Double Negation Research Articles

Adjoint Operations in Twist-Products of Lattices

Given an integral commutative residuated lattices L=(L,∨,∧), its full twist-product (L2,⊔,⊓) can be endowed with two binary operations ⊙ and ⇒ introduced formerly by M. Busaniche and R. Cignoli as well as by C. Tsinakis and A. M. Wille such that it becomes a commutative residuated lattice. For every a∈L we define a certain subset Pa(L) of L2. We characterize when Pa(L) is a sublattice of the full twist-product (L2,⊔,⊓). In this case Pa(L) together with some natural antitone involution ′ becomes a pseudo-Kleene lattice. If L is distributive then (Pa(L),⊔,⊓,′) becomes a Kleene lattice. We present sufficient conditions for Pa(L) being a subalgebra of (L2,⊔,⊓,⊙,⇒) and thus for ⊙ and ⇒ being a pair of adjoint operations on Pa(L). Finally, we introduce another pair ⊙ and ⇒ of adjoint operations on the full twist-product of a bounded commutative residuated lattice such that the resulting algebra is a bounded commutative residuated lattice satisfying the double negation law, and we investigate when Pa(L) is closed under these new operations.

THE SPECIFICS OF ARGUMENTATIVE DISCOURSE REPRESENTATION IN THE PREFACE TO A SHORT NOVEL BY ANDRE GIDE "THE IMMORALIST"

The article represents the experience of interpreting the author’s preface (AP) of one of the most significant pieces of world literature as an actual integrative philological problem. It shows the logic of the transition from literary issues (“pure novel”) to the linguistic aspect of the study. The object of study is the author’s preface as a genre of artistic discourse (AD). The purpose of the study is to identify the elements that determine the specifics of the implementation of the functions of the mini-text. The novelty of the work is the study of the preface as a compositional element of the work within the argumentative aspect. The author’s comprises the application of the author’s own model to the object of analysis. This model includes the categories of argumentative space (epistemic context, causality, modality), as well as a dual understanding of argumentation -- in its narrow (as a process of outing forward arguments) and broad (as a constant, ontological validity) meanings. In a narrow sense, argumentation finds expression in various forms: reasoning as a type of text; cognitive elements of the argumentative process in discourse (hypothesis, concessive, clarification); various syntactic techniques – “argumentative balance”, double negation, parallel constructions. The conclusion is made about the correlation between narrow and broad types of understanding of argumentation based on the unity of three concepts – “explanation – evaluation – comprehension”. “Explanation” and “evaluation” in the narrow sense characterize the argumentative process (“for” and “against”), and in its broad sense they manifest objectivity based on distance aspect. “Comprehension” in the unity of two previous stages indicates the specifics of the implementation of the intention to “prove”, the absence of which – in the beginning and within the ending – creates the framework of the preface. In a broad sense, the analyzed part of a novel is characterized as a genre that performs not an influencing, but an orienting function to understand the creative credo of an objective / unbiased writer. This is facilitated by obvious flexibility of dialogical relations between the participants of the discourse – a great French author and his potential (hereinafter – real) readers, who are able to become equal partners in constructing a relevant picture of the world for themselves. The conclusion is drawn about the position of the author as an artist who is able to engage the maximum number of readers in the dialogue: it can be perceived in two ways – as a withdrawal of the author from his artistic space and as an invitation to a mutual journey.

Przyszłość przeszłości. Retrotopia w narracjach sztucznej inteligencji Stanisława Lema i Łukasza Zawady

The Future Past. Retrotopia in the Narratives of an Artificial Intelligence by Stanisław Lem and Łukasz Zawada In Retrotopia, Zygmunt Bauman derives the title phenomenon from the double negation of Thomas More’s utopia and uses it to describe the returns of the imaginary past, whose resurrected potentials make it possible to return to forgotten ideas. This paper examines the relationship between futuristic technology projections and the retrotopian shift taking place in liquid modernity. To this end, the author’s research focuses on the literary narratives of the artificial intelligence in Stanisław Lem’s Golem XIV (1981) and Łukasz Zawada’s Fragmenty dziennika SI (2018). The languages, medium, and stories of the non-human Other illustrate the mechanisms of the modern prophetic fantasies through repetition act and mediating them in the lost/un-dead past. Simultaneously, the (retro)futuristic voices of the superintelligent computers reveal the difficulties of these narratives – trying to slow down Sci-tech progress and embed the past into the future technologies.

Constructions with negative elements ni kapli and ni razu in Russian

There are many negative polarity items in Russian reinforcing the sentential negation. It may be negative pronouns with affix ni- (ničego, ničut’, nikogo) and quantifiers grammaticalized from smallsize nouns. The paper deals with the new way to express emphatic negation and the process of reinforcement of negation due to including new markers of double negation in Russian. It analyzes the network of constructions with expressions ni kapli and ni razu based on the data from two corpora (General Internet-Corpus of Russian and Russian National Corpus). The paper describes the grammaticalization of the word kaplja ‘drop’ as a part of counting construction. The construction ni razu ne VP combines with a past tense form of a verb and expresses the negation of the experiential meaning. The new construction ni razu / ni kapli ne N arises in non-verbal sentences and expresses emphatic negation of affiliation to a category.

An Application of Classical Logic’s Laws in Formulas of Fuzzy Implications

The crucial role that fuzzy implications play in many applicable areas was our motivation to revisit the topic of them. In this paper, we apply classical logic’s laws such as De Morgan’s laws and the classical law of double negation in known formulas of fuzzy implications. These applications lead to new families of fuzzy implications. Although a duality in properties of the preliminary and induced families is expected, we will prove that this does not hold, in general. Moreover, we will prove that it is not ensured that these applications lead us to fuzzy implications, in general, without restrictions. We generate and study three induced families, the so-called D ′ -implications, QL ′ -implications, and R ′ -implications. Each family is the “closest” to its preliminary-“creator” family, and they both are simulating the same (or a similar) way of classical thinking.

Funções pragmáticas de enunciados com dupla negação em Florianópolis

O português brasileiro conta com formas alternativas para a expressão da negação sentencial. Entre elas está a dupla negação, uma estrutura não canônica, que se manifesta de modo diverso em cada região do Brasil. Este estudo investiga as possíveis funções pragmáticas de enunciados com dupla negação encontrados em 12 entrevistas sociolinguísticas realizadas com falantes nativos da cidade de Florianópolis, Santa Catarina, no início da década de 90. O levantamento realizado revela que os enunciados de dupla negação foram usados para instanciar duas funções pragmáticas: denegação e retorno a tópico quantitativo.

Explaining Away, Augmentation, and the Assumption of Independence.

In reasoning about situations in which several causes lead to a common effect, a much studied and yet still not well-understood inference is that of explaining away. Assuming that the causes contribute independently to the effect, if we learn that the effect is present, then this increases the probability that one or more of the causes are present. But if we then learn that a particular cause is present, this cause “explains” the presence of the effect, and the probabilities of the other causes decrease again. People tend to show this explaining away effect in their probability judgments, but to a lesser extent than predicted by the causal structure of the situation. We investigated further the conditions under which explaining away is observed. Participants estimated the probability of a cause, given the presence or the absence of another cause, for situations in which the effect was either present or absent, and the evidence about the effect was either certain or uncertain. Responses were compared to predictions obtained using Bayesian network modeling as well as a sensitivity analysis of the size of normative changes in probability under different information conditions. One of the conditions investigated: when there is certainty that the effect is absent, is special because under the assumption of causal independence, the probabilities of the causes remain invariant, that is, there is no normative explaining away or augmentation. This condition is therefore especially diagnostic of people’s reasoning about common-effect structures. The findings suggest that, alongside earlier explanations brought forward in the literature, explaining away may occur less often when the causes are assumed to interact in their contribution to the effect, and when the normative size of the probability change is not large enough to be subjectively meaningful. Further, people struggled when given evidence against negative evidence, resembling a double negation effect.

Omissão de sujeito pronominal anafórico e as construções de dupla negação

Neste artigo, investigamos omissão e a expressão de sujeitos expressos pronominais e nulos em construções de dupla negação em português brasileiro. Para isso, analisamos um corpus de língua falada da região Sul do Brasil, o corpus VARSUL. Apesar de a literatura apontar para o fato de que o PB tem privilegiado orações com sujeito pronominal expresso em detrimento de sujeito nulo (cf. Duarte 2012, entre outros), percebemos que as construções de dupla negação, ao contrário da expectativa, favorecem o sujeito nulo. Acreditamos que tal construção favoreça o sujeito nulo porque veicula conteúdos ativados (que, por princípio, podem ser ocultados da superfície da frase). Além desse fator pragmático, investigamos também a relação desses efeitos com um fator semântico que favorece a retomada por sujeito pronominal expresso: o traço de gênero semântico do referente. Analisamos cenários de confluência e conflito entre esses princípios de natureza gramatical distinta distintos e o que encontramos na análise do corpus corrobora empiricamente nossas previsões teóricas.

A new version of the Behaviour of Young Novice Drivers Scale (BYNDS). Insights from a randomised sample of 700 German young novice drivers.

In Germany, every year 66,000 road crashes lead to death or injury of young novice drivers. This makes them twice as likely to be involved in, or cause, vehicle crashes compared to their older and more experienced counterparts. This study aims to address this societal issue by developing a better understanding of the German young driver problem. For this purpose, we created an updated, 55-item strong version of the Behaviour of Young Novice Drivers Scale (BYNDS), originally developed by Scott-Parker et al. in 2010. To make the new version of the BYNDS understandable for German young novice drivers, this research used a new method of translation in combination with extensive pre-testing. As a result, we identified possible threats for response errors such as retrospective formulated questions or double negations. Due the adjustment of the possible sources of error the presented version of the BYNDS is semantically and conceptually different from the original. However, due to the application of the updated version of the BYNDS in a robust sample of 700 participants, this paper presents the first reliable and validated tool to measure novices risky driving behaviour in Germany. Moreover, it offers an updated and extended version of the BYNDS that allows practitioners but also researchers to broaden their understanding of young driver risk.

On Bijective Correspondence between Fuzzy Reflexive Approximation Spaces and Fuzzy Transformation Systems

The objective of this paper is to establish the relationship between fuzzy approximation operators and fuzzy transformation systems. We show that for each upper fuzzy transformation system there exists a fuzzy reflexive approximation space and vice-versa. We further establish such relationship between lower fuzzy transformation systems and fuzzy reflexive approximation spaces under the condition that the underline lattice structure satisfies double negation law.

Existential negation in Turkish: A functional approach

 Existential negation is the one type of negation present in languages, which its item is called “negative existential”, and it provides to tell the case of “absence”, “lack”, “there is not”, “poor”, “empty”, “dead” etc. Negative existentials are generally used for the common similarity of a structure as morphological, syntactic and semantic typologies. In Turkish, existential negation occurs with the independent morpheme yok, which is defined as “absolute absence/non-existence”. Yok is the main negative existential that is different from the standard negation and it is a separate lexical item with negative content. Since it is a powerful negator with its “absolute absence/non-existence” meaning, it can be used in different positions, such as existential negation, possessive negation, emphatic negation, standard negation, short answer “no”, prohibition or double negation. In addition to yok , the bound morpheme -sXz is used with “without/lack” meaning in existential negation by implying the non-existence case. Besides, general rejection item deAŸil, which means “is not”, is used in existential negation, which implies the non-existentiality by rejecting the existence case that is presupposed.

Badanie rozumienia wypowiedzi w afazji – propozycja metodologiczna

The article presents a proposal for methodology to study of understanding spoken and written statements by people who have developed aphasia as a result of focal brain damage within the speech area (usually the middle part of the left hemisphere in right-handed people). The problem of understanding in speech therapy is a category that is still not well known, so there is a need to investigate this activity on the basis of a structured research tool. The proposed methodology, referring to the experience of glottodidactics, which distinguishes four levels of understanding of the text: global, selective, detailed and interactive, allows to determine the degree of dysfunction in the understanding of the text at its different levels. The results obtained from the study of oral and written texts (in and out of context) are complemented by the assessment of understanding of individual language structures of varying levels of grammatical complexity (passive side, syntactic inversion, sentences with double negation, government relations, comparative expressions, prepositionalexpressions) – both in oral and written texts.

Representation of De Morgan and (Semi-)Kleene Lattices

Twist-structure representation theorems are established for De Morgan and Kleene lattices. While the former result relies essentially on the quasivariety of De Morgan lattices being finitely generated, the representation for Kleene lattices does not and can be extended to more general algebras. In particular, one can drop the double negation identity (involutivity). The resulting class of algebras, named semi-Kleene lattices by analogy with Sankappanavar’s semi-De Morgan lattices, is shown to be representable through a twist-structure construction inspired by the Cornish–Fowler duality for Kleene lattices. Quasi-Kleene lattices, a subvariety of semi-Kleene, are also defined and investigated, showing that they are precisely the implication-free subreducts of the recently introduced class of quasi-Nelson lattices.

Classifying material implications over minimal logic

The so-called paradoxes of material implication have motivated the development of many non-classical logics over the years, such as relevance logics, paraconsistent logics, fuzzy logics and so on. In this note, we investigate some of these paradoxes and classify them, over minimal logic. We provide proofs of equivalence and semantic models separating the paradoxes where appropriate. A number of equivalent groups arise, all of which collapse with unrestricted use of double negation elimination. Interestingly, the principle ex falso quodlibet, and several weaker principles, turn out to be distinguishable, giving perhaps supporting motivation for adopting minimal logic as the ambient logic for reasoning in the possible presence of inconsistency.

On the independence of premiss axiom and rule

In this paper, we deal with a relationship among the law of excluded middle, the double negation elimination and the independence of premiss rule ( $$\mathrm {IPR}$$ ) for (many-sorted) intuitionistic predicate logic. After giving a general machinery, we give, as corollaries, several examples of extensions of $$\mathbf {HA}$$ and $$\mathbf {HA}^\omega $$ which are closed under $$\mathrm {IPR}$$ but do not derive the independence of premiss axiom.

«Двойное отрицание» в русском языке: лингводидактический и лингвокультурологический аспекты

Analyzing the so-called “double negation”, that is, the construction of strengthening negation, in the linguistic and didactic aspect, the authors note that in the practice of teaching Russian as a foreign language, the construction of “double negation” is explained in two ways, depending on the native language of the students. When explaining the model, native Chinese speakers need to pay attention to the replacement of pronouns and adverbs, like все (all), всегда (always), везде (everywhere), with negative verbs to negative with the prefix ни (no): никто (nobody), никогда (never), нигде (nowhere), because the Chinese language consciousness does not accept a negative modification of the statement, normative for Russian. The article presents linguistic and conditionally-communicative exercises that contribute to the automation and introduction of this structural model into active speech. Difficulties in the development of this construction, associated precisely with its specificity, are due, according to the authors, primarily to the very possibility of strengthening the negation, its repetition, indicating the specificity of Russian linguistic and cultural consciousness. Considering the construction of “double negation” in the linguistic and culture study aspect, the authors note that its “pleonasm” indicates, on the one hand, the importance of negation for the Russian linguistic consciousness, and on the other hand, the subtle differentiation of logically comparable situations with subjects all / no, etc. Techniques for working with Russian constructions are seen in the mirror of the Chinese language.

Философия Гегеля и диалектика абсолютного и относительногоу Нисиды Китаро и Танабэ Хадзимэ

The study of philosophical teachings through the prism of intercultural philo­sophical dialogue provides an opportunity for a broader view of the history of philosophy overcoming the framework of the East-West dichotomy the limita­tions of which are becoming more and more obvious over time. This article is a further step in this direction. It demonstrates what aspects of Hegel’s thought were taken by Japanese thinkers of Kyoto School and how they were developed in new philosophical and cultural context. In particular, such moments as the concepts of the unity of logic and metaphysics, logic and the historical pro­cess, the scheme of correlation of the absolute and the world, the principles of negation, double negation, contradiction, the dialectic of identity and difference, direct and mediation, individual, special and universal, became the object of con­sideration. The author makes an attempt to reveal the mechanisms of perception and adaptation of elements of a seemingly completely alien religious and cultural tradition. She offers her vision of character and degree of Hegel’s influence upon Nishida Kitaro and Tanabe Hajime, arguing that the points in the teachings of the German philosopher relevant to the key doctrines of Mahayana Buddhism were most attractive to them. The article concludes that Japanese thinkers, not being followers of Hegel, nevertheless made extensive use of his conceptual tools, approaches, and logical constructions to express their own ideas. Equally important is the fact that the appeal of Japanese philosophers to Hegel allowed them to more clearly define their own position regarding the central idea of their philosophy.

POLA PEMBENTUKAN KALIMAT DENGAN NEGASI DALAM BAHASA SASAK

Negasi merupakan bentuk penyangkalan atau peniadaan. Peniadaan menggunakan kata sangkalan yang merujuk pada sesuatu yang telah terjadi atau yang belum terjadi. Tulisan ini bertujuan mengungkapkan pola pembentukan kalimat dengan negasi yang terdapat dalam referensi tertulis bahasa Sasak. Dengan demikian, pendekatan deskriptif kualitatif dianggap paling sesuai untuk tulisan ini. Data diperoleh menggunakan metode simak yang diterapkan pada buku muatan lokal bahasa Sasak kelas 7, 8, dan 9. Data yang dikumpulkan berupa kalimat dengan unsur negasi. Semua pelajaran (1—16) pada setiap jenjang diambil. Data tersebut dianalisis menggunakan metode padan intralingual dengan teknik hubung banding menyamakan (HBS) dan hubung banding membedakan (HBB). Metode tersebut bertujuan mengelompokkan kalimat berdasarkan posisi pemarkah negasinya. Tahapan tersebut dilanjutkan dengan mengerucutkan pengelompokan tersebut menjadi kalimat bernegasi tunggal atau ganda dengan satu verba atau lebih. Simpulan berdasarkan kajian tersebut adalah negasi dalam bahasa Sasak memperkuat sistem topikalisasi yang menjadi ciri bahasa Sasak yang mengedepankan topik pembicaraan.

ФЕНОМЕНОЛОГИЧЕСКАЯ ОНТОЛОГИЯ СУЖДЕНИЯ И ОТРИЦАНИЯ

In the present article we consider the phenomenological conception of judgement and negation in relation to the origin of scientific objectivation. Basing on the later works of Edmund Husserl and on earlier as well as fundamental-ontological period of Martin Heidegger’s thought, analysis of onto-logical status and cognitive value of negative judgements is undertaken. Thus, our investigation addressing the issue of logic as Wissenschaftlehre, goes on to consider the question of the necessary modalization of judgement as manifestation of the scientist’s critical attitude to the world. We set forth the topicalization of judgement in traditional logic understood as the science of science. Through pointing out the intentionality of judgemental activity, we carry out a problematization of negative judgements. At first, our research addresses Heidegger’s fundamental ontology for the clarification of the relation between negation and Nothing, as well as the thesis of ontological difference and the existentials of anxiety (Angst) and being-in-the-world (In-der-Welt-Sein). Attention is also paid to the early academic work of the German thinker where the hermeneutics of negation reaches the originally bimodal character of the copula. After that, this sense-investigation continues within the framework of Husserl’s genetic phenomenology, according to which the origin of judgement in the form “S is not P” is shown to lie in the reality of experience. Both the secondary intentional character of negation and the fundamentality of the normal perception and, consequently, of affirmation is proved. We demonstrate the impossibility of finding out the pre-predicative root for double negation and the proximity of the potential conclusions to the non-classic intuitionist logic. Finally, we make an attempt to explicate the results in the given context of the philosophical foundations of scientific knowledge.

Equality propositional logic and its extensions

We introduce a new formal logic, called equality propositional logic. It has two basic connectives, $boldsymbol{wedge}$ (conjunction) and $equiv$ (equivalence). Moreover, the $Rightarrow$ (implication) connective can be derived as $ARightarrow B:=(Aboldsymbol{wedge}B)equiv A$. We formulate the equality propositional logic and demonstrate that the resulting logic has reasonable properties such as Modus Ponens(MP) rule, Hypothetical Syllogism(HS) rule and completeness, etc. Especially, we provide two ways to prove the completeness of this logic system. We also introduce two extensions of equality propositional logic. The first one is involutive equality propositional logic, which is equality propositional logic with double negation. The second one adds prelinearity which is rich enough to enjoy the strong completeness property. Finally, we introduce additional connective $Delta$(delta) in equality propositional logic and demonstrate that the resulting logic holds soundness and completeness.