamics ◽  
The Public ◽  
Original Analysis ◽  
The Impact

ABSTRACT By replying to Kurt Weyland’s (2020) comparative study of populism, we revisit optimistic perspectives on the health of American democracy in light of existing evidence. Relying on a set-theoretical approach, Weyland concludes that populists succeed in subverting democracy only when institutional weakness and conjunctural misfortune are observed jointly in a polity, thereby conferring on the United States immunity to democratic reversal. We challenge this conclusion on two grounds. First, we argue that the focus on institutional dynamics neglects the impact of the structural conditions in which institutions are embedded, such as inequality, racial cleavages, and changing political attitudes among the public. Second, we claim that endogeneity, coding errors, and the (mis)use of Boolean algebra raise questions about the accuracy of the analysis and its conclusions. Although we are skeptical of crisp-set Qualitative Comparative Analysis as an adequate modeling choice, we replicate the original analysis and find that the paths toward democratic backsliding and continuity are both potentially compatible with the United States.

scholarly journals Rough Approximation Operators on a Complete Orthomodular Lattice

Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 164
Author(s):  
Songsong Dai
Keyword(s):  
Boolean Algebra ◽  
Orthomodular Lattice ◽  
Orthomodular Lattices ◽  
Approximation Operators ◽  
Rough Approximation ◽  
Distributive Law ◽  
Complete Orthomodular Lattice ◽  
The Relationship

This paper studies rough approximation via join and meet on a complete orthomodular lattice. Different from Boolean algebra, the distributive law of join over meet does not hold in orthomodular lattices. Some properties of rough approximation rely on the distributive law. Furthermore, we study the relationship among the distributive law, rough approximation and orthomodular lattice-valued relation.

scholarly journals Congruence pairs of principal MS-algebras and perfect extensions

2020 ◽  
Vol 70 (6) ◽  
pp. 1275-1288
Author(s):  
Abd El-Mohsen Badawy ◽  
Miroslav Haviar ◽  
Miroslav Ploščica
Keyword(s):  
Boolean Algebra ◽  
Congruence Lattices ◽  
Descriptive Solution ◽  
The One ◽  
Special Case ◽  
Congruence Pair

AbstractThe notion of a congruence pair for principal MS-algebras, simpler than the one given by Beazer for K2-algebras [6], is introduced. It is proved that the congruences of the principal MS-algebras L correspond to the MS-congruence pairs on simpler substructures L°° and D(L) of L that were associated to L in [4].An analogy of a well-known Grätzer’s problem [11: Problem 57] formulated for distributive p-algebras, which asks for a characterization of the congruence lattices in terms of the congruence pairs, is presented here for the principal MS-algebras (Problem 1). Unlike a recent solution to such a problem for the principal p-algebras in [2], it is demonstrated here on the class of principal MS-algebras, that a possible solution to the problem, though not very descriptive, can be simple and elegant.As a step to a more descriptive solution of Problem 1, a special case is then considered when a principal MS-algebra L is a perfect extension of its greatest Stone subalgebra LS. It is shown that this is exactly when de Morgan subalgebra L°° of L is a perfect extension of the Boolean algebra B(L). Two examples illustrating when this special case happens and when it does not are presented.

Programs as term transformers

1980 ◽  
Vol 3 (4) ◽  
pp. 419-431
Author(s):  
Stefan Sokołowski
Keyword(s):  
Boolean Algebra ◽  
Mathematical Study ◽  
Partial Correctness

Predicates describing the states of computation may be regarded as functions into the Boolean algebra {false, true} and programs as transformers of those functions. If we do not restrict ourselves to this algebra, we get instead terms describing the states of computation and programs transforming the terms. In many cases this approach turns out to be more natural. This paper is a mathematical study of partial correctness and termination of programs in the language of term transformations.

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