In this article, we study the interactions between so-called fractional relaxations of the integer programs (IPs) which encode homomorphism and isomorphism of relational structures. We give a combinatorial characterization of a certain natural linear programming (LP) relaxation of homomorphism in terms of fractional isomorphism. As a result, we show that the families of constraint satisfaction problems (CSPs) that are solvable by such linear program are precisely those that are closed under an equivalence relation which we call Weisfeiler-Leman invariance . We also generalize this result to the much broader framework of Promise Valued Constraint Satisfaction Problems, which brings together two well-studied extensions of the CSP framework. Finally, we consider the hierarchies of increasingly tighter relaxations of the homomorphism and isomorphism IPs obtained by applying the Sherali-Adams and Weisfeiler-Leman methods, respectively. We extend our combinatorial characterization of the basic LP to higher levels of the Sherali-Adams hierarchy, and we generalize a well-known logical characterization of the Weisfeiler-Leman test from graphs to relational structures.

CMOS logic gates form the foundation of virtually every digital integrated circuit manufactured today. This research presents simulation-based characterization of fundamental logic gates implemented in 180nm CMOS technology, examining propagation delay, power consumption, and noise margin performance across NOT, NAND, NOR, and XOR configurations [1]. Circuit simulations employed industry-standard SPICE models with accurate parasitic extraction to ensure realistic performance predictions. The NOT gate exhibited the fastest propagation delay at 0.16 ns with power consumption of 9.4 µW at 100 MHz switching frequency. NAND gates demonstrated 0.34 ns delay with 17.8 µW power, representing the preferred implementation for complex logic synthesis due to functional completeness [2]. NOR gates showed 0.51 ns delay and 26.2 µW consumption, while XOR gates required 0.98 ns with 43.7 µW due to increased transistor count. Noise margin analysis confirmed adequate immunity with low noise margin exceeding 0.62 V and high noise margin above 0.71 V for all configurations [3]. Temperature simulations from -40°C to 125°C revealed delay variations within 18% across the range, acceptable for commercial and industrial applications. The power-delay product emerged as a useful figure of merit, with NOT gates achieving 1.50 fJ compared to 6.05 fJ for NAND implementations. These simulation results provide reference data for digital designers selecting appropriate gate implementations and establishing timing constraints in synchronous systems [4].

Logical characterization of branching bisimilarity over random processes

Abstract We investigate how compositionality can be preserved when modeling semantic content within an impossible worlds framework based on linguistic ersatzism. After a critical assessment of an existing technique due to Francesco Berto and Mark Jago, we illustrate how to overcome its limitations. We introduce a general method for recovering compositionality across a broad range of alternative notions of content and synonymy, as induced by the syntactic characterizations of popular conceptivist logics. Finally, we discuss the advantages and limitations of the strategy, and conclude with some further critical remarks on linguistic ersatzism.

Abstract This paper presents a novel internal modal weak Kleene semantics and its derived logics. Our approach offers an intuitive understanding of modal operators as first-order weak Kleene quantifiers, drawing inspiration from the standard translation of classical modal logic. We explore the properties of this semantics and its associated logics. Our primary contribution lies in characterization theorems for some of these modal weak Kleene logics, leveraging classical modal logic, augmented with a refined variables inclusion requirement. These results not only extend the established characterization of non-modal weak Kleene logics but also provide fresh insights into the interpretations of our modal weak Kleene logics. Specifically, building on these technical findings, we propose philosophical interpretations for our logics and their semantics that coherently extend those of non-modal weak Kleene logics.

A graph simulation and its variants are widely used in graph pattern matching. Among them, there have been related works involving the addition of regular expressions to graph patterns, which can discover more meaningful data and solve problems in polynomial time. In this research, which is based on Fan’s investigations, we first propose an approximation of graph simulation using the concept of metric and formal verification techniques, and then give the definition of approximate matching between pattern graphs with regular expressions and data graphs, which introduces a symmetric tolerance for errors, bridging exact and approximate matching. Finally, we present a logical characterization of the approximate graph simulation by extending Hennessy–Milner logic.

Purpose In the context of mobile social media, users have adopted resistance practices to escape algorithmic deception and control, given that intelligent recommendation algorithms unintentionally infringe upon users’ autonomy while providing personalized services. This study aims to understand the antecedents and consequences of user algorithmic resistance behavior by examining its formation and influencing mechanisms within the mobile social media intelligent recommendation environment. Design/methodology/approach Semi-structured interviews and grounded theory were employed to investigate 32 digital natives with extensive experience in mobile social media. Through a three-level coding process, a theoretical model was constructed to elucidate the formation mechanism of user algorithmic resistance behavior. Findings Digital natives’ algorithmic resistance behavior, which can be classified into mild and severe categories, is driven by external stimuli (i.e. technical characteristics, social influence, and information characteristics) and internal stimuli (i.e. trust, affective state, privacy concerns, capacity, and risk assessment). Specifically, mild algorithmic resistance behavior results from rational resistance intention, while severe algorithmic resistance behavior is affected by irrational resistance intention. A bidirectional relationship is identified between behavioral performance and algorithm resistance behavior, indicating a mutual effect between mild and severe resistance behaviors. Behavioral performance could trigger the secondary or multiple resistance behaviors in terms of trust and affective state. Originality/value A theoretical model is constructed to explain the formation and influencing mechanisms of digital natives' algorithm resistance behavior within the mobile social media intelligent recommendation environment. It distinguishes between two specific types of algorithmic resistance, namely mild resistance and severe resistance, and identifies their unique transformation mechanisms. Additionally, this study elucidates the relationships among various influencing factors and provides a comprehensive and definitive characterization of the behavioral logic that emerges following the implementation of algorithm resistance behavior.

Abstract This paper presents the logics with second-order quantifiers that range over relations of polylogarithmic size (log-quantifiers). The logic $\text{SO}^{\text{plog}} \text{-} \text{FO}$ is constituted of the formulas that extend first-order formulas by log-quantifier prefixes. We show that $\text{SO}^{\text{plog}} \text{-} \text{FO}$ collapses to its binary fragment where log-quantifiers range only over unary and binary relations. We further investigate the 0-1 law for $\text{SO}^{\text{plog}}\text{-}\text{FO}$, demonstrating that it fails in general, yet holds for its monadic existential fragment over the vocabulary that contains only unary relation symbols. Finally, we study the logical characterizations for complexity classes with limited non-determinism. On ordered structures, we show that if a logic $\mathcal L$ captures a complexity class $\mathcal C$, then the logic $\varSigma ^{\log ^{k}}_{1}\text{-}\mathcal L$ captures the complexity class $GC(\log ^{k+1}(n), \mathcal C)$, where $\mathcal L \in \{\text{DTC}, \text{TC}, \text{IFP}\}$. Consequently, $\varSigma _{1}^{\text{plog}}\text{-} \text{IFP}$ captures $\beta \text{P}$ on ordered structures.

Abstract I argue that the continued focus on the possibility question - whether feminist logic can exist as a respectable practice - has several harmful consequences. First, it invites the association of feminist logic with substantial positions in the philosophy of logic, which unnecessarily leaves room for dismissing the field a priori. Second, it invites a systematic reading of feminist logicians as arguing in isolation from their logical practice, which can hide some genuine possibilities for the field. To avoid these issues, I propose a very broad characterization of feminist logic as a kind of practice which addresses some harmful aspect of dominant practices by focusing on their interaction with logical practices. This characterization trivializes the possibility question, enforces no particular conception of logic to the exclusion of others, yet leaves room for both conservative and radical approaches.

Weakly deterministic functions are a subregular class of functions which have been claimed to describe the complexity of most attested phonological maps. This paper proposes a characterization of the weak deterministic functions within the formalism of Boolean Monadic Recursive Schemes (BMRS), in terms of a simultaneous application operator over BMRS programs. This paper provides proof that more complex patterns such as Sour Grapes harmony are not weakly deterministic, and shows that the proposed definition can decisively distinguish between weakly deterministic and properly regular maps. The consequence of this work is a logical characterization of the weakly deterministic boundary, and a testable hypothesis about the complexity of natural language phonological maps.

Graph neural networks are prominent models for representation learning over graph-structured data. While the capabilities and limitations of these models are well-understood for simple graphs, our understanding remains incomplete in the context of knowledge graphs. Our goal is to provide a systematic understanding of the landscape of graph neural networks for knowledge graphs pertaining to the prominent task of link prediction. Our analysis entails a unifying perspective on seemingly unrelated models and unlocks a series of other models. The expressive power of various models is characterized via a precise logical characterization of the class of functions captured by a class of graph neural networks. The theoretical findings presented in this paper explain the benefits of some widely employed practical design choices, which are validated empirically.

We study Hoare-like logics, including partial and total correctness Hoare logic, incorrectness logic, Lisbon logic, and many others through the lens of predicate transformers à la Dijkstra and through the lens of Kleene algebra with top and tests (TopKAT). Our main goal is to give an overview – a taxonomy – of how these program logics relate, in particular under different assumptions like for example program termination, determinism, and reversibility. As a byproduct, we obtain a TopKAT characterization of Lisbon logic, which – to the best of our knowledge – is a novel result.

Model Checking Spatial Reachability Specifications of Public Transport Networks

Introduction. The relevance of this study stems from the need in both methodological science and school practice to identify ways to address the contradiction between the necessity of instilling traditional Russian values in primary school students and the objective difficulty of diagnosing the progress and effectiveness of this process. Materials and methods. The study describes a comprehensive diagnostic technique designed to reveal the first-graders’ attitude to traditional values, along with the results of an ascertaining experiment conducted in the first grades of six schools in St. Petersburg. Results. The creative works of 297 schoolchildren were analyzed. The figurative representations and logical characterizations of “good” and “bad” life provided by the children were correlated with traditional values. The hierarchy of values as perceived by first-graders was established, and the main trends in their understanding of “good” and “bad” were identified. Discussion and conclusion. The baseline diagnostics presented are utilized by the Federal Innovation Platform working on the dialogue approach to fostering traditional Russian values in primary school students and can assist in planning educational activities for first-graders. Future research will focus on analyzing individual first-graders’ works and documenting the progress and outcomes of innovative activities in grades 1 – 4.

Abstract In the eighties, Immerman showed that the class of languages definable by first-order formulae coincides with the class of languages decidable by unbounded fan-in Boolean circuits of constant depth and polynomial size. We show an analogous result for real-valued computation, i.e. we define circuits of unbounded fan-in operating over real numbers and show that families of such circuits of polynomial size and constant depth decide exactly those sets of vectors of reals that can be defined in first-order logic on real valued structures. Our characterization holds both non-uniformly as well as for many natural uniformity conditions.

Abstract We present an adapted construction of algebraic circuits over the reals introduced by Cucker and Meer to arbitrary infinite integral domains and generalize the $\mathrm{AC}_{\mathbb{R}}$ and $\mathrm{NC}_{\mathbb{R}}^{}$ classes for this setting. We give a theorem in the style of Immerman’s theorem which shows that for these adapted formalisms, sets decided by circuits of constant depth and polynomial size are the same as sets definable by a suitable adaptation of first-order logic. Additionally, we discuss a generalization of the guarded predicative logic by Durand, Haak and Vollmer, and we show characterizations for the $\mathrm{AC}_{R}$ and $\mathrm{NC}_R^{}$ hierarchy. Those generalizations apply to the Boolean $\mathrm{AC}$ and $\mathrm{NC}$ hierarchies as well. Furthermore, we introduce a formalism to be able to compare some of the aforementioned complexity classes with different underlying integral domains.

The success of Graph Neural Networks (GNNs) in practice has motivated extensive research on their theoretical properties. This includes recent results that characterise node classifiers expressible by GNNs in terms of first order logic. Most of the analysis, however, has been focused on GNNs with fixed number of message-passing iterations (i.e., layers), which cannot realise many simple classifiers such as reachability of a node with a given label. In this paper, we start to fill this gap and study the foundations of GNNs that can perform more than a fixed number of message-passing iterations. We first formalise two generalisations of the basic GNNs: recurrent GNNs (RecGNNs), which repeatedly apply message-passing iterations until the node classifications become stable, and graph-size GNNs (GSGNNs), which exploit a built-in function of the input graph size to decide the number of message-passings. We then formally prove that GNN classifiers are strictly less expressive than RecGNN ones, and RecGNN classifiers are strictly less expressive than GSGNN ones. To get this result, we identify novel semantic characterisations of the three formalisms in terms of suitable variants of bisimulation, which we believe have their own value for our understanding of GNNs. Finally, we prove syntactic logical characterisations of RecGNNs and GSGNNs analogous to the logical characterisation of plain GNNs, where we connect the two formalisms to monadic monotone fixpoint logic---a generalisation of first-order logic that supports recursion.

Functional reductionism characterises inter-theoretic reduction as the recovery of the upper-level behaviour described by the reduced theory in terms of the lower-level reducing theory. For instance, finding a statistical mechanical realiser that plays the functional role of thermodynamic entropy allows to establish a reductive link between thermodynamics and statistical mechanics. This view constitutes a unique approach to reduction that enjoys a number of positive features, but has received limited attention in the philosophy of science. This paper aims to clarify the meaning of functional reductionism in science, with a focus on physics, to define both its place with respect to other approaches to reduction and its connection to ontology. To do so, we develop and explore two alternative versions of functional reductionism, called Syntactic Functional Reductionism and Semantic Functional Reductionism, that expand and improve the basic functional reductionist approach along different lines, and make clear how the approach works in practice. The former elaborates on David Lewis’ account, is connected with the syntactic view of theories, employs a logical characterisation of functional roles, and is embedded within Nagelian reductionism. The latter adopts a semantic approach to theories, spells out functional roles mainly in terms of mathematical roles within the models, and is expressed in terms of the related structuralist approach to reduction. The development of these frameworks has the final goal of advancing functional reductionism, making it a fully developed account of reduction in science.

We study a standard operator on classes of languages: unambiguous polynomial closure. We prove that for every class C of regular languages satisfying mild properties, the membership problem for its unambiguous polynomial closure UPol(C) reduces to the same problem for C. We also show that unambiguous polynomial closure coincides with alternating left and right deterministic closure. Moreover, we prove that if additionally C is finite, the separation and covering problems are decidable for UPol(C). Finally, we present an overview of the generic logical characterizations of the classes built using unambiguous polynomial closure.

Inductive definitions in logic versus programs of real-time cellular automata