Intuitionistic Logic Research Articles

Meaning and identity of proofs in a bilateralist setting: A two-sorted typed Lambda-calculus for proofs and refutations

Abstract In this paper, I will develop a $\lambda $-term calculus, $\lambda ^{2Int}$, for a bi-intuitionistic logic and discuss its implications for the notions of sense and denotation of derivations in a bilateralist setting. Thus, I will use the Curry–Howard correspondence, which has been well-established between the simply typed $\lambda $-calculus and natural deduction systems for intuitionistic logic, and apply it to a bilateralist proof system displaying two derivability relations, one for proving and one for refuting. The basis will be the natural deduction system of Wansing’s bi-intuitionistic logic 2Int, which I will turn into a term-annotated form. Therefore, we need a type theory that extends to a two-sorted typed $\lambda $-calculus. I will present such a term-annotated proof system for 2Int and prove a Dualization Theorem relating proofs and refutations in this system. On the basis of these formal results, I will argue that this gives us interesting insights into questions about sense and denotation as well as synonymy and identity of proofs from a bilateralist point of view.

A Hypersensitive Intelligent Filter for Detecting Explicit Content in Learning Environments

In today’s digital age, educational institutions aim to ensure safe learning environments in the light of pervasive explicit and inappropriate content. This study proposes an innovative approach to enhance safety by integrating convolutional neural networks (CNNs) for visual analysis with an intuitionistic fuzzy logic (IFL) filter for explicit content identification. Additionally, it utilizes GPT-3 to generate contextual warnings for users. A large-scale dataset comprising explicit and educational materials is used to evaluate the system. The results show that this hypersensitive filter has high accuracy performance, particularly in handling ambiguous or borderline content. The proposed approach provides an advanced solution to tackle the challenges of detecting explicit content and promotes safer learning environments by showcasing the potential of combining generative AI techniques across various domains.

Semiconic idempotent logic I: Structure and local deduction theorems

Semiconic idempotent logic is a common generalization of intuitionistic logic, relevance logic with mingle, and semilinear idempotent logic. It is an algebraizable logic and it admits a cut-free hypersequent calculus. We give a structural decomposition of its characteristic algebraic semantics, conic idempotent residuated lattices, showing that each of these is an ordinal sum of simpler partially ordered structures. This ordinal sum is indexed by a totally ordered residuated lattice, which serves as its skeleton and is both a subalgebra and nuclear image. We equationally characterize the totally ordered residuated lattices appearing as such skeletons. Further, we describe both congruence and subalgebra generation in conic idempotent residuated lattices, proving that every variety generated by these enjoys the congruence extension property. In particular, this holds for semilinear idempotent residuated lattices. Based on this analysis, we obtain a local deduction theorem for semiconic idempotent logic, which also specializes to semilinear idempotent logic.

Effect of Liquid Fertilizer on Seedling Enhalus acoroides Seeds (Linnaeus f.) Royle 1839 (Fam: Hydrocharitaceae)

The decrease in seagrass coverage and ecosystem harm to seagrass meadows is an annual occurrence resulting from both natural and human activities. Seagrass seeding has been deemed an effective restoration method, but its application is restricted by suboptimal environmental conditions and constraints associated with directly planting seagrass seeds in their natural habitat. The influence of environmental parameters, particularly nutrients, significantly affect on seagrass seed survival. NPK liquid fertilizer is commonly used in aquatic plants and is readily accessible in the market. It serves as a crucial source of macronutrients for seagrass. This study investigates the impact of different concentrations of NPK liquid fertilizer on the survival rate, growth, and chlorophyll, a content of E. acoroides seedlings. The study took place between March and May 2023 at the marine biology laboratory of the marine science study program at Diponegoro University's Faculty of Fisheries and Marine Science. According to the Manova statistical test, the NPK liquid fertilizer had an impact on the growth rate, biomass, and chlorophyll-a. The seagrass seeding container of E. acoroides treated with a liquid fertilizer concentration of 4.5 ml/100l exhibited the highest average growth rate of 0.29 cm/day and a chlorophyll-a value of 12.395 mg/g, with a survival rate of 100%. Causal connections between statements ensure logical construction. In contrast, seedlings without liquid fertilizer treatment showed the lowest growth rate of 0.19 cm/day and chlorophyll-a values of 5.169 mg/g, with a survival rate of 85.19%. Technical term abbreviations such as 'cm/day' and 'mg/g' are explained when first used to ensure clarity. Based on these findings, using liquid fertilizer with a concentration of 4.5 ml/l exhibits potential for restoring seagrass ecosystems.

Urban identity and perception of the city in management discourse

The discourse on the city, its forms, planning and management under uncertainty is undoubtedly the most widespread and relevant in the last ten years. The prospects for the development of the city and its urban community depend rather on the articulation and representation of the content of social demand from society, the population of specific cities, than on external factors. Citizens have a clear vision for the future and present of their city. The city perception of its inhabitants is correlated with the citizens’ ideas about the modern city and appears as a discourse in their judgments, opinions and assessments. Urban discourse is defined as positioning, representation of urban identity of citizens and reflection of the perception of the city identity. The presence of this discourse is found in the citizens’ narratives about the city. The study is based on the personal experience narratives, specifically the informants’ reflections upon their evaluation and perception of their city were analyzed. Narrative analysis, supplemented by sentiment analysis (positive or negative presentation of the material) was chosen as a research tactic, the research method is content analysis. The major purpose of this work is to study the perception of the identity of the city by citizens. The novelty of the work is determined by the design of the study, combining qualitative and quantitative approaches, the method of triangulation according to N. Denzin., as well as the choice of a subjective parameter (perception by citizens of their city) as a guideline for managerial actions in shaping the identity of the city in order to achieve connectivity “city – citizen”. An additional contribution of this paper is the construction of a paired logic of connectivity: “city – citizen” through the correlation between the citizens urban identity indicators and the identity of the city on the basis of empirical data of six cities in the Tyumen region. The study showed that citizens with a high level of urban identity perceive the city through personal participation in its life, through the manifestation of subjectivity.

The Operation Logic of Constructing China's National Original IP to Empower the Peripheral Design of Game Brands: Based on the Case Investigation of Mihoyo

Game original IP, especially China's national original IP, has become a new momentum in the game industry, and with the attention of game companies to IP cultivation, the IP derivatives market has also developed accordingly. The construction of game brand's national original IP and the application of construction results are two important stages to realize the design of China's national original IP-empowered brand peripheral products, and the summary and analysis of a set of thinking models will intuitively show the operational logic of empowerment, which will help the original innovative dissemination of Chinese traditional culture through interactive media works such as games, and guide the smooth promotion of brand IP marketing. This paper uses a case study of Genshin Impact IP under Mihoyo brand, summarizes the thinking model according to the topic of this paper by progressively studying the IP construction logic and the application mode of IP empowerment peripheral products after construction, sorts out the IP architecture and the general theoretical logic of each stage of the task, summarizes the core "carrier + concept" of national original IP construction, and discusses in detail the thinking factors and methodologies of national original IP construction in the main work IP stage, derivative IP stage, and peripheral product service stage.

Logical Intuitive Aspect of the Story in the Quran: Sayyid Quthb’s Perspective

The content explains the intuitive and logical aspects of the stories in the Koran. Intuition is a source of knowledge based on belief and experience. This dimension is found in the story of the Qur'an in various forms, initially in nature and unseen. It cannot be measured, but ultimately, it becomes logical because it is based on the laws that apply in society and can be validated through modern scientific approaches. It is what is called logical Intuition. This intuitive, logical aspect is found in Qur'an stories, which are attached to the principal or supporting characters and the story's plot. It is not revealed in the storyline, characterization, and message. Different from what was crystallized by Sayyid Quthb. He is an interpreter and writer who is clever at using persuasive narratives to arouse mental awareness and is straightforward so that it can be accepted by reason because it is by the realities of life and the laws that apply and develop in society. Perspective This is used as an approach to show the intuitive and logical aspects of the stories in the Qur'an.

Symmetric and conflated intuitionistic logics

Abstract Two new propositional non-classical logics, referred to as symmetric intuitionistic logic (SIL) and conflated intuitionistic logic (CIL), are introduced as indexed and non-indexed Gentzen-style sequent calculi. SIL is regarded as a natural hybrid logic combining intuitionistic and dual-intuitionistic logics, whereas CIL is regarded as a variant of intuitionistic paraconsistent logic with conflation and without paraconsistent negation. The cut-elimination theorems for SIL and CIL are proved. CIL is shown to be conservative over SIL.

The Translation of (Jadal)Argumentation (Dialectic) Discourse in the Holy Qur’an into English: An Investigation of the Logical Construction of Dialectic in the Source Text

The present research seeks to investigate the equivalence of translating argumentative topics, which include the dialectic (controversial) style in the Holy Qur’an. It designs to know how the discourse of the Qur’anic controversy is manifested, based on a set of logical arguments and points of view. The research also aims to find out the extent to which the English translations succeeded in conveying the same dialectical logical structure connotation, taking into account the challenges faced by the translators: Hilali, Khan, and Abdel Haleem in translating the meanings of the Holy Qur’an, especially the dialectic style. Therefore, the translator must strive to convey the dialectical discourse with its stylistic features in terms of clarity, accuracy, and objectivity. The study adopts an eclectic method. It is a combination of a semantic approach, text discussion, analysis, and extracting a suggested translation, with applying the back-translation technique. All of this is in light of an applied approach to examples of the Holy Ayat (verses) for the controversial style. The study concluded that translating of the dialectical style and its links represent a real challenge for translators. So, they must resort to consult exegesis (tafsir), rhetoric books and other Arabic sources, in addition to the translation theories to overcome these challenges. The study recommends that the translator of the meanings of the Holy Qur’an must be familiar with the sciences of the Holy Qur’an and the Arabic language, such as interpretation, rhetoric, etc. The translator also need to seek help from language dictionaries to choose the specific meaning of the dialectical style. Moreover, the translator, before embarking on the translation, must consult scholars and experts when submitting a suggested translation. This suggested translation must be emanating from authentic Islamic visions. This due to verify the intended Qur’anic meaning for argumentative (Al-Hajjaj) dialectical and others rhetorical styles.

Base-extension semantics for modal logic

Abstract In proof-theoretic semantics, meaning is based on inference. It may seen as the mathematical expression of the inferentialist interpretation of logic. Much recent work has focused on base-extension semantics, in which the validity of formulas is given by an inductive definition generated by provability in a ‘base’ of atomic rules. Base-extension semantics for classical and intuitionistic propositional logic have been explored by several authors. In this paper, we develop base-extension semantics for the classical propositional modal systems $K$, $KT$, $K4$ and $S4$, with $\square $ as the primary modal operator. We establish appropriate soundness and completeness theorems and establish the duality between $\square $ and a natural presentation of $\lozenge $. We also show that our semantics is in its current form not complete with respect to euclidean modal logics. Our formulation makes essential use of relational structures on bases.

Development of Synthesis as a General Logical Method of Cognition in the Process of Teaching Mathematics of Students and Future Teachers

General logical cognitive actions form the basis of almost all cognitive methods. This determines the necessity of their purposeful formation in the process of subject teaching. A special role in the development of cognitive methods belongs to mathematics, in the process of teaching which these actions manifest themselves in the most explicit form. In the article we consider the formation of synthesis as a basic general logical method. The purpose of our study is to develop approaches to the organization of subject-based teaching aimed at the formation and development of synthetic thinking of school students and teacher education students. The methodology of the research is the theory of funding of logical constructions, developed on the basis of the concept of funding in education (V. D. Shadrikov, E. I. Smirnov). The results of the study. Examples demonstrating the main types of synthesis in mathematics learning are considered. These types include: synthesis as a leading action in the construction a mathematical model and synthesis as a representation of a logically justified solution to a problem. The problems of synthesis implementation by students in the process of solving mathematical problems are analyzed. The specificity of educational tasks that contribute to the formation of synthetic thinking is studied. The role of combinatorial tasks as tasks with prevailing logical component in the formation of synthetic thinking of students is described. In conclusion, on the basis of the theory of funding, the typification of types of synthesis in school mathematical education is proposed.

Harnessing Multistability: A Novel Approach to Optical Logic Gate Construction Using Erbium-Doped Fiber Lasers

We present an innovative method harnessing multistability within a diode-pumped erbium-doped fiber laser to construct logic gates. Our approach involves manipulating the intensity of external noise to regulate the probability of transitioning among four concurrent attractors. In this manner, we facilitate the realization of OR, AND, NOR, and NAND logic operations, aligning with the coexisting period-1, period-3, period-4, and period-5 orbits. Employing detrended fluctuation analysis, we establish equilibrium in the probability distributions of these states. The obtained results denote a substantial advancement in the field of optical logic gate development, representing a pivotal stride toward the seamless integration of an all-optical logic gate within laser oscillator-based systems.

Routes to relevance: Philosophies of relevant logics

AbstractRelevant logics are a family of non‐classical logics characterized by the behavior of their implication connectives. Unlike some other non‐classical logics, such as intuitionistic logic, there are multiple philosophical views motivating relevant logics. Further, different views seem to motivate different logics. In this article, we survey five major views motivating the adoption of relevant logics: Use Criterion, sufficiency, meaning containment, theory construction, and truthmaking. We highlight the philosophical differences as well as the different logics they support. We end with some questions for future research.

Reorientation of the Russian fuel and energy complex to new sales markets and changing export opportunities under sanctions pressure: challenges and prospects

The article is devoted to the study of Russia's interaction with key partners in the energy sector after a new round of sanctions pressure from the United States and Western countries. The article hypothesizes that the stability of the Russian fuel and energy sector after the introduction of restrictive measures is associated with the substitution of energy exports to eastern markets. The purpose of the work is to assess the prospects for the development of the fuel and energy complex of the Russian Federation under the conditions of sanctions pressure. The author examines such aspects of the topic as: changes in the volume and directions of exports of Russian energy resources, measures taken by Russian companies and the state to circumvent sanctions. Special attention is paid to the analysis of Russia's trade relations with China and India, including the dynamics of oil and gas exports, the impact of secondary sanctions on the business of these countries, and the adaptation of financial mechanisms to continue cooperation. The problems related to the trade balance and the use of national currencies in mutual settlements are also considered. In this paper, the author analyzes Russia's interaction with key partners in the fuel and energy sector through the paradigm of neorealism in the international relations theory. The methodological basis of this work is a problem-chronological scientific approach. The author also applied other general scientific research methods, including induction and deduction, as well as logical construction based on trend extrapolation. The author concluded that Russia has successfully reoriented energy exports to the markets of China and India after a new round of sanctions pressure in 2022. Secondary US sanctions put pressure on Chinese and Indian companies, in connection with which states refuse to conduct some transactions, but this does not lead to a significant decrease in energy supplies from Russia. The development of trade relations with China and India contributes to the preservation of Russian budget revenues from the oil and gas sector. A special contribution of the author is the analysis of adaptation strategies used by Russia, China and India to circumvent sanctions restrictions. The impact of sanctions on financial mechanisms and the trade balance between these countries is also assessed. At the same time, a comprehensive analysis of current and prospective export directions of Russian energy resources in the context of sanctions pressure has been carried out.

Analysis on the political construction of scale of state-level new areas

The State-level New Area is an emerging type of regional space produced by the national strategy of Regional Coordinated Development in China. It is not a fixed material entity nested in the practice of spatial production, but contains multiple scales of dynamic changes. Therefore, from the multi-dimensional connotations of scale, this paper discusses the internal logic and institutional shaping of political construction of scale. It is suggested that the State-level New Area has the geographic scale characteristics of vast and cross-regional area, the administrative scale characteristics of testability and recursion, and the power scale characteristics of flexibility and flattening. Finally, this paper highlighted that the ‘rigid’ political scale represented by the State-level New Area can directly promote the rise of city-regions, and can establish a new type of ‘central-local’ governance relationship. Thus, it is of great significance for China’s social and economic transformation and regional governance innovation to make good use of the ‘rigid’ scale tool of the State-level New Area.

DEGREE OF SATISFIABILITY IN HEYTING ALGEBRAS

Abstract We investigate degree of satisfiability questions in the context of Heyting algebras and intuitionistic logic. We classify all equations in one free variable with respect to finite satisfiability gap, and determine which common principles of classical logic in multiple free variables have finite satisfiability gap. In particular we prove that, in a finite non-Boolean Heyting algebra, the probability that a randomly chosen element satisfies $x \vee \neg x = \top $ is no larger than $\frac {2}{3}$ . Finally, we generalize our results to infinite Heyting algebras, and present their applications to point-set topology, black-box algebras, and the philosophy of logic.

Combining Intuitionistic and Classical Propositional Logic: Gentzenization and Craig Interpolation

Combining Intuitionistic and Classical Propositional Logic: Gentzenization and Craig Interpolation

Enriched Presheaf Model of Quantum FPC

Selinger gave a superoperator model of a first-order quantum programming language and proved that it is fully definable and hence fully abstract. This paper proposes an extension of the superoperator model to higher-order programs based on modules over superoperators or, equivalently, enriched presheaves over the category of superoperators. The enriched presheaf category can be easily proved to be a model of intuitionistic linear logic with cofree exponential, from which one can cave out a model of classical linear logic by a kind of bi-orthogonality construction. Although the structures of an enriched presheaf category are usually rather complex, a morphism in the classical model can be expressed simply as a matrix of completely positive maps. The model inherits many desirable properties from the superoperator model. A conceptually interesting property is that our model has only a state whose “total probability” is bounded by 1, i.e. ‍does not have a state where true and false each occur with probability 2/3. Another convenient property inherited from the superoperator model is a ωCPO-enrichment. Remarkably, our model has a sufficient structure to interpret arbitrary recursive types by the standard domain theoretic technique. We introduce Quantum FPC , a quantum λ-calculus with recursive types, and prove that our model is a fully abstract model of Quantum FPC.

VULNERABILITIES TRANSPOSED BY CLIMATE CHANGE EFFECTS IN ECOLOGICAL RISKS AND THREATS TO THE NATIONAL SECURITY

Climate changes effects determine major transformations of interactions between socio-economic and natural environment, phenomena that directly affect the overall security (international, national, regional) systems. In the security equation, vulnerabilities in different sectors expose systems to threats and associated risks and their existence represents gaps and malfunctions in assuring systems’ overall resilience. In this paper, we start from the research hypothesis that vulnerabilities are a constitutive element of the climate security equation seen as a logical construction of a causal nature, respectively: the effects of climate changes are the source of ecological threats and associated risks facilitated or multiplied by exploited vulnerabilities whose presence/absence gives the measure of the impact over the respective security system. In this regard, our topic is focused on a narrower subject, namely the identification of vulnerabilities that have the potential to be exploited in generating ecological threats and associated risks against Romanian national security. In order to achieve our goal, concepts like “environmental security”, “climate security”, “ecology”, “climate change”, “vulnerability”, “ecological risks and threats”, and “resilience” will be approached in the capacity of their interdisciplinary entanglement between security and ecology.

Constructive Logic is Connexive and Contradictory

It is widely accepted that there is a clear sense in which the first-order paraconsistent constructive logic with strong negation of Almukdad and Nelson, QN4, is more constructive than intuitionistic first-order logic, QInt. While QInt and QN4 both possess the disjunction property and the existence property as characteristics of constructiveness (or constructivity), QInt lacks certain features of constructiveness enjoyed by QN4, namely the constructible falsity property and the dual of the existence property. This paper deals with the constructiveness of the contra-classical, connexive, paraconsistent, and contradictory non-trivial first-order logic QC, which is a connexive variant of QN4. It is shown that there is a sense in which QC is even more constructive than QN4. The argument focuses on a problem that is mirror-inverted to Raymond Smullyan’s drinker paradox, namely the invalidity of what will be called the drinker truism and its dual in QN4 (and QInt), and on a version of the Brouwer-Heyting-Kolmogorov interpretation of the logical operations that treats proofs and disproofs on a par. The validity of the drinker truism and its dual together with the greater constructiveness of QC in comparison to QN4 may serve as further motivation for the study of connexive logics and suggests that constructive logic is connexive and contradictory (the latter understood as being negation inconsistent).