The logic IK is the intuitionistic variant of modal logic introduced by Fischer Servi, Plotkin and Stirling, and studied by Simpson. This logic is considered a fundamental intuitionistic modal system as it corresponds, modulo the standard translation, to a fragment of intuitionistic first-order logic. In this paper we present a label-free bi-nested sequent calculus for IK. This proof system comprises two kinds of nesting, corresponding to the two relations of bi-relational models for IK: a pre-order relation, from intuitionistic models, and a binary relation, akin to the accessibility relation of Kripke models. The calculus provides a decision procedure for IK by means of a suitable proof-search strategy. This is the first label-free calculus for IK which allows direct counter-model extraction: from a single failed derivation, it is possible to construct a finite countermodel for the formula at the root. We further show the bi-nested calculus can simulate both the (standard) nested calculus and labelled sequent calculus, which are two best known calculi proposed in the literature for IK.

With the diversification of social media, WeChat status has become a significant channel for young people to document their daily life. This study adopts a literature review and online ethnography, based on Goffman's dramaturgical theory, to investigate users' self-presentation and identity construction on WeChat status. By analyzing a number of WeChat status updates collected from November 2025 to January 2026, this paper examines how the media features of WeChat status shape users' self-presentation strategies and the underlying logic of digital identity construction. The findings indicate that the immediacy, semi-privacy and weak interaction of WeChat status provide users with a low-pressure expressive space. Users flexibly adjust their self-presentation between intimate social relations and real-life pressure through strategies including circle adaptation, dynamic expression and permission management. WeChat status can be regarded as a transitional zone between the front stage and back stage in daily digital interaction, which mirrors the genuine needs of contemporary young people for self-exploration and emotional expression in the digital era.

With the rapid development of e-commerce platforms, many ordinary dates have gradually changed into people's shopping festivals. This conceals a profound cultural logic behind it. This research tries to explore the inherent logic of the e-commerce platform's construction of the "520" e-commerce festival and the contradictory feelings of consumers about such e-commerce festivals. This study is based on the "invented tradition" theory and employs two research methods for a combined analysis. The research method uses text analysis to analyze and decode advertising slogans to show how businesses can shape a "sense of ritual" through time limitation and symbolism. At the same time, an online questionnaire survey was conducted among the target audience to find out their recognition of the "520" ritualistic feelings and the emotional pressure they experienced. The study found that commercial capital uses symbols and emotional bindings to rationalize consumption behavior and uses time-limited words to create anxiety. The questionnaire survey shows that although consumers have a strong agreement with the rituals, they also feel the pressure from society and experience emotional anxiety. This study finally pointed out that the "520" consumption festival is an "emotional ritual" built by the business system. Its inherent logic is to connect consumers' emotions to consumption, showing the mechanism of commercial operation of emotions in the digital age.

Kindergarten curriculum construction occupies a pivotal position in early childhood education, as the decisions made regarding curriculum content, design logic, and foundational starting points carry far-reaching implications for children's development, learning trajectories, and long-term life outcomes. This review examines the theoretical and empirical literature on the logic and starting points that underpin kindergarten curriculum construction, synthesising diverse perspectives drawn from developmental psychology, sociocultural theory, comparative education, and curriculum studies. Using a narrative review approach, the paper analyses peer-reviewed and policy-related literature selected from major academic databases to identify recurrent curriculum logics, foundational starting points, and points of tension across international scholarship. Drawing on scholarly work spanning multiple national contexts, the review identifies four principal starting points for curriculum construction: the child as a developing being, sociocultural and community contexts, structured knowledge domains, and value-laden educational goals. Its main analytical contribution is to bring these starting points into a single comparative framework and to show how they interact with competing curriculum logics rather than functioning as isolated or mutually exclusive foundations for curriculum design. The dominant logics shaping curriculum design — including child-centred, subject-centred, play-based, and emergent curriculum logics — are analysed alongside the tensions and complementarities between these perspectives. Comparative analyses of curriculum models from Nordic, Anglo-Saxon, East Asian, and Reggio Emilia traditions illuminate how socio-political contexts shape curriculum philosophy and practice. Contemporary challenges, including the growing pressure for academic readiness, the demand for inclusive and equitable curricula, and the implications of digitalisation, are also addressed. The review concludes that a coherent and ethically grounded logic for kindergarten curriculum construction must integrate developmental appropriateness, cultural relevance, professional agency, and a holistic conception of the child as simultaneously a being and a becoming.

In this study, Charentsavan (Kotayk province, Armenia) is considered a bottom-up Soviet industrial city, whose material infrastructure and symbolic identity were created simultaneously through industrialization, mass housing construction, and cultural myth-making. The study explores how the “new city” arose and what makes Charentsavan noteworthy not only in the Armenian context. The research adopts a micro-historical and semiotic approach. The city is considered a semiotic object. The toponymy (Lusavan/Charentsavan), naming practices, and urban narratives were analyzed as tools of symbolic construction. The empirical basis includes archival visual materials documenting Soviet-era construction and everyday urban spaces. Furthermore, literary and essayistic texts in Armenian were studied, particularly the anthology Gangraher Tghayi Kaghaky: Aknarkner Yev Banasteghtsut’yunner [Curly Boy’s City: Essays and Poems] (1987), as well as the collection of memoirs (2007). This corpus of texts was read using Peirce’s discursive analysis and semiotics, which is based on the relationship between the representative, the interpretant, and the object. Additionally, a demographic analysis of the context was conducted. Industrial data was used to reconstruct the logic of rapid urban growth and housing construction. The analysis revealed that Soviet Charentsavan was shaped by a planned industrial and urban structure, including factories, transportation, and residential areas, as well as a mythological foundation. This is evident in the 1967 renaming of Lusavan in honor of the rehabilitated poet Yeghishe Charents. This toponymic shift altered the ideological codes of modernity, labor, and collective memory, uniting a diverse population under an industrial civic identity. By providing English-speaking researchers with a Soviet Armenian corpus of scientifically based, propagandistic texts about the city, the study broadens the comparative discussion about Soviet mass housing and urban heritage. Thus, this study demonstrates how industrial projects create sustainable symbols of the city, beyond just architectural forms.

The in-depth development of green buildings has introduced new requirements for the knowledge structure of architecture professionals, and the traditional course model of building physics, which teaches by sub-disciplines based on physical phenomena, struggles to meet the demands of green building design centered on comprehensive performance optimization. To this end, this study aims to construct a modular teaching system for the building physics course under the guidance of green building. The research first analyzes the intrinsic relationship between green building performance goals and the core elements of building physics, pointing out that modern teaching needs to complete a paradigm shift from "element decomposition" to "system integration." On this basis, this study proposes a modular knowledge restructuring strategy based on problem orientation and system integration, and elaborates in detail on the construction logic of core modules such as the integration of thermal environment and energy consumption regulation, as well as the synergy of light, sound environment and spatial quality. Furthermore, this study plans the logical connection of module sequences and the dynamic teaching process, and explores the teaching strategy of deeply embedding performance simulation tools into design tasks. The research also designs a multi-dimensional feedback mechanism covering knowledge, skills, and thinking to drive the self-optimization of the teaching system. This system aims to transform building physics knowledge from isolated calculation and verification into the core competence and thinking framework that drives innovative green building design.

Integrated Accounting, Control and Analysis System: Structural Conceptualization and Construction Logic

This study uses a process-based technical approach combining X-ray radiography, visible and raking-light examination, and cross-modal image comparison to assess the construction logic of a Cubist-period painting associated with Pablo Picasso. Across the X-ray dataset, the painting shows orientation-dependent structural coherence, hierarchically organized planning seams with mechanically sensible terminations, and a multistage base-layer construction that remains interpretable under grayscale inversion and rotation. Visible and raking-light images reveal physically incised inscriptions, names, places, and numerals with later paint settling into grooves and, in some areas, bridging over them, establishing a clear sequence in which inscriptions precede overpainting. Reduced color and polarity-inversion checks confirm that these features are carried by luminance and surface relief rather than color artifacts. Together, these converging lines of evidence support an interpretation of a multi-campaign, orientation-aware construction process consistent with documented working methods from Picasso’s relevant period and difficult to replicate by superficial imitation.

The relevance of the article is due to the spatial turn in the humanities which has fundamentally reoriented scholarly understandings of spatial marginality, moving away from economic and geographical determinism to conceptualizing it as a complex product of cultural and symbolic construction. The aim of the article is to identify and analyze the discursive mechanisms of constructing spatial marginality using the example of Inner Mongolia, China, as a complex, historically changing phenomenon. The stated goal predetermines the tasks: 1) to identify the mechanisms of discursive construction of Inner Mongolia as the Borderland in the imperial period; 2) to analyze the transformation of the Province mode in the republican period; 3) to trace how, after 1949, the Periphery and Province modes became dominant, conditioned by the logic of socialist construction; 4) to formulate the concept of integrative marginality as a hybrid regime of territory. The research materials include a corpus of official narratives of the Chinese authorities (government documents, legal acts, policy directives, and political rhetoric), as well as a wide pool of foreign and Russian works on the history of the integration of Inner Mongolia. Methodologically, the study utilizes a critical discourse analysis of official state narratives spanning three distinct historical-political formations — the Qing Empire (since 1636), the Republic of China, and the contemporary People's Republic of China — as well as a decomposition method based on the adapted version of Vladimir Kagansky's cultural landscape matrices model. The result of the study and its key empirical and theoretical contribution is the development of an original four-modal analytical model of spatial marginality and the formulation of its central theoretical concept integrative marginality, describing a sustainable reproduction of the subordinate status of Inner Mongolia through its gradual incorporation within the “homogenous” Chinese Nation. The study concludes that during the imperial period, marginality was constructed primarily through the Borderland mode, based on a Sino-centric perception of the region as a dangerous Other. During the republican period, the crisis of central authority led to a fierce struggle to define the Province mode, making the region a field of clashing external interests. With the establishment of the Communist Party of China (CPC), the logic of dual—economic and cultural-political — integration became dominant. The current stage is characterized by the formation of a hybrid regime of integrative marginality, where the full administrative-economic inclusion of the region is combined with the persistent reproduction of its symbolic subordination through the combination and fusion of all four modes.

Aiming at the practical dilemmas of insufficient cultural infiltration and disjointed literacy cultivation in the construction of quality curriculum systems for maritime majors in higher vocational colleges, this study takes the dual integration of maritime culture and professional literacy as the core research perspective. By adopting the research methods of literature review, case analysis and field investigation, it systematically combs the theoretical connotation and educational value of dual integration-oriented education, conducts an in-depth analysis of the internal construction logic of the quality curriculum system, and explores operable practical implementation paths. The research results show that the construction of the dual integration-driven quality curriculum system must be rooted in the industrial characteristics and post demands of the maritime field, and can be realized through the progressive logical chain of core element identification → dual integration logical coupling → three-dimensional framework construction. The three-dimensional practical path of scenario-based implantation + school-enterprise collaborative education + data-driven dynamic optimization constructed in this study can effectively improve the industry adaptability of maritime talent cultivation and the systematisms of coordinated education between culture and literacy. This research provides theoretical support and practical paradigms for the high-quality reform of quality curriculum systems for maritime majors in higher vocational colleges, and also offers a reference for the integration of professional culture and literacy cultivation in vocational education.

Mechanical computing represents a highly promising paradigm for environment-adaptive information processing. However, existing implementations are generally constrained by limited architectural scalability, and their modes of application in practical scenarios remain insufficiently defined. Here, we develop a light-programmable mechanical computing system that not only performs scalable logic operations but also enables environment-adaptive optical camouflage. The system is based on a polyaniline composite film (PCF) that integrates light-responsive expansion-contraction elements with a flexible conductive layer. Light illumination dynamically modulates the conductive pathways, giving rise to optically controlled single-pole single-throw (SPST) and single-pole double-throw (SPDT) relays that reconfigure signal transmission routes. Interconnecting these relays enables the construction of basic logic gates and 2-bit full-adder circuits, establishing a scalable paradigm for light-programmable mechanical computation. Moreover, we implement an adaptive camouflage function that senses environmental textures and generates matching optical patterns, demonstrating potential for intelligent skin applications capable of environmental interaction. This work establishes a light-programmable, pathway-reconfigurable mechanical computing framework, expanding possibilities for autonomous and adaptive intelligent systems.

Abstract Following a suggestion of Birkhoff & von Neumann [Ann. Math. 1936;37:23–32], we pursue a joint study of quantum logic and intuitionistic logic. We exhibit a linear-time translation which for each quantum logic Q and each superintuitionistic logic I yields an axiomatization of Q∩I from axiomatizations of Q and I. The translation is centred around a certain axiom (Ex) which (together with introduction and elimination rules for connectives) is shown to axiomatize the intersection of orthologic and intuitionistic logic, solving a problem of Holliday [Logics 2023;1:36–79]. We prove that the lattice of all super-Ex logics is isomorphic to the product of the lattices of quantum logics and superintuitionistic logics. We prove that there are infinitely many sub-Ex logics extending Holliday’s fundamental logic.

Under the multiple backgrounds of global geopolitical conflicts, supply chain fluctuations and the deepening of the "dual carbon goals", the coordinated promotion of enterprise operational resilience and sustainable development has become the key to survival and development. As a new production factor, data provides technical support and practical pathways for the deep integration of the two. From the perspective of data, this paper analyzes the internal relationship between enterprise operational resilience and sustainable development, reveals the core logic of data-driven resilience construction, combs the practical directions such as supply chain collaboration, production optimization, and ecological linkage, analyzes the practical obstacles such as data silos, compliance costs, and talent gaps, and extracts implications from the real practice of the industry. Research shows that data-lifecycle management can effectively improve enterprise risk resistance and resource utilization efficiency, provide feasible solutions for enterprises to achieve the dual goals of "risk resistance" and "green transition or green development", and provide references for the transformation of enterprises of different sizes and industries.

The aim of this paper is to make the philosophical point explicit that the sequent calculus as such is a formal metatheory for classical reasoning about the derivability relation in natural deduction. As a consequence, it is neither suitable for foundational intuitionistic research on intuitionistic logic(s) nor adequate as a basis of intuitionistic proof-theoretic semantics.

Recently, Large Language Models (LLMs) have shown promising results in code generation, and several automated test generation approaches based on LLMs have been proposed. Although these approaches achieve promising performance, they suffer from two limitations. First, they lack the intrinsic understanding of the semantic intricacies and logical constructs inherent to the focal method. Second, they ignore the diversity of the generated tests and generate tests with limited code coverage. To alleviate these two limitations, in this work, we propose a novel approach named TestCTRL that optimizes LLMs for unit test generation by the Chain-of-Thought (CoT) prompt and Reinforcement Learning (RL) strategy. Specifically, we first build a new CoT dataset, containing the focal methods, corresponding unit tests, and CoT prompts. The CoT prompt includes the intention and possible test input values. Then, the CoT dataset is used to fine-tune one LLM (i.e., CodeLlama 7B) that can be seen as the policy model in RL. Meanwhile, we fine-tune another LLM (i.e., CodeGPT) as the reward model by predicting the line coverage of the focal method and its test. Moreover, we employ the Proximal Policy Optimization (PPO) algorithm to optimize the policy model and generate unit tests. We use the Defects4J benchmark to evaluate our approach from three perspectives (i.e., naturalness, validity, and code coverage). To avoid data leakage threats, we filtered out data from the CoT dataset that have the same focal method and test case names as those in the Defects4J. The experimental results demonstrate that TestCTRL outperforms state-of-the-art baselines in line and branch coverages, respectively. Besides, TestCTRL improves bug detection performance. We also investigate the reason for the proposed approach’s superiority.

(1) Background: The Ming dynasty represented the peak period in the artistic development of drama printed editions, with Suzhou editions being particularly representative. In the course of localized evolution, these illustrations not only absorbed the brushwork techniques of the Wu School of painting but also integrated the literary sensibilities and aesthetic ideals of Suzhou-based writers, thereby forming an aesthetic character that combined literati elegance with secular expressiveness. In terms of visual representation, Suzhou illustrators and engravers paid particular attention to the depiction of Jiangnan garden landscapes. According to statistical analysis of more than 200 surviving illustrated drama printed editions from Ming-dynasty Suzhou, architectural landscape images account for 98%, making them the dominant visual type in regional printed illustrations. Taking this corpus of architectural landscape illustrations as its research object, this study explores their visual construction logic and spatial patterns within the developmental trajectory of printed drama illustrations. (2) Methods: This study adopts an integrated methodological approach combining iconographic analysis and visual narrative theory. Through documentary research and textual verification, it examines the contextual conditions underlying the formation of architectural landscape visual schemas. Case study analysis is further employed to investigate the morphological typologies and visual rhetoric embodied in these images. (3) Results: Architectural landscape illustrations exhibit clear characteristics of formalization in terms of schema typology, compositional structure, and layout conventions. Their representational language, decorative motifs, and spatial organization collectively enhance the immediacy and lyrical quality of the imagetext narrative system. These features reflect deeper cultural tendencies in Ming society, particularly the growing emphasis on individual emotional expression and the aesthetic refinement of everyday living spaces. (4) Conclusion: Influenced by the emergence of early capitalist economic forms and the convergence of elite and popular cultural traditions, architectural landscape schemas in Ming drama printed editions extensively assimilated techniques from traditional painting as well as engraving practices associated with the Jinling and Huizhou publishing schools. Drawing upon Jiangnan gardens as their primary visual prototype, these illustrations established a distinctive visual paradigm for architectural landscape representation. At the narrative level, they were profoundly shaped by the concept of expressive representation (xieyi) and literati aesthetics, achieving both the visual translation of textual narratives and the construction of poetic aesthetic realms within the visual narrative field.

ABSTRACT Architectural form can be understood as the outcome of an interaction between formal and stylistic dimensions. The formal dimension addresses geometry, proportion, materiality, and tectonic articulation, in which tectonic form is associated with the constructive logic of assembling architectural elements, while stereotomic form is characterized by mass and continuity. The stylistic dimension reflects regional, temporal, climatic, and cultural conditions and develops through processes of contextual adaptation rather than direct imitation. In modern architecture, form is shaped by structural systems, material properties, and functional and environmental requirements. These factors influence spatial organization and contribute to the perceptual experience of architecture. While architectural space may be understood through phenomenological approaches, this study focuses primarily on tectonic expression as an analytical framework for examining architectural form. Based on theoretical perspectives developed by Bötticher, Semper, Wölfflin, Giedion, and Schmarsow, this paper investigates the relationship between tectonic form, spatial structure, and cultural context in modern architecture. The French Embassy in Seoul, designed by Kim Chung up, is examined as a case study, with particular attention to the chancery and residence. Through an analysis of structural articulation, and spatial organization, discusses how modern architectural form can mediate between international modernist principles and regional architectural traditions.

It was proved by Maksimova in 1977 that exactly eight varieties of Heyting algebras have the amalgamation property, and hence exactly eight axiomatic extensions of intuitionistic propositional logic have the deductive interpolation property. The prevalence of the deductive interpolation property for axiomatic extensions of substructural logics and the amalgamation property for varieties of pointed residuated lattices, their equivalent algebraic semantics, is far less well understood, however. Taking as our starting point a formulation of intuitionistic propositional logic as the full Lambek calculus with exchange, weakening, and contraction, we investigate the role of the exchange rule--algebraically, the commutativity law--in determining the scope of these properties. First, we show that there are continuum-many varieties of idempotent semilinear residuated lattices that have the amalgamation property and contain non-commutative members, and hence continuum-many axiomatic extensions of the corresponding logic that have the deductive interpolation property in which exchange is not derivable. We then show that, in contrast, exactly sixty varieties of commutative idempotent semilinear residuated lattices have the amalgamation property, and hence exactly sixty axiomatic extensions of the corresponding logic with exchange have the deductive interpolation property. From this latter result, it follows also that there are exactly sixty varieties of commutative idempotent semilinear residuated lattices whose first-order theories have a model completion.

ABSTRACT ‘If you cannot explain a concept to a six-year-old child, it means you do not fully understand it.' This study investigates the 'Les Petits Constructeurs' program, where architecture Master’s students are tasked with transmitted complex concepts of structural morphology and construction logic to children aged 6-10. Research aims to determine if this mediation enhances students' technical understanding. A comparative evaluation with a control group reveals that students involved in teaching children showed a significantly higher progression in technical knowledge acquisition. Paradoxically, their self-reported confidence and perception of the discipline exhibited limited variation, highlighting a dissociation between measured learning outcomes and perceived competence. Ultimately, the findings suggest that knowledge mediation—simplifying expertise for a non-specialist audience—is a powerful pedagogical tool. It enhances conceptual clarity more effectively than standard methods, proving that the challenge of explaining “how things hold up” to a six-year-old is a rigorous path to professional expertise.

This paper explores the mathematical properties, advanced applications, and theoretical contributions of Intuitionistic L-Fuzzy Sets of Third Type (ILFSTTs), an extension of traditional fuzzy set theory that incorporates three degrees of uncertainty—membership, non-membership, and uncertainty. Building on the concept of Intuitionistic Fuzzy Sets (IFS) and Type-3 Fuzzy Logic Systems (T3FLSs), ILFSTTs provide a more nuanced approach to modeling uncertainty in real-world systems, particularly in dynamic, nonlinear, and complex environments. The paper presents formal definitions and operations for ILFSTTs, including union, intersection, complement, and support, and demonstrates their closure and stability under these operations. Theoretical results are validated through two novel theorems that establish the stability of ILFSTTs under union and intersection, as well as their adherence to De Morgan’s laws for complementation. These findings ensure that ILFSTTs are mathematically consistent and robust for handling higher-order uncertainties. Additionally, the paper showcases practical applications of ILFSTTs in control systems, robotics, and predictive modeling, where ILFSTT-based models outperform traditional fuzzy systems in terms of accuracy, adaptability, and predictive reliability. A bibliometric analysis is also conducted to identify emerging trends and research directions in the field of type-3 fuzzy logic systems. This research highlights the potential of ILFSTTs as a powerful tool for intelligent systems, offering a robust framework for managing complex uncertainties in a wide range of applications