Hongyu Lin, Samer Abdallah, Makar Valentinov
et al.
Large Language Models (LLMs) have shown strong performance on code understanding tasks, yet they fundamentally lack the ability to perform precise, exhaustive mathematical reasoning about program behavior. Existing benchmarks either focus on mathematical proof automation, largely disconnected from real-world software, or on engineering tasks that do not require semantic rigor. We present CodeLogician, a neurosymbolic agent for precise analysis of software logic, integrated with ImandraX, an industrial automated reasoning engine deployed in financial markets and safety-critical systems. Unlike prior approaches that use formal methods primarily to validate LLM outputs, CodeLogician uses LLMs to construct explicit formal models of software systems, enabling automated reasoning to answer rich semantic questions beyond binary verification outcomes. To rigorously evaluate mathematical reasoning about software logic, we introduce code-logic-bench, a benchmark targeting the middle ground between theorem proving and software engineering benchmarks. It measures reasoning correctness about program state spaces, control flow, coverage constraints, and edge cases, with ground truth defined via formal modeling and region decomposition. Comparing LLM-only reasoning against LLMs augmented with CodeLogician, formal augmentation yields substantial improvements, closing a 41-47 percentage point gap in reasoning accuracy. These results demonstrate that neurosymbolic integration is essential for scaling program analysis toward rigorous, autonomous software understanding.
Jorge Fandinno, Christoph Glinzer, Zachary Hansen
et al.
Anthem 2.0 is a tool to aid in the verification of logic programs written in an expressive fragment of Clingo's input language named mini-gringo, which includes arithmetic operations and simple choice rules but not aggregates. It can translate logic programs into formula representations in the logic of here-and-there, and analyze properties of logic programs such as tightness. Most importantly, Anthem 2.0 can support program verification by invoking first-order theorem provers to confirm that a program adheres to a first-order specification, or to establish strong and external equivalence of programs. This paper serves as an overview of the system's capabilities. We demonstrate how to use Anthem 2.0 effectively and interpret its results.
We study the model enumeration problem of the function-free, finite domain fragment of first-order logic with two variables ($FO^2$). Specifically, given an $FO^2$ sentence $Γ$ and a positive integer $n$, how can one enumerate all the models of $Γ$ over a domain of size $n$? In this paper, we devise a novel algorithm to address this problem. The delay complexity, the time required between producing two consecutive models, of our algorithm is quadratic in the given domain size $n$ (up to logarithmic factors) when the sentence is fixed. This complexity is almost optimal since the interpretation of binary predicates in any model requires at least $Ω(n^2)$ bits to represent.
In answer set programming, two groups of rules are considered strongly equivalent if they have the same meaning in any context. Strong equivalence of two programs can be sometimes established by deriving rules of each program from rules of the other in an appropriate deductive system. This paper shows how to extend this method of proving strong equivalence to programs containing the counting aggregate.
Pedro H. Azevedo de Amorim, Satoshi Kura, Philip Saville
We give a denotational account of logical relations for call-by-push-value (CBPV) in the fibrational style of Hermida, Jacobs, Katsumata and others. Fibrations -- which axiomatise the usual notion of sets-with-relations -- provide a clean framework for constructing new, logical relations-style, models. Such models can then be used to study properties such as effect simulation. Extending this picture to CBPV is challenging: the models incorporate both adjunctions and enrichment, making the appropriate notion of fibration unclear. We handle this using 2-category theory. We identify an appropriate 2-category, and define CBPV fibrations to be fibrations internal to this 2-category which strictly preserve the CBPV semantics. Next, we develop the theory so it parallels the classical setting. We give versions of the codomain and subobject fibrations, and show that new models can be constructed from old ones by pullback. The resulting framework enables the construction of new, logical relations-style, models for CBPV. Finally, we demonstrate the utility of our approach with particular examples. These include a generalisation of Katsumata's $\top\top$-lifting to CBPV models, an effect simulation result, and a relative full completeness result for CBPV without sum types.
Abstract Clear cell renal cell carcinoma (ccRCC), the most common subtype of RCC, requires accurate pathological grading for effective prognosis. However, current grading methods rely heavily on subjective pathologist assessment, leading to variability. While generative artificial intelligence (GenAI) has shown promise in medical imaging, its application in digital pathology remains underexplored. This study evaluates the performance of three multimodal GenAI models—GPT‐4o, Claude‐3.5‐Sonnet, and Gemini‐1.5‐Pro—in ccRCC grading and prognosis prediction. A total of 499 ccRCC slides from The Cancer Genome Atlas and 349 external samples from two independent cohorts were analyzed. A standardized prompt repetition mechanism and variance‐based stability validation method guided GenAI models in extracting 17 pathological features. Feature stability was assessed using intraclass correlation coefficient (ICC). These features, combined with 3 clinical variables, were used to build grading and prognostic models via logistic regression and 113 machine learning algorithms. Performance was benchmarked against CellProfiler, ResNet‐50, DenseNet‐121, attention‐based multiple instance learning (MIL) and Pathology Language and Image Pre‐training, using the concordance index (C‐index) and area under the receiver operating characteristic curve (AUC). Claude‐3.5‐Sonnet outperformed the other two GenAI models (ICC = 0.76; micro‐average AUC = 0.87), exceeding ResNet‐50 (AUC = 0.78) and attention‐based MIL (AUC = 0.70). Its top prognostic models achieved an average C‐index of 0.739, effectively stratifying high‐ and low‐risk patients. Key predictors included stage, calcification, sarcomatoid differentiation, and vascular networks. GenAI, particularly Claude‐3.5‐Sonnet, enhances accuracy and consistency in ccRCC pathology, showing strong potential for clinical use, especially in resource‐limited settings.
ABSTRACT Biomolecular condensates play crucial roles in cellular physiology and are implicated in neurodegenerative diseases and cancer. However, the mechanisms governing their formation and spatial organization remain poorly understood, largely due to technical challenges. Here, using FUS as a paradigmatic system, we reveal how single‐protein sequences determine condensate architecture that is intrinsically linked to biological function. We demonstrate a domain‐specific preferential distribution organization: the low‐complexity domain (LCD), which drives condensate formation, localizes to the inner layer, while the RNA recognition motif (RRM) preferentially occupies the interfacial layer. This spatial arrangement enhances RNA‐binding accessibility, suggesting a direct structure–function relationship. We further propose a sequence–structure–function paradigm for biomolecular condensates: through the cooperation emerging from multiple “stickers,” individual domains function as integrated units in shaping the structure and functionality of biomolecular condensates, which may represent a broader mode of protein–protein interaction (PPI) within condensates. Our findings elucidate the evolutionary logic of protein sequences in driving liquid–liquid phase separation (LLPS) and provide a foundation for designing therapeutics targeting aberrant condensates in disease.
Abstract Nonlinear nanophotonic circuits, renowned for their compact form and integration capabilities, hold potential for advancing high-capacity optical signal processing. However, limited practicality arises from low nonlinear conversion efficiency. Transition metal dichalcogenides (TMDs) could present a promising avenue to address this challenge, given their superior optical nonlinear characteristics and compatibility with diverse device platforms. Nevertheless, this potential remains largely unexplored, with current endeavors predominantly focusing on the demonstration of TMDs’ coherent nonlinear signals via free-space excitation and collection. In this work, we perform direct integration of TMDs onto a plasmonic nanocircuitry. By controlling the polarization angle of the input laser, we show selective routing of second-harmonic generation (SHG) signals from a MoSe2 monolayer within the plasmonic circuit. Routing extinction ratios of 14.86 dB are achieved, demonstrating good coherence preservation in this hybrid nanocircuit. Additionally, our characterization indicates that the integration of TMDs leads to a 13.8-fold SHG enhancement, compared with the pristine nonlinear plasmonic nanocircuitry. These distinct features—efficient SHG generation, coupling, and controllable routing—suggest that our hybrid TMD-plasmonic nanocircuitry could find immediate applications including on-chip optical frequency conversion, selective routing, switching, logic operations, as well as quantum operations.
Oubelaid Adel, Belkhier Youcef, Ali Ahmed Abdussalam
et al.
Currently, Hybrid Electric Vehicles (HEVs) are gaining traction in the market due to their low or zero carbon footprint. In this study, the power management of a Fuel Cell (FC) and Battery Electric Vehicle (BEV) using Fuzzy Logic Control (FLC) is investigated. Due to its sensitivity and low power density, the FC is used in parallel with a battery that serves as a storage element during regenerative braking periods. The DC link voltage is regulated via a control loop associated with the battery. However, a current regulation loop is used in conjunction with the FC to condition its power flow. The simulation results obtained using MATLAB/Simulink confirm the effectiveness of the proposed fuzzy energy management strategy. Additionally, the presented results demonstrate the ability of FLC to provide convenient power sharing between the utilized power sources without exhausting any source.
The first manga café was established in Japan in the late 1970s. The original concept of a small library collection in a café, where visitors could stay longer than just the time it takes to drink one beverage, has been developed over several decades. Today, there are thousands of such cafés across the country, many of which are open 24 hours a day. This paper aims to highlight the significance of these alternative library spaces, which further promote reading practices. The phenomenon of manga cafés is viewed from a cultural perspective as a specialized public space that, in addition to providing a reading space, also functions as a potential sanctuary to those less socially secure. The trend of manga cafés has spread beyond the borders of Japan, with such spaces opened in East Asia, North America, and Europe. However, the concepts of manga cafés outside of Japan vary and are adapted to the logic of sustainability and profitability to the local culture.
Bibliography. Library science. Information resources
The article is devoted to the discussion of the late 19th century between the priest Ioann Petropavlovsky and the famous archbishop Savva (Tikhomirov) on the problem of the moral perfections of Christ according to His human nature. The published academic lecture by Petropavlovsky "Jesus Christ is the God-Man", its criticism in the "Diary" of Savva (Tikhomirov), Petropavlovsky's response to criticism and response to the discussion by protopresbyter Ioann Yanyshev are analyzed. According to Petropavlovsky, who acted for reasons of proving the divinity of Christ, the Savior, during His earthly life, struggled with the instincts of His humanity, what was an important moment on the path of His free acquisition of His moral perfections. Thus, Christ can be an effective example for us to follow. Savva (Tikhomirov) considered this position to be contrary to the teaching of the Church, while Yanyshev supported ideas of Petropavlovsky. I examine the genesis of this problem about the nature of the moral perfections of Christ in Russian theology, which is rooted in the theology of st. Innokenty of Kherson. The latter, accepting the Kantian setting of practical philosophy – freedom of choice between good and evil is the possibility of moral development – was the first in the history of Russian theological thought to put forward the hypothesis that Christ could have sinned during His earthly life, but did not sin. The hypothesis made sense as a response to Kant's subtle criticism of traditional Christology, put forward by him in his work "Religion within the Limits of Reason Alone". Along with the consideration of these problems, the article attempts to clarify the genesis of the moral-apologetic logic used by Petropavlovsky to prove the divinity of Christ. At the end of the article, Petropavlovsky's theses are considered on the subject of their self-contradictions and examined in the context of patristic theology.
The field of Multicriteria Decision Making (MCDM) has advanced significantly, with methods like QUALIFLEX playing a key role by integrating concordance and discordance measures for robust decision outcomes. This paper introduces an innovative extension, neutrosophic QUALIFLEX, which incorporates neutrosophic sets to better handle uncertainty and indeterminacy. Neutrosophic logic manages truth, indeterminacy, and falsity simultaneously, offering a nuanced approach compared to traditional models. The scope of this article is the application of neutrosophic QUALIFLEX to staff selection in business, a scenario often plagued by high uncertainty. Preliminary results show that neutrosophic QUALIFLEX provides superior performance, delivering more accurate and reliable rankings of candidates. This method addresses the limitations of conventional MCDM approaches, improving decision-making accuracy and expanding the theoretical foundations of MCDM for future research and applications in complex environments. This contribution to the literature bridges a critical gap by addressing the limitations of conventional MCDM methods in dealing with ambiguous and indeterminate information. The integration of neutrosophic sets into the QUALIFLEX framework not only improves decision-making accuracy but also expands the theoretical foundations of MCDM, paving the way for future research and application in complex decision environments.
Optical computing offers advantages such as high bandwidth and low loss, playing a crucial role in signal processing, communication, and sensing applications. Traditional optical logic gates, based on nonlinear fibers and optical amplifiers, suffer from poor robustness and large footprints, hindering their on-chip integration. All-optical logic gates based on topological photonic crystals have emerged as a promising approach for developing robust and monolithic optical computing systems. Expanding topological photonic crystal logic gates from a single operating band to dual bands can achieve high throughput, significantly enhancing parallel computing capabilities. This study integrates the topological protection offered by valley photonic crystals with linear interference effects to design and implement seven optical computing logic gates on a silicon substrate. These gates, based on dual-band valley photonic crystal topological protection, include OR, XOR, NOT, NAND, NOR, and AND. The robustness of the implemented OR logic gates was verified in the presence of boundary defects. The results demonstrate that multi-band parallel computing all-optical logic gates can be achieved using topological photonic crystals, and these gates exhibit high robustness. The all-optical logic gates designed in this study hold significant potential for future applications in optical signal processing, optical communication, optical sensing, and other related areas.
We investigate how the sentence choice semantics (SCS) for propositional superposition logic (PLS) developed in \cite{Tz17} could be extended so as to successfully apply to first-order superposition logic(FOLS). There are two options for such an extension. The apparently more natural one is the formula choice semantics (FCS) based on choice functions for pairs of arbitrary formulas of the basis language. It is proved however that the universal instantiation scheme of FOL, $(\forall v)\varphi(v)\rightarrow\varphi(t)$, is false, as a scheme of tautologies, with respect to FCS. This causes the total failure of FCS as a candidate semantics. Then we turn to the other option which is a variant of SCS, since it uses again choice functions for pairs of sentences only. This semantics however presupposes that the applicability of the connective $|$ is restricted to quantifier-free sentences, and thus the class of well-formed formulas and sentences of the language is restricted too. Granted these syntactic restrictions, the usual axiomatizations of FOLS turn out to be sound and conditionally complete with respect to this second semantics, just like the corresponding systems of PLS.
An approach for encoding abstract dialectical frameworks and their semantics into classical higher-order logic is presented. Important properties and semantic relationships are formally encoded and proven using the proof assistant Isabelle/HOL. This approach allows for the computer-assisted analysis of abstract dialectical frameworks using automated and interactive reasoning tools within a uniform logic environment. Exemplary applications include the formal analysis and verification of meta-theoretical properties, and the generation of interpretations and extensions under specific semantic constraints.
The interactions between the economy and nature are little reflected in the management tools of capitalism. The impacts on the latter remain largely invisible to economic processes. This is the narrative behind the proposal to integrate nature into a central instrument of capitalism: accounting. However, nature accounting is shaped by a diversity of actors, practices, objectives and effects. Taking a chronological approach, we show how three successive approaches that we call “accounting worlds” have developed over time and coexist today. The first is public accounting expressed in biophysical, material and energy units, with the aim of exposing the exploitation and unequal exchange of natural resources as an extension of unbalanced trading relations. This was followed by the gradual development of natural capital monetary accounting projects, aimed at internalizing environmental externalities, initially at the national level and later extended to private accounting. A third and final project has recently emerged in connection with traditional accounting and financial standards. Its purpose is to assess the impact of nature and its degradation on the economic and hence financial performance of firms. Based on an analysis of these three worlds, we suggest that the growing influence of accounting thought and practices on nature, especially in their most recent forms, leads not so much to its commodification or financialization as to its invisibility or dilution in the logic of financial capitalist reproduction. Finally, we question the possible emergence of a unified regime of accounting for nature.
In this paper, we rigorously prove the existence of type-level ordered pairs in Quine’s New Foundations with atoms, augmented by the axiom of infinity and the axiom of choice (NFU + Inf + AC). The proof uses the cardinal squaring principle; more precisely, its instance for the (infinite) universe (VCSP), which is a theorem of NFU + Inf + AC. Therefore, we have a justification for proposing a new axiomatic extension of NFU, in order to obtain type-level ordered pairs almost from the beginning. This axiomatic extension is NFU + Inf + AC + VCSP, which is equivalent to NFU + Inf + AC, but easier to reason about.