Basic Logic Research Articles

Bertrand Russell’s Philosophy and the Problem of Object: Logical Analysis versus Linguistic Analysis.

Objectives: This study discusses the content, the form, and the independence of the external objects. It also examines the object’s relationship to other linguistic and scientific issues. Perceiving the object is what the words means. While what words refer to is the logical object, material objects are what constitute a fact. The role of the concepts of subject, object, logical form, universals, particulars, and relations in the solution of the problem of scientific knowledge are identified for the purpose of justifying the scientific knowledge. Methods: A linguistic logical analysis method is used to examine sentence structure and word meaning, order and their role in concepts construction. Syntax is used to understand the linguistic and logical constructions by reducing them to symbols and logical forms and reconstruction process starting from empirical meaning to formal level exemplified in a proposition . Results: Our findings show that the difficulty of distinguishing the form of the object from its empirical content leads to call objects facts. for the same reason, the object, which becomes a sense datum, also turns out to be a sensible percept. Therefore, the logical form is favored since it is is presented as the basis of certainty. Conclusions: The study shows that the logical objects became fused with Russell’s objective in reconstructing mathematics by justifying its logical basis on one side, and renders the scientific philosophy to mathematical philosophy on the other side. Yet, metaphysics is used for justification, and every thing becomes an object; in the most general sense, it is an object-based metaphysics.

All Light Controlled Five State Logic Gates on a Ferroelectric Ceramic Chip.

Differentiating photoelectric response in a single material with a simple approach is desirable for all-in-one optoelectronic logical devices. In ferroelectric materials, significantly distinct photoelectric features should be observed if they are in diverse polarization states, unveiling a possible pathway to realize multifunctional optoelectronic logic gates through ferroelectric polarization design. In this study, the Ti3+ self-doping strategy is first applied to 0.5Ba(Zr0.2Ti0.8)O3-0.5(Ba0.7Ca0.3)TiO3 ferroelectric ceramics (BZT-BCT-xT) through co-firing metallic Ti powders and BZT-BCT powders to enhance photoelectric output. Subsequently, on the BZT-BCT-3T ceramic surface that has optimal photoelectric properties, three individual regions are separated and heterogeneously polarized by using a novel planar three-electrodes structure. Intriguing illumination region-dependent photocurrent directions are demonstrated in this as-fabricated device. Based on this, five basic optoelectronic logic gates are integrated into single ferroelectric ceramic via fully light-controlled methods, including "AND", "OR", "NOT", "NAND" and "NOR". These gates can be readily switched by simply altering the output electrodes or light intensity of 405nm LED modulating light. This work not only puts forward an innovative strategy for designing ferroelectric optoelectronic logic gates, but also provides feasibility for more ferroelectric materials to be applied in logical devices.

All-Optical Single-Channel Plasmonic Logic Gates.

Optical computing, renowned for its light-speed processing and low power consumption, typically relies on the coherent control of two light sources. However, there are challenges in stabilizing and maintaining high optical spatiotemporal coherence, especially for large-scale computing systems. The coherence requires rigorous feedback circuits and numerous phase shifters, introducing system instability and complexity. Here we propose an innovative logic gate using a single light source, with frequency and polarization serving as two virtual inputs. Our design leverages frequency-polarization multiplexed metasurfaces to achieve all basic logic operations by selectively routing surface plasmon polaritons. This single-channel logic gate maintains inherent coherence between frequency and polarization, thereby considerably eliminating stringent light-source specifications and numerous rigid phase controls and resulting in higher stability. Our device showcases unique application potentials in on-chip readout of encryption information by using random sequences as a one-time pad, unlocking fresh prospects for information protection and optical computing with other simple light sources.

Rhetorical means of communicative success using question-answer procedures as an example.

The article is devoted to the study of the role of question-answer procedures in modern communication conditions. The subject of the study is question-answer procedures. The article explains one of the main distinctions for the topic of the study - the concepts of "ignorance" and “lack of knowledge”. Particular attention is focused on identifying and clarifying the role of the question in modern communication: the characteristics / attributes of the question in modern communication are identified; logical and rhetorical aspects of questions are analyzed; the key concept of "interrogative" for the formal description of questions in logic is clarified; the specificity of the logical basis of the question is shown; the difference between logical and grammatical subjects and predicates is shown; cognitive and manipulative functions of questions are formulated. The article clarifies the meaning of the concept of "communicative goal", and also proposes a variant of dividing questions into correct and incorrect depending on the communicative goal. The article proposes a classification of incorrect questions and a method for answering questions of different types in both personal and professional communicative interaction; general recommendations for response procedures are provided, and types of correct and incorrect answers are demonstrated and analyzed. The article uses methods of comparative and contextual analysis, generalization, classification, and the logical method. The text is accompanied by visual, expressive examples, which allows the reader to better understand the main ideas of the study. The article will be useful for both students, postgraduates studying rhetoric, argumentation theory, communication techniques, and a wide range of readers.

Advancements and Applications of Hardware Adders: Principles, Functions, and Future Challenges

This paper reviews the principles and applications of various types of adders, including Half Adder, Full Adder, Ripple-Carry Adder (RCA), Lookahead Carry Adder (LCA), Carry-Bypass Adder (CBA), and Carry Select Adder (CSA). The basic logic of each adder type is analyzed, emphasizing their performance characteristics, such as area, power consumption, and delay. Applications of adders in fields like image processing, portable electronics, and medical data encryption are discussed, highlighting how different types of adders are tailored to specific performance requirements. Approximate Full Adders (AFA) and low-power, high-speed adders are introduced as solutions for energy-efficient image processing and portable electronic applications, respectively. Challenges in reducing power consumption and improving approximate computing accuracy are addressed, with a focus on novel design approaches such as powerless AND gates, groundless OR gates, and error detection and correction methods. Future expectations for adder optimization are explored, including trends in power reduction, computing efficiency, and improved performance for various application scenarios.

THE PRACTICE OF USING FUZZY LOGIC FOR SIMULATION OF COMPLEX SYSTEMS

Simulation modeling is one of the popular methods for studying complex systems of different nature. The paper analyzes the existing experience of using the fuzzy logic apparatus for simulation modeling of processes and systems. The main directions of integration of fuzzy logic and simulation modeling are considered. Examples of computer models from different subject areas, built on the basis of fuzzy logic, in the context of simulation modeling methods are given. The ways of technical implementation of the integration of the two considered means are noted. The authors conclude that fuzzy logic can be used to model the resilience of regional socio-economic systems.

The Freudian subject in the digital sphere: on systems and the alethosphere

AbstractModern concepts of information based in computation are centrally reliant on the idea of the system as a holistic and encompassing structure that might be complex, but never includes true indeterminacy. The unconscious of the Freudian subject on the other hand is centrally marked by an indeterminacy that is not transferable to the digital sphere. How to conceptualize these competing ontologies and their effect on the subject? The current zeitgeist more often than not implies a universal computability, especially with the genesis of modern AI. However, by taking the logical basis of computability into account a different picture appears. To demarcate where psychoanalysis and continental philosophy’s concept of the subject leave the realm of the computable, the foundational logics of Heidegger and Lacan are utilized.

On the Functional Nature of Cognitive Systems

The functional nature of cognitive systems is outlined as a general conceptual model where typical notions of cognition are analyzed apart from the physical realization (biological or artificial) of such systems. The notion of function, one of the main logical bases of mathematics, logic, linguistics, physics, and computer science, is shown to be a unifying concept in analyzing cognition components: learning, meaning, comprehension, language, knowledge, and consciousness are related to increasing levels in the functional organization of cognition.

Inferentialist Resource Semantics

In systems modelling, a 'system' typically comprises located resources relative to which processes execute. One important use of logic in informatics is in modelling such systems for the purpose of reasoning (perhaps automated) about their behaviour and properties. To this end, one requires an interpretation of logical formulae in terms of the resources and states of the system; such an interpretation is called a 'resource semantics' of the logic. This paper shows how inferentialism -- the view that meaning is given in terms of inferential behaviour -- enables a versatile and expressive framework for resource semantics. Specifically, how inferentialism seamlessly incorporates the assertion-based approach of the logic of Bunched Implications, foundational in program verification (e.g., as the basis of Separation Logic), and the renowned number-of-uses reading of Linear Logic. This integration enables reasoning about shared and separated resources in intuitive and familiar ways, as well as about the composition and interfacing of system components.

Design and analysis of 2D photonic crystals based all optical logic gates

Abstract All-optical basic logic gates play a pivotal role in the development of ultra-fast and energy-efficient computing systems. In this communication, we have designed an alternative method of all-optical logic OR, AND, XOR, and XNOR gates using 2-dimensional photonic crystals with a hexagonal lattice structure. The OptiFDTD software and finite-difference time-domain (FDTD) method has been used to verify the proposed designs and analyzed by calculating the contrast ratio and bit rate. The contrast ratios of the OR, AND, XOR, and XNOR gates are 43.20 dB, 36.40 dB, 41.46 dB and 37.63 dB, respectively. The output of the proposed logic gates may efficiently enhance the optical communication system.

A basic system of paraconsistent Nelsonian logic of conditionals.

We define a Kripke semantics for a conditional logic based on the propositional logic , the paraconsistent variant of Nelson's logic of strong negation; we axiomatize the minimal system induced by this semantics. The resulting logic, which we call , shows strong connections both with the basic intuitionistic logic of conditionals introduced earlier in (Olkhovikov, 2023) and with the -based modal logic introduced in (Odintsov and Wansing, 2004) as one of the possible counterparts to the classical modal system . We map these connections by looking into the embeddings which obtain between the aforementioned systems.

A Proof Calculus for Automated Deduction in Propositional Product Logic

Propositional product logic belongs to the basic fuzzy logics with continuous t-norms using the product t-norm (defined as the ordinary product of real numbers) on the unit interval [0,1]. This paper introduces a proof calculus for the product logic which is suitable for automated deduction. The calculus provides one of possible generalisations of the family of modifications of the procedure (algorithm) of Davis, Putnam, Logemann, and Loveland (DPLL) in the context of fuzzy logics. We show that the calculus is refutation sound and finitely complete as well. The deduction, satisfiability, and validity problems are solved in the finite case. The achieved results contribute to the theoretical (logic and computational) description of multi-step fuzzy inference.

One‐Step Van der Waals Integration of Multi‐Threshold 2D Functional Circuits

AbstractTransition‐metal dichalcogenides (TMDs), as atomically thin semiconductors, have shown immense promise for next‐generation electronics due to their high mobility and potential for creating van der Waals heterostructures. However, precise control of the threshold voltage (Vth) in field‐effect transistors (FETs) remains a significant challenge, impeding the development of 2D material circuits with tailored electronic functions. Herein, a graphene‐assisted one‐step van der Waals integration technique is presented for fabricating multi‐threshold 2D functional circuits. Graphene's unique property of having a surface without dangling bonds is utilized as an intermediary layer, allowing for the transfer of electrodes with various work functions and high‐κ dielectric layers onto 2D channel materials in a single step. This technique has successfully produced Al‐gated MoS2 FETs with a Vth of −0.2 V and Au‐gated MoS2 FETs with a Vth of 1.9 V. This precision enables the development of functional devices such as rail‐to‐rail inverters with large noise margins. Furthermore, more complex multi‐threshold 2D circuits are achieved, including basic logic gates (NOT, NAND, NOR), six‐transistor static random‐access memory (6T‐SRAM), and ring oscillators (RO). This work showcases a scalable and effective strategy for threshold voltage engineering in 2D material‐based circuits, paving the way for sophisticated electronic and optoelectronic applications.

Basis is also explanation: Interpretable Legal Judgment Reasoning prompted by multi-source knowledge

The task of Legal Judgment Prediction (LJP) aims to forecast case outcomes by analyzing fact descriptions, playing a pivotal role in enhancing judicial system efficiency and fairness. Existing LJP methods primarily focus on improving representations of fact descriptions to enhance judgment performance. However, these methods typically depend on the superficial case information and neglect the underlying legal basis, resulting in a lack of in-depth reasoning and interpretability in the judgment process of long-tail or confusing cases. Recognizing that the basis for judgments in real-world legal contexts encompasses both factual logic and related legal knowledge, we introduce the interpretable legal judgment reasoning framework with multi-source knowledge prompted. The essence of this framework is to transform the implicit factual logic of cases and external legal knowledge into explicit basis for judgment, aiming to enhance not only the accuracy of judgment predictions but also the interpretability of the reasoning process. Specifically, we design a chain prompt reasoning module that guides a large language model to elucidate factual logic basis through incremental reasoning, aligning the model prior knowledge with task-oriented knowledge in the process. To match the above fact-based information with legal knowledge basis, we propose a contrastive knowledge fusing module to inject external statutes knowledge into the fact description embedding. It pushes away the distance of similar knowledge in the semantic space during the encoding of external knowledge base without manual annotation, thus improving the judgment prediction performance of long-tail and confusing cases. Experimental results on two real datasets indicate that our framework significantly outperforms existing LJP baseline methods in accuracy and interpretability, achieving new state-of-the-art performance. In addition, tests on specially constructed long-tail and confusing case datasets demonstrate that the proposed framework possesses improved generalization abilities for predicting these complex cases.

Design and Implementation of a 3-bit ALU with Integrated 7-Segment Display on FPGA

This paper describes the design and implementation of a 3-bit Arithmetic Logic Unit (ALU) with integrated 7-segment display output, deployed on an FPGA platform. The objective of this project is to efficiently perform and display basic arithmetic and logic operations, including addition, subtraction, AND, OR, XOR, and NOT, with an FPGA-based ALU. A control signal selects the operation, and the ALU's 3-bit result is decoded and displayed on a 7-segment interface for clear output visualization. The ALU design is coded in Verilog and includes logic to manage carry and overflow in arithmetic functions. A display decoder module maps the ALU’s binary output to the correct LED segments on the 7-segment display, allowing intuitive real-time readout of operation results. The system was synthesized, simulated, and tested on an Artix-7 FPGA using the Xilinx Vivado development environment, achieving accurate and expected functionality across all operations. This work showcases the effectiveness of FPGA technology in integrating computation and display within a compact digital system, with potential applications in both educational and embedded system design settings where real-time processing and display are essential. Keywords: FPGA, ALU, 7-segment display, Verilog, Digital system design, Embedded computing.

Uniform lyndon interpolation for basic non-normal modal and conditional logics

Abstract In this paper, a proof-theoretic method to prove uniform Lyndon interpolation (ULIP) for non-normal modal and conditional logics is introduced and applied to show that the logics, $\textsf{E}$, $\textsf{M}$, $\textsf{EN}$, $\textsf{MN}$, $\textsf{MC}$, $\textsf{K}$, and their conditional versions, $\textsf{CE}$, $\textsf{CM}$, $\textsf{CEN}$, $\textsf{CMN}$, $\textsf{CMC}$, $\textsf{CK}$, in addition to $\textsf{CKID}$ have that property. In particular, it implies that these logics have uniform interpolation (UIP). Although for some of them the latter is known, the fact that they have uniform LIP is new. Also, the proof-theoretic proofs of these facts are new, as well as the constructive way to explicitly compute the interpolants that they provide. On the negative side, it is shown that the logics $\textsf{CKCEM}$ and $\textsf{CKCEMID}$ enjoy UIP but not uniform LIP. Moreover, it is proved that the non-normal modal logics, $\textsf{EC}$ and $\textsf{ECN}$, and their conditional versions, $\textsf{CEC}$ and $\textsf{CECN}$, do not have Craig interpolation, and whence no uniform (Lyndon) interpolation.

Digital Architectural Form Generation Through Pixel System-Driven Image Feature Information

This study analyzes valuable information (image feature information) from pixel-based images to systematize the form generation process utilizing this information. Information in architecture is mainly used as an analytical tool for functional design optimization. However, the Fourth Industrial Revolution and advances in information and communication technology have positioned information as a core value-creating tool. Consequently, there is a growing need to develop methodologies for effectively applying information to architectural design generation. This study combines digital technology with images, which directly influence architectural design, transforming them into numerical information. By systematizing the three-dimensional form generation process using low-level image feature information, it analyzes the relationship between the characteristics of valuable information and the generated forms. This approach helps identify the interrelationships between the characteristics of valuable information and the generated forms, the complementarity needed to mitigate the limitations of valuable information, and the potential for architectural applications of the three-dimensional form generation methodology utilizing image information. This approach reduces labor and enhances architectural aesthetics by instantly generating diverse early design alternatives. Such research can provide a more logical basis for avoiding intuitive judgments during the design decision-making process. It can also lay the groundwork for information-centric design systems in architecture.

Analog Implementation of a Spiking System for Performing Arithmetic Logic Operations on Mixed‐Signal Neuromorphic Processors

In recent years, physical limitations in the integration of transistors in computers have forced the search for low‐computational‐power alternatives in hardware design. Although doubts may arise regarding the limit of the relationship between performance and power consumption in computers, these disappear when considering the brain, which is one of the most efficient computing systems. In this way, bioinspired applications try to benefit from the low‐power consumption present in the biological nervous system. Previous work has shown the feasibility of implementing spiking neural networks that operate in a Boolean manner on digital platforms, such as SpiNNaker, using basic logic gates and a spiking memory, which suggests the potential for constructing a low‐power consumption spiking computer. This work takes a first step in the implementation of a spiking central processing unit by developing an arithmetic logic unit, which is an essential block for instruction execution, demonstrating its correct operation on Dynap‐SE1. The results confirm the feasibility of using this Boolean approach on this platform, despite certain limitations in the number of inputs and operating frequencies of the blocks, and pave the way for the construction of a spiking computer.

STEPS OF TEACHING PROBLEM SOLVING IN PRIMARY GRADES AND ITS LOGICAL BASIS

In this article, the importance of teaching primary school students to solve problems, through which the stages of development of logical thinking in students are mentioned. Information about the stages of teaching problem solving is provided.

A DPLL Procedure with Dichotomous Branching for Propositional Product Logic

The propositional product logic is one of the basic fuzzy logics with continuous t-norms, employing the product t-norm on the unit interval [Formula: see text]. Our aim is to combine well-established automated deduction (theorem proving) with fuzzy inference. As a first step, we devise a modification of the procedure of Davis, Putnam, Logemann, and Loveland (DPLL) with dichotomous branching for inference in the product logic. We prove that the procedure is refutation sound and finitely complete. As a consequence, solutions to the deduction, satisfiability, and validity problems will be proposed for the finite case. The presented results are applicable to a design of intelligent systems, exploiting some kind of multi-step fuzzy inference.