Search Results (70)

The zero-error capacity of discrete memoryless channels (DMCs), introduced by Shannon, is a fundamental concept in information theory with significant operational relevance, particularly in settings where even a single transmission error is unacceptable. Despite its importance, no general closed-form expression or algorithm is known for computing this capacity. In this work, we investigate the computability-theoretic boundaries of the zero-error capacity and establish several fundamental limitations. Our main result shows that the zero-error capacity of noisy channels is not Banach–Mazur-computable and therefore is also not Borel–Turing-computable. This provides a strong form of non-computability that goes beyond classical undecidability, capturing the inherent discontinuity of the capacity function. As a further contribution, we analyze the deep connections between (i) the zero-error capacity of DMCs, (ii) the Shannon capacity of graphs, and (iii) Ahlswede’s operational characterization via the maximum-error capacity of 0–1 arbitrarily varying channels (AVCs). We prove that key semi-decidability questions are equivalent for all three capacities, thus unifying these problems into a common algorithmic framework. While the computability status of the Shannon capacity of graphs remains unresolved, our equivalence result clarifies what makes this problem so challenging and identifies the logical barriers that must be overcome to resolve it. Together, these results chart the computational landscape of zero-error information theory and provide a foundation for further investigations into the algorithmic intractability of exact capacity computations. Full article

It is shown that the analysis of rotating circular images containing n = 2^p−1 pixels, the state of which is described by variables of binary logic, and p is an integer, is expedient to carry out using digital spectra obtained using the Fourier–Galois transformation, and the basis corresponding to such a transformation is formed by the method of classical algebraic extensions of the main Galois field GF(2) corresponding to binary logic. It is shown that the use of Fourier–Galois spectra makes it possible to reduce the analysis of a rotating image to the analysis of a still image by using the operation of digital logarithm. It is shown that the proposed approach is of interest, including from the point of view of improving equipment designed to study the rheological properties of liquids, in particular, polymer solutions in which non-trivial branched structures are formed. In this case, the use of the proposed approach provides an opportunity to modernize the classical method of measuring Stokes viscosity, focused on the study of mechanochemical reactions. The design of a viscometer that implements the proposed approach has been developed. In it, a digital image is formed by a set of optoelectronic pairs that track the circular motion of the ball in a cuvette driven by rotation. The electronic circuits of this type of viscometer are based on a Fourier–Galois spectrum analyser and a digital logarithm operation. The possibilities of generalizing the proposed approach to the analysis of rotating images of other types are considered. Full article

We address the scientific “time” concept in the context of more general relaxation processes toward the Wärmetod of thermodynamic equilibrium. More specifically, we sketch a construction of a conceptual ladder of chemical reaction steps that can rigorously bridge a description from the microscopic domain of molecular quantum chemistry to the macroscopic materials domain of Gibbsian thermodynamics. This conceptual reformulation follows the pioneering work of Kenichi Fukui (Nobel 1981) in rigorously formulating the intrinsic reaction coordinate (IRC) pathway for controlled description of non-equilibrium passages between reactant and product equilibrium states of an overall material transformation. Elementary chemical reaction steps are thereby identified as the logical building-blocks of an integrated mathematical framework that seamlessly spans the gulf between classical (pre-1925) and quantal (post-1925) scientific conceptions and encompasses both static and dynamic aspects of material change. All modern chemical reaction rate studies build on the apparent infallibility of quantum-chemical solutions of Schrödinger’s wave equation and its Dirac-type relativistic corrections. This infallibility may now be properly accepted as an added“inductive law” of Gibbsian chemical thermodynamics, the only component of 19th-century physics that passed intact through the revolutionary quantum upheavals of 1925. Full article

Chromatic quantum contextuality is a criterion of quantum nonclassicality based on (hyper)graph coloring constraints. If a quantum hypergraph requires more colors than the number of outcomes per maximal observable (context), it lacks a classical realization with n-uniform outcomes per context. Consequently, it cannot represent a “completable” noncontextual set of coexisting n-ary outcomes per maximal observable. This result serves as a chromatic analogue of the Kochen-Specker theorem. We present an explicit example of a four-colorable quantum logic in dimension three. Furthermore, chromatic contextuality suggests a novel restriction on classical truth values, thereby excluding two-valued measures that cannot be extended to n-ary colorings. Using this framework, we establish new bounds for the house, pentagon, and pentagram hypergraphs, refining previous constraints. Full article

As a non-associative connective in fuzzy logic, the analysis and research of overlap functions have been extended to many generalized cases, such as interval-valued and intuitionistic fuzzy overlap functions (IFOFs). However, overlap functions face challenges in the Pythagorean fuzzy (PF) environment. This paper first extends overlap functions to the PF domain by proposing PF overlap functions (PFOFs), discussing their representable forms, and providing a general construction method. It then introduces a new PF similarity measure which addresses issues in existing measures (e.g., the inability to measure the similarity of certain PF numbers) and demonstrates its effectiveness through comparisons with other methods, using several examples in fractional form. Based on the proposed PFOFs and their induced residual implication, new generalized PF rough sets (PFRSs) are constructed, which extend the PFRS models. The relevant properties of their approximation operators are explored, and they are generalized to the dual-domain case. Due to the introduction of hesitation in IF and PF sets, the approximate accuracy of classical rough sets is no longer applicable. Therefore, a new PFRS approximate accuracy is developed which generalizes the approximate accuracy of classical rough sets and remains applicable to the classical case. Finally, three multi-criteria decision-making (MCDM) algorithms based on PF information are proposed, and their effectiveness and rationality are validated through examples, making them more flexible for solving MCDM problems in the PF environment. Full article

Mobile robots represent one of the most relevant areas of study within robotics due to their potential for designing and developing new nonlinear control structures that can be implemented in simulations and applications in specific environments. In this work, a fuzzy steering controller with a symmetric distribution of fuzzy numbers is proposed and designed for implementation in the kinematic model of a non-holonomic mobile robot. The symmetry in the distribution of triangular fuzzy numbers contributes to a balanced response to disturbances and minimizes systematic errors in direction estimation. Additionally, it improves the system’s adaptability to various reference paths, ensuring accurate tracking and optimized performance in robot navigation. Furthermore, this fuzzy logic-based controller emulates the behavior of a classic PID controller by offering a robust and flexible alternative to traditional methods. A virtual environment was also developed using the UNITY platform to evaluate the performance of the fuzzy controller. The results were evaluated by considering the average tracking error, maximum error, steady-state error, settling time, and total distance traveled, emphasizing the trajectory error. The circular trajectory showed high accuracy with an average error of 0.0089 m, while the cross trajectory presented 0.01814 m, reflecting slight deviations in the turns. The point-to-point trajectory registered a more significant error of 0.9531 m due to abrupt transitions, although with effective corrections in a steady state. The simulation results validate the robustness of the proposed fuzzy controller, providing quantitative insights into its precision and efficiency in a virtual environment, and demonstrating the effectiveness of the proposal. Full article

For well over a century, unresolved ambiguities in defining land as a finite, non-renewable resource have often facilitated rent-seeking and shaped inequitable distributions of wealth derived from nature and collective contributions. In the absence of clear conceptual and legal distinctions between land’s intrinsic worth and the incremental value conferred by human-made improvements, communities and ecosystems were frequently denied their rightful share, thereby influencing inequitable economic, social, and environmental trajectories. Though not universal, these historical patterns now reemerge in “digital land” platforms, where data, user engagement, and communal knowledge are likewise subject to private appropriation. By bridging these classical land debates with emerging forms of digital exploitation, this article offers a novel theoretical framework that reveals how unresolved land-valuation ambiguities reappear in user-generated data ecosystems. Without robust conceptual frameworks and effective regulatory oversight, such digital spheres risk replicating the exploitative logic once attached to physical land. By clarifying these parallels, this article underscores the urgent need for well-informed governance inspired by past land policy debates—particularly those focused on equity, transparency, and sustainability. Ensuring that resource management, whether rooted in soil or servers, consistently adheres to principles of fairness and shared prosperity is essential to avert new forms of unregulated extraction and to advance more inclusive, sustainable development. Full article

A derivation of a tight-binding model from Schrödinger formalism for various topologies of position-based semiconductor qubits is presented in the case of static and time-dependent electric fields. The simplistic tight-binding model enables the description of single-electron devices at a large integration scale. The case of two electrostatically Wannier qubits (also known as position-based qubits) in a Schrödinger model is presented with omission of spin degrees of freedom. The concept of programmable quantum matter can be implemented in the chain of coupled semiconductor quantum dots. Highly integrated and developed cryogenic CMOS nanostructures can be mapped to coupled quantum dots, the connectivity of which can be controlled by a voltage applied across the transistor gates as well as using an external magnetic field. Using the anti-correlation principle arising from the Coulomb repulsion interaction between electrons, one can implement classical and quantum inverters (Classical/Quantum Swap Gate) and many other logical gates. The anti-correlation will be weakened due to the fact that the quantumness of the physical process brings about the coexistence of correlation and anti-correlation at the same time. One of the central results presented in this work relies on the appearance of dissipation-like processes and effective potential renormalization building effective barriers in both semiconductors and in superconductors between not bended nanowire regions both in classical and in quantum regimes. The presence of non-straight wire regions is also expressed by the geometrical dissipative quantum Aharonov–Bohm effect in superconductors/semiconductors when one obtains a complex value vector potential-like field. The existence of a Coulomb interaction provides a base for the physical description of an electrostatic Q-Swap gate with any topology using open-loop nanowires, with programmable functionality. We observe strong localization of the wavepacket due to nanowire bending. Therefore, it is not always necessary to build a barrier between two nanowires to obtain two quantum dot systems. On the other hand, the results can be mapped to the problem of an electron in curved space, so they can be expressed with a programmable position-dependent metric embedded in Schrödinger’s equation. The semiconductor quantum dot system is capable of mimicking curved space, providing a bridge between fundamental and applied science in the implementation of single-electron devices. Full article

Broilers are particularly sensitive to heat stress, which can impair growth, and lower conversion efficiency and survival rates. Under a climate change scenario, maintaining optimal thermal conditions within broiler houses becomes more complex and energy-intensive. Climate change can worsen air quality issues inside broiler houses by increasing the concentration of harmful gases, and proper mechanical ventilation systems are essential for diluting and removing these gases. The present study aimed to develop and validate a model for the ideal broiler housing strategy by applying the Paraconsistent Annotated Evidential Logic Eτ. A database from four broiler houses in a commercial farm, rearing 157,700 birds from the 1st to the 42nd day of growth, was used in the research. All environmental data were recorded weekly inside the houses, and on day 42, flock mortality, overall feed-to-gain ratio, and body weight were calculated and registered. The Cohen’s Kappa statistics for each environmental parameter classification compared to the paraconsistent classification. Results indicated that temperature shows good agreement, relative humidity shows slight agreement, air velocity presents a good agreement, CO₂ concentration has a slight agreement, and NH₃ concentration is classified by slight agreement. The environmental and productivity variables as a function of the broiler age using the extreme True paraconsistent state indicate the model validation. The paraconsistent analysis presented the ideal scenario for broilers’ growth, maintaining the environmental variables level within a particular threshold and providing greater profit to broiler farmers. Full article

The new approach to quantum mechanics (QM) is that the mathematics of QM is the linearization of the mathematics of partitions (or equivalence relations) on a set. This paper develops those ideas using vector spaces over the field ${\mathbb{Z}}_2=\left\{0.1\right\}$ as a pedagogical or toy model of (finite-dimensional, non-relativistic) QM. The $0,1$-vectors are interpreted as sets, so the model is “quantum mechanics over sets” or QM/Sets. The key notions of partitions on a set are the logical-level notions to model distinctions versus indistinctions, definiteness versus indefiniteness, or distinguishability versus indistinguishability. Those pairs of concepts are the key to understanding the non-classical ‘weirdness’ of QM. The key non-classical notion in QM is the notion of superposition, i.e., the notion of a state that is indefinite between two or more definite- or eigen-states. As Richard Feynman emphasized, all the weirdness of QM is illustrated in the double-slit experiment, so the QM/Sets version of that experiment is used to make the key points. Full article

The logico-pluralist LogiKEy knowledge engineering methodology and framework is applied to the modelling of a theory of legal balancing, in which legal knowledge (cases and laws) is encoded by utilising context-dependent value preferences. The theory obtained is then used to formalise, automatically evaluate, and reconstruct illustrative property law cases (involving the appropriation of wild animals) within the Isabelle/HOL proof assistant system, illustrating how LogiKEy can harness interactive and automated theorem-proving technology to provide a testbed for the development and formal verification of legal domain-specific languages and theories. Modelling value-oriented legal reasoning in that framework, we establish novel bridges between the latest research in knowledge representation and reasoning in non-classical logics, automated theorem proving, and applications in legal reasoning. Full article

The new logic of partitions is dual to the usual Boolean logic of subsets (usually presented only in the special case of the logic of propositions) in the sense that partitions and subsets are category-theoretic duals. The new information measure of logical entropy is the normalized quantitative version of partitions. The new approach to interpreting quantum mechanics (QM) is showing that the mathematics (not the physics) of QM is the linearized Hilbert space version of the mathematics of partitions. Or, putting it the other way around, the math of partitions is a skeletal version of the math of QM. The key concepts throughout this progression from logic, to logical information, to quantum theory are distinctions versus indistinctions, definiteness versus indefiniteness, or distinguishability versus indistinguishability. The distinctions of a partition are the ordered pairs of elements from the underlying set that are in different blocks of the partition and logical entropy is defined (initially) as the normalized number of distinctions. The cognate notions of definiteness and distinguishability run throughout the math of QM, e.g., in the key non-classical notion of superposition (=ontic indefiniteness) and in the Feynman rules for adding amplitudes (indistinguishable alternatives) versus adding probabilities (distinguishable alternatives). Full article

In recent years, the increasing environmental problems, especially the issue of global warming, have motivated demand for a cleaner, more sustainable, and economically viable energy source. In this context, wind energy plays a significant role due to the small negative impact it has on the environment, which makes it among the most widespread potential sustainable renewable fuel nowadays. However, wind turbine control systems are important factors in determining the efficiency and cost-effectiveness of a wind turbine (WT) system for wind applications. As wind turbines become more flexible and larger, it is difficult to develop a control algorithm that guarantees both efficiency and reliability as these are conflicting objectives. This paper reviews various control strategies for the three main control systems of WT, which are pitch, torque, and yaw control, in different operational regions considering multi-objective control techniques. The different control algorithms are generally categorized as classical, modern (soft computing) and artificial intelligence (AI) for each WT control system. Modern and soft computing techniques have been showing remarkable improvement in system performance with minimal cost and faster response. For pitch and yaw systems, soft computing control algorithms like fuzzy logic control (FLC), sliding mode control (SMC), and maximum power point tracking (MPPT) showed superior performance and enhanced the WT power performance by up to 5% for small-scale WTs and up to 2% for multi-megawatt WTs. For torque control systems, direct torque control (DTC) and MPPT AI-based techniques were suitable for reducing generator torque fluctuations and estimating the torque coefficient for different wind speed regions. Classical control techniques such as PI/PID resulted in poor dynamic response for large-scale WTs. However, to improve classical control techniques, AI algorithms could be used to tune the controller’s parameters to enhance its response, as a WT is a highly non-linear system. A graphical abstract is presented at the end of the paper showing the pros/cons of each control system category regarding each WT control system. Full article

Existing decision-making models are generally based on the classical normative paradigm, which seldom considers the limited cognitive and environmental resources of humans when making decisions in real environments. We draw on the theory of Artificial General Intelligence technology, Non-Axiomatic Reasoning System and heuristic-primed decision-making processes of psychology to propose a heuristic-primed decision-making model under the assumption of bounded resources. Firstly, we propose a spreading activation belief network based on experience-grounded semantics, which takes concepts as nodes and semantic relevance as edges, and changes the weights of logical reasoning links according to the evidence presented using multiple inferences rules so as to achieve the self-organization of its network topology. Next, multiple dynamically changing and conflicting goals are represented by a Non-Axiomatic Logic statement with two-dimensional desire-values. Finally, a controlled concurrent heuristic algorithm that can dynamically allocate limited computational resources and perform multiple inferences is proposed. Full article

The purpose of this paper is to revisit the concepts of a third in logic and philosophy that have existed since antiquity, widely separated in time and space, but expressing what we consider a higher level of understanding, without going outside the boundaries of science. We claim that the logic applicable to real complex processes combines a non-standard Western “Logic in Reality” and insights from classical Indian and contemporary Japanese logics for which the former provides the necessary grounding. Full article