Logical Means Research Articles

Differential and integral calculus for logical operations. A matrix-vector approach

A variety of problems emerged investigating electronic circuits, computer devices and cellular automata motivated a number of attempts to create a differential and integral calculus for Boolean functions. In the present article, we extend this kind of calculus in order to include the semantic of classical logical operations. We show that this extension to logics is strongly helped if we submerge the elementary logical calculus in a matrix-vector formalism that naturally includes a kind of fuzzy-logic. In this way, guided by the laws of matrix algebra, we can construct compact representations for the derivatives and the integrals of logical functions. Inside this semantic-algebraic calculus, we obtain expressions for the derivatives of some of the basic logical operations and show the general way to obtain the derivatives of any well-formed formula of propositional calculus. We show that some of the basic tautologies (Excluded middle, Modus ponens, Hypothetical syllogism) are members of a kind of hierarchical system linked by the differentiation algorithm. In addition using the logical derivatives we show that relatively complex formulas can collapse in simple expressions that reveal clearly their hidden logical meaning. The search for the antiderivatives produces naturally an integral calculus. Within this logical formalism an indefinite integral can always be found for any logical expression. Moreover, particular integrals can be constructed based on detachment properties that lead to logical expressions of growing complexity. We show that these particular integrals have some similarities with the 'generalizing deduction' procedures investigated by Lukasiewicz.

Translating Genre of News Stories and the Correlated Grammar in Analysing Student Translation Errors

In translation studies, genre and grammar have each flourished in their own right as a subject of study by a number of scholars. But research solely dedicated to the complementary relations between genre and grammar has been rare, particularly from the translation education perspective. Neither genre nor grammar can function properly without the other in a text because context (genre) and ‘wording’ (grammar) are inseparable. The aim of this paper is to examine the correlation between genre structure and grammar in the analysis of errors in student translations of news story texts. Drawing on Systemic Functional Linguistics (SFL), translations of two subtypes of news-reporting texts from English to Korean are analyzed. The main data include two source texts and their translations by nine Masters’students. The findings of this paper show that a large majority of translation mistakes arise from a lack of knowledge of genre structure and its interconnection with logical meaning (how clauses, sentences and paragraphs are combined). The research reported in this paper indicates that genre structure and grammar together constitute useful resources for teaching the translation of news-reporting texts, with more studies of genre structure in other subject fields desired.

The Acquisition of Logical Connectives in Child Mandarin

This study investigates 2–5-year-old Mandarin-speaking children’s interpretation of the disjunction word huozhe (‘or’) in two positions in ruguo (‘if’)-conditional statements, i.e., in the antecedent clause versus in the consequent clause. The findings from three experiments show that the meanings children assign to disjunction and to ruguo-conditionals conform closely to the meanings that are assigned to the corresponding logical connectives in classical logic. Experiment 1 demonstrates that children assign an inclusive-or interpretation to disjunction in both the antecedent clause and in the consequent clause of conditional statements, whereas adults assign an exclusive-or interpretation to disjunction when it appears in the consequent clause of conditional statements. The findings of Experiment 2 provide evidence of children’s adherence to a putative semantic universal—that disjunction licenses a conjunctive entailment in the antecedent clause of conditional statements, but not in the consequent clause. It is shown in Experiment 3, moreover, that children’s knowledge doesn’t stem from their mistaking disjunction as conjunction. Because the logical meanings of connectives emerge early in the course of language acquisition, and without decisive evidence from the adult input, these findings suggest that children draw upon an innate logical vocabulary at the initial stages of language acquisition.

Experimental investigation into the size effect of bidirectional fiber patch anchors in strengthening of concrete structures

The strengthening of existing reinforced concrete structures using fiber reinforced polymers (FRP’s) as externally bonded reinforcement is gaining increasing attention due to the materials superior mechanical properties and light weight. However, a serious limitation in the use of FRP as a strengthening material comes from separation of the FRP from the concrete surface by premature debonding at a strain level which is well below the ultimate tensile strength of the material. A logical means to improve the performance of externally bonded FRP by mitigating the processes of debonding is by the provision of end anchorage. Of the many anchorages investigated by researchers, the use of bi-directional fiber patch anchors has shown exceptional promise. Due to the limitations of experimental data in this area, the current paper presents the first comprehensive experimental program into the size effect FRP patch anchors.

Making sense of iconic symbols: a study of preschool children conducting a refuse-sorting task

This article is part of a larger project focusing upon explanatory illustrations that children encounter in pre- and primary school education. The research questions concerned (a) how preschool children make sense of iconic symbols when placing items of refuse on illustrations of refuse bins in a sorting task and (b) what stumbling blocks they encounter when interpreting these symbols. Video data were collected with 30 children between four and five years of age. From the children’s verbal and non-verbal interactions, four different categories of sense-making were constructed: by material, by object type, by appearance and by function. Three stumbling blocks were identified. The first had to do with giving the symbols a different logical meaning to the intended one; the second related to what materials the different refuse items were made of; the third was being able to stick to one correct way of interpreting each symbol.

Theology and Rhetoric: Redefining the relationship between Res and Verba

After discussing three models defining the relationship between rhetoric (linguistic form, verba) and theology (content, res) in scholarship’s history (part I), a theoretical discussion attempts to further undergird the third model according to which verba produce res (part II). As a first step, the inseparable intertwinement of res and verba is shown by empirical studies. The linguistic form always carries unspoken semantic content. Altering this form changes the content, even if a phrase’s logical meaning remains the same. As a farther-reaching second step, constructivist philosophy of language is used, holding that language creates reality. “Reality” is defined as constructed by the brain and language and differentiated from ontic reality. Four sources of evidence are identified that make such reality constructs plausible to groups. Part III discusses the theological concept of “new creation” in light of the second part’s findings. Part IV shows a way to overcome postmodern indifference with regard to “truth.”

The Logical Meanings of the Traditional Wedding Speeches of the Batak Toba People

This research deals with the logical meanings of the clause complexes in the Batak Toba People wedding speeches. The problem investigated deals with the types of the logical meanings existed in the traditional wedding speeches of the Batak Toba people and the way each of those types is created. The theoretical frameworks in this research are the logical meanings and the logico-semantic relation theories. The research design refers to an object as multiple realities as a qualitative research. The research subject is the Batak Toba people creating the wedding speeches in the wedding ceremony. The object is the logical meaning in the structure of a clause complex. The data are 142 clause complexes from the 15 recorded wedding speeches. The technique of the data collection and analysis follow the concept of the researcher concurrent activities, they are data collection, reduction, display, and drawing conclusion. The findings are that the logical meanings the Batak Toba people wedding speeches are expansion, such as elaboration, extension, and enhancement; and projection, such as locution projection, idea projection and idea.

Paul Ehrenfest’s final years

New access to his correspondence sheds light on the tragic life and death of one of the pioneers of modern physics.

On Dialogues, Predication and Elementary sentences

In its origins Dialogical logic constituted the logical foundations of an overall new movement called the Erlangen Schoo l or Erlangen Constructivism that should provide a new start to a general theory of language and of science. In relation to the theory of language, according to the Erlangen-School, language is not just a fact that we discover, but a human cultural accomplishment whose construction reason can and should control. The constructive development of a scientific language was called the Orthosprache-project . Unfortunately, the Orthosprache-project was not further developed and somehow seemed to fade away. Perhaps, one could say that one of the reasons is that the semantic links between dialogical logic, that was restricted to logical constants, and the more general linguistic aspirations of the Orthosprache were not sufficiently developed and then the new theory of meaning of dialogical logic seemed to be cut off from the project of setting the basis for a general theory of meaning. In the present paper we would like to contribute to precise one possible way in which a general dialogical theory of meaning could be linked to dialogical logic. More precisely, the main aim of the article is to set the basis for the meaning of elementary sentences in the context of dialogical interaction.

On Dialogues, Predication and Elementary sentences

En sus orígenes la lógica dialógica constituyó la fundamentación lógica de un nuevo movimiento llamado Escuela de Erlangen o Constructivismo de Erlangen, el que debía proporcionar un nuevo comienzo a una teoría general del lenguaje y de la ciencia. En lo referente a teoría general del lenguaje, la Escuela de Erlangen afirma que el lenguaje no es un hecho que descubrimos, sino una realización cultural humana cuya construcción puede y debe ser controlada. El proyecto de un desarrollo constructivo de un lenguaje científico fue llamado Orthosprache. Desafortunadamente, este proyecto no fue continuado y de alguna manera parecía desvanecerse. Quizás podríamos decir que una de las razones es que los lazos semánticos entre lógica dialógica, que se restringió a la semántica de la constantes lógicas y las aspiraciones lingüísticas más generales de la Orthosprache, no fueron desarrollados suficientemente y, entonces, la nueva teoría del significado de la lógica dialógica parecía haber sido separada del proyecto de establecer una teoría general del significado.En este artículo nos proponemos presentar una forma posible en la cual una teoría dialógica general del significado podría estar relacionada con lógica dialógica. Más precisamente, el objetivo principal del artículo es establecer las bases para el significado de las frases elementales en el contexto de la interacción dialógica.

Human intervention and the safety of complex structural systems

Structural reliability theory based on probability provides a systematic, logical and consistent means to make estimates of the safety of complex structural systems. However, its application currently leaves it open to criticism that its predictions do not necessarily compare with reality and with accepted risk criteria in other contexts. Herein, it is proposed that this is because applications have not dealt satisfactorily with the issues of human error and particularly human intervention in the management of loads and resistances. Probability-based models for loads can be modified to include the influence of human intervention such as through including the effect of the degree of enforcement of regulatory requirements. Similarly, the standard of enforcement of minimum standards of material quality should be added to probability-based models for resistances. This is relevant particularly for the assessment and prediction of the future reliability and safety of existing structures.

Kronecker in Contemporary Mathematics, General Arithmetic as a Foundational Programme

Kronecker called his programme of arithmetization “General Arithmetic” (Allgemeine Arithmetik). In his view, arithmetic is the building block of the whole edifice of mathematics. The aim of this paper is to show that Kronecker’s arithmetical philosophy and mathematical practice have exerted a permanent influence on a long tradition of mathematicians from Hilbert to Weil, Grothendieck and Langlands. The conclusion hints at a constructivist finitist stance in contemporary mathematical logic, especially proof theory, beyond Hilbert’s programme of finitist foundations which can be seen as the continuation of Kronecker’s arithmetization programme by metamathematical or logical means. It is finally argued that the introduction of higher-degree polynomials by Kronecker inspired Hilbert’s notion of functionals, which in turn influenced G¨odel’s functional Dialectica interpretation for his intuitionistic proof of the consistency of arithmetic.

The next generation of RAGE modulators: implications for soluble RAGE therapies in vascular inflammation

The next generation of RAGE modulators: implications for soluble RAGE therapies in vascular inflammation

Eko-Spiritualisme: Sebuah Keniscayaan pada Era Kontemporer

This paper provides a new perspective of looking at our natural environment with a spiritual perspective. The main argument of this paper was inspired by the emergence of the reality of our natural environment is increasingly damaged by the implications of a variety of viewpoints, attitudes and human behavior are destructive and counterproductive. The influences of modern science and philosophy have reduced logical meaning of the universe solely on technical functions-economical to fulfill the needs of humans (anthropocentric). In effect, we are witnessing the natural environment is being weakened only in different parts of the world. So this paper is an effort to return to the community awareness of the contemporary world that still cares for the future of our natural environment better. This paper provides an alternative framework as well as a new optimism for our natural environment lasting and sustainable return by optimizing intrinsic qualities inherent in every human being as a spiritual being. Then become eco-spiritual as a necessity for our contemporary world society today.

Ben-Gurion's view of the place of Judaism in Israel

The article examines David Ben-Gurion's ideas on the place of Judaism in Israeli society during his term as prime minister, claiming that his stand on Judaism as a culture and religion was derived from his civic ideas. Ben-Gurion understood Judaism as a national culture extending beyond religion, based on the humanistic-political principles articulated by the biblical prophets, which had served as a moral compass throughout Jewish history and also guided the present developing society in Israel, spurring it to be a model society. In contrast to his extensive preoccupation with the nature of Judaism as a national culture, Ben-Gurion barely touched upon the question of the place of the Jewish religion in Israeli public life. He accepted religious-secular coexistence as a given, and was convinced that disputes over questions of faith could not be decided by empirical or logical means. He therefore deemed that the religious and secular should forgo futile arguments over culture and belief and instead endeavor to establish mutual tolerance and partnership as citizens of a common society.

Parent’s/Caregiver’s Relationship and the Impact on Nutrition

The social–emotional interactions between parent and child are critical to an adaptive eating pattern. A complete assessment of feeding and nutrition requires inquiry into the caregiver/parent–child relationship during eating. This article details the 6 areas of social functioning derived from the six functional emotional milestones of the DIR/Floortime (DIR = Developmental, Individual Difference, Relationship) approach. When inquiry into these six areas is included in a comprehensive feeding assessment, there are direct implications for treatment planning and ultimately treatment effectiveness. These six areas are (1) the mood or emotional tone in the mealtime interaction; (2) pleasure in the introduction and exploration of new foods together with parents; (3) the parent’s ability to attune to child’s communicative attempts; (4) the parent’s ability to support the child’s drive to independence; (5) the parent’s ability to engage in play and conversation about feelings, imagination, and creative ideas; and (6) the parents’ ability to provide logical and accurate meanings to the child’s behavior and questions. By gaining a thorough assessment of the child’s interactions with their caregiver/parent, a clinician will be able to formulate intervention strategies that take advantage of the strengths in the relationship, and identify areas where they can support further developmental growth.

ASSESSING CONCEPTUAL UNDERSTANDING IN MATHEMATICS: Using Derivative Function to Solve Connected Problems

Open and distance education plays an important role in the actualization of cultural goals as well as in societal developments. This is an independent teaching and learning method for mathematics which forms the dynamic of scientific thinking. Distance education is an important alternative to traditional teaching applications. These contributions brought by technology enable students to participate actively in having access to information and questioning it. Such an application increases students’ motivation and teaches how mathematics can be used in daily life. Derivative is a mathematical concept which can be used in many areas of daily life. The aim of this study is to enable the concept of derivatives to be understood well by using the derivative function in the solution of various problems. It also aims at interpreting difficulties theoretically in the solution of problems and determining mistakes in terms of teaching methods. In this study, how various aspects of derivatives are understood is emphasized. These aspects concern the explanation of concepts and process, and also their application to certain concepts in physics. Students’ depth of understanding of derivatives was analyzed based on two aspects of understanding; theoretical analysis and contextual application. Follow-up interviews were conducted with five students. The results show that the students preferred to apply an algebraic symbolic aspect instead of using logical meanings of function and its derivative. In addition, in relation to how the graph of the derivative function affects the aspect of function, it was determined that the students displayed low performance.

Scalar implicatures and downward entailment in child Mandarin

This study aims to test whether or not the computation of scalar implicatures in child Mandarin is influenced by the entailment properties of linguistic contexts. Experiment 1 compared adults’ and children’s interpretations of the scalar term huozhe ‘or’, when it appeared in the two arguments of the universal quantifier mei ‘every’. The results showed that Mandarin-speaking adults accepted huozhe as compatible with he ‘and’ in the (downward entailing) restrictor of mei, but not in the (non-downward entailing) nuclear scope of mei, indicating that adults’ calculation of scalar implicatures is sensitive to the influence of entailment patterns. Unlike adults, 4–5-year-old Mandarin-speaking children persistently interpreted huozhe as compatible with he in both contexts. Two further experiments confirmed that children were insensitive to scalar implicatures related to huozhe in non-downward entailing contexts (Experiment 2), unless alternative sentences containing the scalar terms huozhe and he were explicitly presented (Experiment 3). Taken together with previous child studies, the experimental findings suggest that scalar implicatures are not derived in downward entailing contexts. In addition, young children do not spontaneously compute scalar implicatures to the same extent as adults do in non-downward entailing contexts. In both cases, then, young children appear to interpret disjunction as its meaning in classical logic, i.e., inclusive-or.

Function-Related Positioning of the Type II Secretion ATPase of Xanthomonas campestris pv. campestris

Gram-negative bacteria use the type II secretion (T2S) system to secrete exoproteins for attacking animal or plant cells or to obtain nutrients from the environment. The system is unique in helping folded proteins traverse the outer membrane. The secretion machine comprises multiple proteins spanning the cell envelope and a cytoplasmic ATPase. Activity of the ATPase, when copurified with the cytoplasmic domain of an interactive ATPase partner, is stimulated by an acidic phospholipid, suggesting the membrane-associated ATPase is actively engaged in secretion. How the stimulated ATPase activity is terminated when secretion is complete is unclear. We fused the T2S ATPase of Xanthomonas campestris pv. campestris, the causal agent of black rot in the crucifers, with fluorescent protein and found that the ATPase in secretion-proficient cells was mainly diffused in cytoplasm. Focal spots at the cell periphery were detectable only in a few cells. The discrete foci were augmented in abundance and intensity when the secretion channel was depleted and the exoprotein overproduced. The foci abundance was inversely related to secretion efficiency of the secretion channel. Restored function of the secretion channel paralleled reduced ATPase foci abundance. The ATPase foci colocalized with the secretion channel. The ATPase may be transiently associated with the T2S machine by alternating between a cytoplasmic and a machine-associated state in a secretion-dependent manner. This provides a logical means for terminating the ATPase activity when secretion is completed. Function-related dynamic assembly may be the essence of the T2S machine.

Policies for promoting walking and cycling in England: A view from the street

Transport policies to increase active and sustainable travel in Britain have focused mainly on persuading people of the health benefits of walking and cycling for short trips, and have assumed that if people can be persuaded that more active travel has personal benefits then behavioural change will follow. Research reported in this paper, based mainly on detailed qualitative research in four English towns, argues that the complexities and contingencies that most people encounter in everyday life often make such behavioural change difficult. Attention is focused on three sets of factors: perceptions of risk; constraints created by family and household responsibilities; and perceptions of normality. It is suggested that unless such factors are tackled directly then policies to increase levels of walking and cycling will have limited success. In particular, it is argued that there needs to be a much more integrated approach to transport policy that combines interventions to make walking and (especially) cycling as risk-free as possible with restrictions on car use and attitudinal shifts in the ways in which motorists view other road users. Such policies also need to be linked to wider social and economic change which, in combination, creates an environment in which walking or cycling for short trips in urban areas is perceived as the logical and normal means of travel and using the car is viewed as exceptional.