On formulas in which no individual variable occurs more than twice

1966 ◽  
Vol 31 (1) ◽  
pp. 1-6 ◽  
Author(s):  
Stanisław Jaśkowski
Keyword(s):  
Sentential Calculus ◽  
Individual Variable ◽  
Individual Variables

In Jaśkowski [1], some properties of the consequences of formulas of the sentential calculus with no more than two occurrences of any variable have been settled. Analogous problems may be raised concerning the consequences of equalities in which the same restriction relates to individual variables. In the present paper, problems of this kind are solved and more general theorems are proved about the logical consequences of some formulas, called here multiconditionals.

On the definition of ‘formal deduction’

1956 ◽  
Vol 21 (2) ◽  
pp. 129-136 ◽  
Author(s):  
Richard Montague ◽  
Leon Henkin
Keyword(s):  
Functional Calculus ◽  
Modus Ponens ◽  
Formal Proof ◽  
Axiom Schema ◽  
First Order ◽  
Individual Variable ◽  
Individual Variables ◽  
Definition Of ◽  
Formal Rules

The following remarks apply to many functional calculi, each of which can be variously axiomatized, but for clarity of exposition we shall confine our attention to one particular system Σ. This system is to have the usual primitive symbols and formation rules of the pure first-order functional calculus, and the following formal axiom schemata and formal rules of inference.Axiom schema 1. Any tautologous wff (well-formed formula).Axiom schema 2. (a) A ⊃ B, where A is any wff, a and b are any individual variables, and B arises from A by replacing all free occurrences of a by free occurrences of b.Axiom schema 3. (a)(A ⊃ B)⊃(A⊃ (a)B). where A and B are any wffs, and a is any individual variable not free in A.Rule of Modus Ponens: applies to wffs A and A ⊃ B, and yields B.Rule of Generalization: applies to a wff A and yields (a)A, where a is any individual variable.A formal proof in Σ is a finite column of wffs each of whose lines is a formal axiom or arises from two preceding lines by the Rule of Modus Ponens or arises from a single preceding line by the Rule of Generalization. A formal theorem of Σ is a wff which occurs as the last line of some formal proof.

A theory of restricted quantification I

1957 ◽  
Vol 22 (1) ◽  
pp. 19-35 ◽  
Author(s):  
Theodore Hailperin
Keyword(s):  
Recursive Function ◽  
Function Theory ◽  
Predicate Calculus ◽  
Individual Variable ◽  
Restricted Quantification ◽  
Explicit Mention ◽  
The Common ◽  
Individual Variables ◽  
And Mathematics ◽  
Common Device

The notion of a variable restricted in range to some set of values, or to values having some property, is widespread in logic and mathematics. To avoid continual explicit mention of such a restriction the common device is to resort to a typographically different set of letters for such variables. But a notation of this kind is clearly inadequate when a general discussion, including more than one kind of restriction, is under consideration. For example, two restrictions may have some inner connection, as in the case of mutually exclusive restrictions, and this the usual symbolism doesn't depict; or, one may wish to study the dependence of such restrictions upon one or more parameters as in the case of bounded quantifiers of recursive function theory; or, one can even conceive of restrictions which may in turn depend upon restricted variables. In each of these cases the currently used notation is deficient.If x is an individual-variable and Q a formula of the predicate calculus, then for the idea ‘x such that Q’ the notation ‘vxQ’ is proposed as one having the requisite degree of notational multiplicity – the ‘vx’ acting as a binding operator for free occurrences of x in Q. The expression ‘vxQ’ is referred to as a restricted-variable and it may occupy positions in formulas appropriate to individual-variables, in argument places as well as in quantifiers. In § 2 a first-level predicate calculus, called ‘‘, is presented in which the restricted-variable is an integral part.

Development of a German-Language Questionnaire to Measure Collective Orientation as an Individual Attitude

2017 ◽  
Vol 76 (3) ◽  
pp. 91-105 ◽  
Author(s):  
Vera Hagemann
Keyword(s):  
Team Performance ◽  
Reliability And Validity ◽  
Future Research ◽  
German Language ◽  
Team Members ◽  
Collective Orientation ◽  
Team Research ◽  
German Speaking ◽  
Individual Variables ◽  
The Individual

Abstract. The individual attitudes of every single team member are important for team performance. Studies show that each team member’s collective orientation – that is, propensity to work in a collective manner in team settings – enhances the team’s interdependent teamwork. In the German-speaking countries, there was previously no instrument to measure collective orientation. So, I developed and validated a German-language instrument to measure collective orientation. In three studies (N = 1028), I tested the validity of the instrument in terms of its internal structure and relationships with other variables. The results confirm the reliability and validity of the instrument. The instrument also predicts team performance in terms of interdependent teamwork. I discuss differences in established individual variables in team research and the role of collective orientation in teams. In future research, the instrument can be applied to diagnose teamwork deficiencies and evaluate interventions for developing team members’ collective orientation.

Examining the interrelationships among reward systems, organisational climate and cultural changes in the hospitality industry

2020 ◽  
Author(s):  
Christos Kakarougkas ◽  
Theodoros Stavrinoudis
Keyword(s):  
Cultural Change ◽  
Latent Variable ◽  
Structural Equation ◽  
Reward System ◽  
Senior Executives ◽  
Cultural Changes ◽  
Organisational Climate ◽  
Individual Variables ◽  
The Impact ◽  
Method Of Extraction

This paper aims to explore the impact of a hotel’s reward system on strengthening: positiverelationships and communication among employees; the creation of a change-friendlyorganisational climate and cultural change barriers, within the context of a cultural changeprocess in a hotel. Quantitative data were collected from a proportionally stratified,representative sample of 207 Greek five-star hotels’ senior executives and analysed with theprincipal component method of extraction and Structural Equation Modelling. This led to thecreation and validation of three prototype second-order latent variable models, whichhighlight and depict the impact of individual variables and their importance for a rewardsystem creating an organisational climate for or against cultural change in hotels. Theoriginality of the paper lays on both theoretical and practical levels. On a theoretical level, thepaper’s findings manage to fill a knowledge gap through a novel modelling of a rewardsystem on a hotel’s organisational climate in times of cultural change. On a practical level, thepaper findings enable hotels’ executives to focus on specific variables of a reward system thatcan enhance and/or prevent a cultural change initiative.

Teachers' Attitudinal Orientation Towards the Socially Disadvantaged Students and their Education

2017 ◽  
Vol 7 (2) ◽  
pp. 47-72
Author(s):  
Anna Petr Šafránková ◽  
Tereza Humenská
Keyword(s):  
Inclusive Education ◽  
Family Environment ◽  
Self Efficacy ◽  
Pearson Correlation ◽  
Teaching Experience ◽  
Research Survey ◽  
Socially Disadvantaged ◽  
Individual Variables ◽  
Questionnaire Method ◽  
The Relationship

In the context of education of socially disadvantaged pupils and the perspective of inclusive education, the teacher occupies a significant position. The presented study focuses on the issue of education of socially disadvantaged pupils, respectively its aim is to present results of the research survey focused on the attitudinal orientation of teachers in Pardubice, Liberec and Ústí nad Labem regions (n = 122) towards the socially disadvantaged pupils. Further, its goal is to find out whether there exists a relation between the teacher's attitudinal orientation and the region, his/her age, the length of the teaching experience, his/her experience with socially disadvantaged pupils education and their self-efficacy. In order to achieve research goals the Likert-type questionnaire method was used and as a research tool Teacher self-efficacy. The obtained data were subjected to factor analysis, in order to verify the relation between individual variables ANOVA was used, further Kruskal-Wallis test, Mann-Whitney test and Pearson correlation coefficient were used. It was found out that teachers evaluate the group of socially disadvantaged pupils rather negatively, on the other hand, they evaluate the possibility to reduce or overcome their disadvantage originating from the family environment they come from rather positively and also they perceive the relationship between the school and the socially disadvantaged pupils rather positively. The teachers' attitudinal orientation is not related to the previous experience with the education of socially disadvantaged pupils, the length of their teaching experience and region where the teachers work. On the contrary, the relation between teachers' attitudinal orientation and age and self-efficacy was proved.

scholarly journals Informed Geoheritage Conservation: Determinant Analysis Based on Bibliometric and Sustainability Indicators Using Ordination Techniques

Land ◽  
2021 ◽  
Vol 10 (5) ◽  
pp. 539
Author(s):  
Boglárka Németh ◽  
Károly Németh ◽  
Jon N. Procter
Keyword(s):  
Correspondence Analysis ◽  
Conservation Planning ◽  
Earth Science ◽  
Multiple Correspondence Analysis ◽  
Contributing Factors ◽  
Usual Model ◽  
Development Indicators ◽  
Individual Variables ◽  
Business As Usual ◽  
World Development

Ordination methods are used in ecological multivariate statistics in order to reduce the number of dimensions and arrange individual variables along environmental variables. Geoheritage designation is a new challenge for conservation planning. Quantification of geoheritage to date is used explicitly for site selection, however, it also carries significant potential to be one of the indicators of sustainable development that is delivered through geosystem services. In order to achieve such a dominant position, geoheritage needs to be included in the business as usual model of conservation planning. Questions about the quantification process that have typically been addressed in geoheritage studies can be answered more directly by their relationships to world development indicators. We aim to relate the major informative geoheritage practices to underlying trends of successful geoheritage implementation through statistical analysis of countries with the highest trackable geoheritage interest. Correspondence analysis (CA) was used to obtain information on how certain indicators bundle together. Multiple correspondence analysis (MCA) was used to detect sets of factors to determine positive geoheritage conservation outcomes. The analysis resulted in ordination diagrams that visualize correlations among determinant variables translated to links between socio-economic background and geoheritage conservation outcomes. Indicators derived from geoheritage-related academic activity and world development metrics show a shift from significant Earth science output toward disciplines of strong international agreement such as tourism, sustainability and biodiversity. Identifying contributing factors to conservation-related decisions helps experts to tailor their proposals for required evidence-based quantification reports and reinforce the scientific significance of geoheritage.

scholarly journals Eight Simple Guidelines for Improved Understanding of Transformations and Nonlinear Effects

2021 ◽  
pp. 109442812199190
Author(s):  
Mikko Rönkkö ◽  
Eero Aalto ◽  
Henni Tenhunen ◽  
Miguel I. Aguirre-Urreta
Keyword(s):  
Generalized Linear Model ◽  
Functional Form ◽  
Nonlinear Models ◽  
Nonlinear Effects ◽  
Recent Past ◽  
Organizational Research ◽  
Common Practices ◽  
Individual Variables ◽  
The Individual ◽  
The Relationship

Transforming variables before analysis or applying a transformation as a part of a generalized linear model are common practices in organizational research. Several methodological articles addressing the topic, either directly or indirectly, have been published in the recent past. In this article, we point out a few misconceptions about transformations and propose a set of eight simple guidelines for addressing them. Our main argument is that transformations should not be chosen based on the nature or distribution of the individual variables but based on the functional form of the relationship between two or more variables that is expected from theory or discovered empirically. Building on a systematic review of six leading management journals, we point to several ways the specification and interpretation of nonlinear models can be improved.

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