scholarly journals An Investigation on the Logical Structure of Mathematics (VI): Consistent V-System T(V) (With Corrections to Part (XII))

1959 ◽  
Vol 14 ◽  
pp. 95-107
Author(s):  
Sigekatu Kuroda
Keyword(s):  
Logical Structure ◽  
Consistency Proof ◽  
Truth Values ◽  
Definition Of

The V-system T(V) is defined in §2 by using §1, and its consistency is proved in §3. The definition of T(V) is given in such a way that the consistency proof of T(V) in §3 shows a typical way to prove the consistency of some subsystems of UL. Otherwise we could define T(V) more simply by using truth values. After T(V)-sets are treated in §4, it is proved in §5 as a T(V)-theorem that T(V)-sets are all equal to V.

La trattazione vetero-stoica dell’ira: componenti logiche e caratteri fisiologici

Elenchos ◽  
2018 ◽  
Vol 39 (2) ◽  
pp. 323-347
Author(s):  
Francesca Alesse
Keyword(s):  
Logical Structure ◽  
Human Soul ◽  
Definition Of

Abstract The paper compares the two components of the Stoic definition of pathos, the logico-linguistic component and the physiological, ‘pneumatic’ one, in order to examine the role that each of them plays in the onset of pathos, its persistence in the human soul, its possible eradication. The analysis is focused on anger (ὀργή) which reveals some peculiarities, especially as regards its logical structure, due to the fact that this passion seems to be the combination of two different feelings. The anger indeed is classified as a species of desire but the description of its onset also includes pain.

scholarly journals Architecture of Component-based Information Systems over the J2EE Platform

2018 ◽  
Vol 8 (1) ◽  
Author(s):  
Daniel Perovich ◽  
Leonardo Rodrıguez Rodrıguez ◽  
Andres Vignaga
Keyword(s):  
Information Systems ◽  
Methodological Approach ◽  
Logical Structure ◽  
The Other ◽  
Model Driven ◽  
J2ee Platform ◽  
Component Based Development ◽  
Abstract Level ◽  
Definition Of ◽  
Different Levels

Component-based development can be addressed from two different fronts, or more precisely, from two different levels. One of them regards the technology used for system implementation, and the other is a previous and more abstract level, where the focus is set to the logical structure of the solution and where technological issues are not considered. Model Driven Architecture promotes such separation by distinguishing platform independent models from platform specific models. In alignment with this approach, this article proposes a mapping from the tiered and platform independent architecture for information systems resulting from the application of a widely known methodological approach, to the available constructs in the J2EE platform. This mapping allows the definition of transformations between platform independent models, resulting from the referred methodology where it is possible to abstractly reason about the solution, and platform specific models which are aligned with technological constructs and are directly implemented.

The cylindric algebras of three-valued logic

1998 ◽  
Vol 63 (4) ◽  
pp. 1201-1217
Author(s):  
Norman Feldman
Keyword(s):  
Effective Procedure ◽  
Cylindric Algebras ◽  
Truth Values ◽  
Recursive Functions ◽  
Partial Recursive Functions ◽  
Truth Value ◽  
The One ◽  
Definition Of

In this paper we consider the three-valued logic used by Kleene [6] in the theory of partial recursive functions. This logic has three truth values: true (T), false (F), and undefined (U). One interpretation of U is as follows: Suppose we have two partially recursive predicates P(x) and Q(x) and we want to know the truth value of P(x) ∧ Q(x) for a particular x0. If x0 is in the domain of definition of both P and Q, then P(x0) ∧ Q(x0) is true if both P(x0) and Q(x0) are true, and false otherwise. But what if x0 is not in the domain of definition of P, but is in the domain of definition of Q? There are several choices, but the one chosen by Kleene is that if Q(X0) is false, then P(x0) ∧ Q(x0) is also false and if Q(X0) is true, then P(x0) ∧ Q(X0) is undefined.What arises is the question about knowledge of whether or not x0 is in the domain of definition of P. Is there an effective procedure to determine this? If not, then we can interpret U as being unknown. If there is an effective procedure, then our decision for the truth value for P(x) ∧ Q(x) is based on the knowledge that is not in the domain of definition of P. In this case, U can be interpreted as undefined. In either case, we base our truth value of P(x) ∧ Q(x) on the truth value of Q(X0).

Forcing for the impredicative theory of classes

1972 ◽  
Vol 37 (1) ◽  
pp. 1-18 ◽  
Author(s):  
Rolando Chuaqui
Keyword(s):  
General Theory ◽  
Set Theory ◽  
Continuum Hypothesis ◽  
Reflection Principle ◽  
Inaccessible Cardinal ◽  
Consistency Proof ◽  
Suitable Form ◽  
Definition Of ◽  
Class Construction ◽  
The Continuum

The purpose of this work is to formulate a general theory of forcing with classes and to solve some of the consistency and independence problems for the impredicative theory of classes, that is, the set theory that uses the full schema of class construction, including formulas with quantification over proper classes. This theory is in principle due to A. Morse [9]. The version I am using is based on axioms by A. Tarski and is essentially the same as that presented in [6, pp. 250–281] and [10, pp. 2–11]. For a detailed exposition the reader is referred there. This theory will be referred to as .The reflection principle (see [8]), valid for other forms of set theory, is not provable in . Some form of the reflection principle is essential for the proofs in the original version of forcing introduced by Cohen [2] and the version introduced by Mostowski [10]. The same seems to be true for the Boolean valued models methods due to Scott and Solovay [12]. The only suitable form of forcing for found in the literature is the version that appears in Shoenfield [14]. I believe Vopěnka's methods [15] would also be applicable. The definition of forcing given in the present paper is basically derived from Shoenfield's definition. Shoenfield, however, worked in Zermelo-Fraenkel set theory.I do not know of any proof of the consistency of the continuum hypothesis with assuming only that is consistent. However, if one assumes the existence of an inaccessible cardinal, it is easy to extend Gödel's consistency proof [4] of the axiom of constructibility to .

scholarly journals Aristotle and Diodorus Cronus: Principle of bivalence and principle of plenitude

2010 ◽  
Vol 53 (1) ◽  
pp. 109-123
Author(s):  
Drago Djuric
Keyword(s):  
The Other ◽  
Future Event ◽  
Master Argument ◽  
Truth Values ◽  
The Future ◽  
De Interpretatione ◽  
Valid Principle ◽  
Definition Of

Aristotle in De Interpretatione 9 considers the use of predicates in combination with subjects which are forming propositions, each of which is necessarily either true or false. This necessity was later named as Principle of bivalence (of truth values). Although he grants the truth or falsity of propositions about past and present events, propositions about the future seem problematic. If a proposition about tomorrow is true (or false) today, then the future event it describes will happen (or not happen) necessary. It leads to (logical) determinism. Aristotle attempts to avoid it. His solution was to maintain that the disjunction is necessarily true today even though neither of its disjuncts is. Thus, it is necessary that either tomorrow's event will occur or it will not, but it is neither necessary that it will occur nor necessary that it will not occur. Because of fact that according to Aristotle Principle of bivalence is not valid for a propositions about future, for him is not valid Principle of plenitude also. On the other side, according to his Master argument and his definitions of modalities for Diodorus Cronus possible is something what is or will be. In opposition to Aristotle, for him does not exists any non-actualized possibility. In some sense Diodorus implicit respects Principle of bivalence. It is compatible with the Principle of plenitude which is also respected from Diodorus Cronus. Aristotle attempts to save difference between modal categories (necessity and possibility), and trys to reject logical determinism. According to his definition of possibility in Diodorus Cronus conception this difference collapses in to determinism.

scholarly journals ADVERTISING AS AN ELEMENT OF CLIP CULTURE OF INFORMATION SOCIETY

2019 ◽  
pp. 28-30
Author(s):  
V.V. Kuzmin ◽  
Yu. S. Obidina
Keyword(s):  
Information Society ◽  
Modern Society ◽  
Logical Structure ◽  
Imaginative Thinking ◽  
Definition Of ◽  
The Impact

The article discusses the modern phenomenon of the information society - clip culture. Aim - to analyze the impact of advertising on modern society as an element of clip culture. The approaches to the definition of the “clip-like” phenomenon in foreign and domestic studies are identified. The genesis of clip culture in the context of the development of audiovisual advertising is considered. It is concluded that advertising in clip culture directly contributes to the decomposition of the linear logical structure of society, forming a new kind of person with fragmented, emotionally-imaginative thinking - Homo Figuralis (from the Latin. "Shaped man").

A relative consistency proof

1954 ◽  
Vol 19 (1) ◽  
pp. 21-28 ◽  
Author(s):  
Joseph R. Shoenfield
Keyword(s):  
Set Theory ◽  
Functional Calculus ◽  
Direct Method ◽  
Axiom System ◽  
Similar Process ◽  
Consistency Proof ◽  
First Order ◽  
Definition Of ◽  
A Direct Method ◽  
Exact Definition

LetCbe an axiom system formalized within the first order functional calculus, and letC′ be related toCas the Bernays-Gödel set theory is related to the Zermelo-Fraenkel set theory. (An exact definition ofC′ will be given later.) Ilse Novak [5] and Mostowski [8] have shown that, ifCis consistent, thenC′ is consistent. (The converse is obvious.) Mostowski has also proved the stronger result that any theorem ofC′ which can be formalized inCis a theorem ofC.The proofs of Novak and Mostowski do not provide a direct method for obtaining a contradiction inCfrom a contradiction inC′. We could, of course, obtain such a contradiction by proving the theorems ofCone by one; the above result assures us that we must eventually obtain a contradiction. A similar process is necessary to obtain the proof of a theorem inCfrom its proof inC′. The purpose of this paper is to give a new proof of these theorems which provides a direct method of obtaining the desired contradiction or proof.The advantage of the proof may be stated more specifically by arithmetizing the syntax ofCandC′.

scholarly journals Building a Metaframework for Sustainable Transport Indicators

2015 ◽  
Vol 2531 (1) ◽  
pp. 103-112 ◽  
Author(s):  
Yannick Cornet ◽  
Henrik Gudmundsson
Keyword(s):  
Performance Measures ◽  
Logical Structure ◽  
Sustainable Transportation ◽  
Sustainable Transport ◽  
And Performance ◽  
Definition Of ◽  
Transportation Research ◽  
Brundtland Report ◽  
Indicator Frameworks ◽  
Selection Of

Several recent papers presented at the annual meeting of the Transportation Research Board, Washington, D.C., and elsewhere have reported on efforts to make sustainability manageable. To this end, the papers suggested the use of indicators and performance measures to help conceptualize and operationalize sustainability for transportation-related planning and decision making. Often these studies presented frameworks that would allow sustainability indicators and measures to be included in, for example, agency strategies and practices. Moreover, some papers suggested criteria for the selection of individual indicators and performance measures. The studies, however, did not always agree on the definition of a framework or how to use one to make sustainability-based decisions, and they tended to differ on underscored aspects and concerns. The current study addressed the issue of frameworks more generically and explored what was termed a “metaframework” with a set of associated criteria to guide the framing of indicators for sustainable transportation. On the basis of an explicit framework theory, the three functions of conceptualization, operationalization, and utilization were found to provide a logical structure of complementary features with which to build indicator frameworks. Characteristics of robust indicator frameworks were evaluated in terms of their significance for the three key functions, and they were collected in a list of criteria. A review of the Brundtland Report provided an example of how a more finely grained understanding of sustainability can inform the conceptualization criterion ranking of sustainability impacts. The metaframework was intended primarily as a basis for empirical analysis and for meta-evaluation of existing practice frameworks with respect to the strength of the level of sustainability that they are likely to provide.

scholarly journals CULTURE OF EVERYDAY LIFE: TO THE PROBLEM OF LOGIC OF STRUCTURE AND CONTENT OF THE EDUCATIONAL DISCIPLINE. PART I

2021 ◽  
pp. 15-19
Author(s):  
V. G. Napadysta
Keyword(s):  
Everyday Life ◽  
Social Groups ◽  
Logical Structure ◽  
Subject Field ◽  
Scientific Training ◽  
The Everyday ◽  
Wide Variability ◽  
The Subject ◽  
Definition Of ◽  
Life Phenomenon

The article discusses the logic of structuring and content of the discipline "Culture of Everyday Life", due to the complexity and versatility of the phenomenon of everyday life and interdisciplinarity of methodological optics of its research, the variety of theoretical tools, which, in turn, determines the ambiguity of views on the very essence of the phenomenon of everyday life and its components. The analysis of educational programs on "Culture of Everyday Life", that are among the elements of educational-professional and educational-scientific training programs on "Culturology" in higher education institutions in Ukraine, demonstrated the wide variability of their content and structure. The first part of the article substantiates the need to discuss among stakeholders the boundaries and basic elements of the subject field of the discipline, which would determine its specifics and features when considering the phenomenon of everyday life. A certain model of the logical structure of the "Culture of Everyday Life" as a discipline is proposed, the main elements of its structure and their content are considered. The main stages and thematic directions of historiography of the phenomenon of everyday life in accordance with the scientific specializations of researchers are analyzed. The main achievements in the study of the everyday life phenomenon, initiated by experts of life of certain social groups representing different cultural and historical epochs, as well as the work of historians, philosophers, sociologists, carried out during the XXth century, are considered. The most common definitions of the phenomenon of everyday life, which operate in different segments of modern socio-humanitarian knowledge are analyzed, to understand the situation in modern "everyday science" in terms of systematization / structuring of accumulated knowledge about the phenomenon of everyday life, defining the boundaries of everyday life and its opposing worlds, which more clearly outline the contours of everyday life and thus contribute to the definition of the thematic field of the discipline "Culture of Everyday Life".

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