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Urgency of the research. We consider crucial to distinguish between the original Boole’s logic and its modern development as Boolean logic in order to understand their theoretical and applied capacities. In addition, the development of Boolean logic constitutes a strong example about the relationships between logic, an algebraic language of thoughts, and computation. Target setting. Boole’s logic is generally perceived as equivalent to Boolean logic despite their mathematical and conceptual differences. The influences of Boolean logic on computer science are recognized especially in their applications in circuits design. However, it appears that the influence of this logic on Cryptography is less cited in the literature when studying the relationships between logic and computer science. Actual scientific researches and issues analysis. Studies of cryptographic Boolean functions and applications have been realized by scholars such as T. Cusick, and P. Stanica. Boolean methods in Mathematics are studied by Y. Crama and P. L. Hammer. Some differences between the original Boole’s logic and the modern Boolean logic have been pointed out and promoted by N. J. Wild berger. Boole’s algebra as a mathematical language of thought has been presented in many fundamental handbooks such as those written or edited by D. M. Gabbay, J. Woods, W. Kneale, M. Kneale, and L. Haaparanta. The research objective. The first objective of this research is to formally explain the theoretical differences between Boole’s logic and the modern Boolean logic. The second objective is to show the immense role of Boolean logic in computer science through the developments of circuits design and cryptography. The statement of basic material. The developments of an algebraic logical language of thoughts by G. Boole are considered using historical and theoretical perspectives. The technical implementations of Boolean logic in combinational circuits and in modern cryptography show strong influences of a 19th century logic on the latest technologies of computing. Conclusions. In this research we came to the following results: 1) Boolean logic is different but derived from the original logic of Boole; it has been obtained due to a transformational process that led to a two-valued logic. 2) This two-valued logic made possible its digital implementation into a binary system. 3) The use of Boolean logic in circuits’ analysis and design constitutes a strong example of the influences of logic on computer science. 4) The use of Boolean logic in cryptography constitutes another strong example of the role of logic in modern computation. [ABSTRACT FROM AUTHOR]

Suppose we are given a set Φ of m Boolean formulas with the information that e of these formulas are unconfirmed, while the actual set of unconfirmed formulas is not disclosed to us. Let us denote by Rest(Φ,e) the family of all subsets of Φ having m-e elements. We are interested in the problem whether a Boolean formula ω is a consequence of Ψ for each Ψ∊Rest(Φ,e). More generally, given for each i=1,#8230;,h a set Φi of mi Boolean formulas and an integer 0⩽ei1⋀#8230;⋀Ψh for every choice of Ψi ∊Rest(Φi,ei)?We construct a quadratic reduction of this problem to the consequence problem in infinite-valued Łukasiewicz propositional logic Ł∞. Our reduction shows the usefulness of Ł∞ for the formal handling of unreliable Boolean information. [ABSTRACT FROM AUTHOR]

Moore's law relies on device size reduction for progress, but an energy tax due to Boolean logic properties could block this progress. There are alternatives. [ABSTRACT FROM AUTHOR]

In geotechnical modelling, some minor stratigraphic features are usually discarded in order to simplify the problem, avoiding to deal with further uncertainties about their position, thickness and lateral extent. The study proposes a new method based on the stochastic generation of different soil layers configurations, following a boolean logic: the material is either matrix or layer (i.e., gravel lenses in a clay-rich matrix).The method has been called BoSG (Boolean Stochastic Generation). The methodology allows to randomize the presence of a specific material interdigitated in a uniform matrix thus enabling to gather a dataset which could be analysed automatically, in order quantify the error associated with the adopted simplification. The commercial codes FLAC and FLAC3D were used for the geotechnical modelling. A specifically-coded MatLab program allows to generate randomly the different soil configurations and then to automate the computation with the commercial software in order to maximize the sample number. In this paper the methodology is applied with reference to a simplified slope in 2D and in 3D. Results show that within a low resistance matrix, the presence of layers with higher friction angle can significantly affect significantly the stability and the displacement pattern of an unstable slope. Therefore, a method to investigate the influence of the spatial distribution of these layers can be particularly useful. [ABSTRACT FROM AUTHOR]

We discuss the role and importance of dynamics in the brain and biological neural networks and argue that dynamics is one of the main missing elements in conventional Boolean logic and circuits. We summarize a simple dynamics based computing method, and categorize different techniques that we have introduced to realize logic, functionality, and programmability. We discuss the role and importance of coupled dynamics in networks of biological excitable cells, and then review our simple coupled dynamics based method for computing. In this paper, for the first time, we show how dynamics can be used and programmed to implement computation in any given base, including but not limited to base two. [ABSTRACT FROM AUTHOR]

This paper discusses the formalization of the binary number system and the groundwork that was laid for the future of digital circuitry, computers, and the field of computer science. The goal of this paper is to show how Gottfried Leibniz formalized the binary number system and solidified his thoughts through an analysis of the Chinese I Ching. In addition, Leibniz's work in logic and with computing machines is presented. This work laid the foundation for Boolean algebra and digital circuitry which was continued by George Boole, Augustus De Morgan, and Claude Shannon in the centuries following. Some have coined Leibniz the world's first computer scientist, and this paper will attempt to demonstrate a validation of this conjecture. [ABSTRACT FROM AUTHOR]

In this paper, we propose a modified low power 10-T Adder design using 10 transistors & 12 transistors featuring higher computing speed, lower operating voltage, and lower energy consumption compared with peer designs. The simulation results, based on 0.18um process models, indicate that the proposed design has the lowest working Vdd and highest working frequency among all designs using 10 transistors & 12 transistors. It also features the lowest energy consumption per addition among these designs. In addition, the performance edge of the proposed design in both speed and energy consumption becomes even more significant as the word length of the adder increases. [ABSTRACT FROM AUTHOR]

Abstract: We present a unifying semantical and proof-theoretical framework for investigating depth-bounded approximations to Boolean Logic, namely approximations in which the number of nested applications of a single structural rule, representing the classical Principle of Bivalence, is bounded above by a fixed natural number. These approximations provide a hierarchy of tractable logical systems that indefinitely converge to classical propositional logic. The framework we present here brings to light a general approach to logical inference that is quite different from the standard Gentzen-style approaches, while preserving some of their nice proof-theoretical properties, and is common to several proof systems and algorithms, such as KE, KI and Stålmarck’s method. [Copyright &y& Elsevier]

The orbital LANDSAT-8/OLI sensor and SRTM altimetric images combined with Boolean algebra and complemented by fieldwork and XRD, chemical and spectroradiometric analysis, allowed to develop a mathematical model for mapping the tropical regolith in the Midwest of Brazil. It was used four mapping classes following the arithmetic band operations of 4/2 and (4+6)/5 to identify lateritic duricrusts, loosed iron concretions, nodules and pisoliths, (6/7)/(5/4) to parent rock, saprolite, mottled horizon and soil, and (5–4)/(5+4) to vegetation. Hyperspectral Hyperion/EO-1 image endorse the mathematical model identifying the pure pixels of kaolinite, goethite, and hematite in the lateritic duricrusts, loosed iron concretions, nodules and pisoliths occurrence pixels. Narrow and low reflectance spectroscopy concavity between 400 and 600 nm and a broad medium concavity between 800 and 1100 nm are the typical spectral features of the study lateritic duricrusts, highlighting the strong influence of the goethite and hematite contents. The development of these LANDSAT-8/OLI and Hyperion/EO-1 classification models and the identification of the specific reflectance spectroscopy features for the tropical lateritic terrains, provide a more precise regolith-geological architecture. It is very helpful for mineral exploration, for developed strategies for understanding the regolith landscape better and how surficial geochemical anomalies are formed, and for geomorphology interpretation in deeply weathered regions. • Orbital LANDSAT-8/OLI sensor and SRTM images combined with Boolean algebra allowed developed the regolith mathematical model. • Hyperspectral Hyperion/EO-1 image endorse the mathematical model. • Medium concavity between 800 and 1100 nm are the typical spectral features of the lateritic duricrusts. • It was provided a more precise regolith-geological map. • Useful for mineral exploration and regolith and geomorphology interpretation in deeply weathered regions. [ABSTRACT FROM AUTHOR]

Recently, a systematic procedure was proposed to derive a minimum input quantum circuit for any given classical logic with the generalized quantum Toffoli gate, which is universal in Boolean logic. Since quantum Boolean circuits are reversible, we can apply this property to build quantum iterative logic array (QILA). QILA can be easily tested in constant time (C-testable) if stuck-at fault model is assumed. In this paper, we use Hadamard and general controlled-controlled not gates to make QILA 1-testable. That is, for any quantum Boolean circuit, the number of test patterns is independent of both the size of the array and the length of the inputs. [ABSTRACT FROM PUBLISHER]

A systems method based on a Boolean approach is used to predict medium- to long-term behaviour of estuary morphology. Boolean networks are formed for various types of generic estuaries by taking into account the feedback involved between various estuary elements and external forcing which drive morphological evolution. A logical framework is then developed, and the Boolean matrix is derived. Various different potential morphological evolutionary pathways are then selected from the Boolean matrix, analysed, and discussed. The Boolean method provides a complementary approach for qualitative modelling of complex estuary systems. The method was applied to the Ribble Estuary in northwest England, and the predictions from the Boolean approach were in very good qualitative agreement with the observed morphological evolution of the Ribble Estuary during the last 150 years. [ABSTRACT FROM AUTHOR]

The author develops a new game-theoretic approach, anchored not in Boolean two-valued logic but instead in linguistic fuzzy logic. The latter is characterized by two key features. First, the truth values of logical propositions span a set of linguistic terms such as true, very true, almost false, very false, and false. Second, the logic allows logical categories to overlap in contrast to Boolean logic, where the two possible logical categories, "true" and "false," are sharply distinct. A game becomes a linguistic fuzzy logic game by turning strategies into linguistic fuzzy strategies, players' preferences into linguistic fuzzy preferences, and the rules of reasoning and inferences of the game into linguistic fuzzy reasoning operating according to linguistic fuzzy logic. This leads to the introduction of a new notion of linguistic fuzzy domination and linguistic Nash equilibrium. [ABSTRACT FROM AUTHOR]

Logic Regression is an adaptive regression methodology mainly developed to explore high-order interactions in genomic data. Logic Regression is intended for situations where most of the covariates in the data to be analyzed are binary. The goal of Logic Regression is to find predictors that are Boolean (logical) combinations of the original predictors. In this article, we give an overview of the methodology and discuss some applications. We also describe the software for Logic Regression, which is available as an R and S-Plus package. [Copyright &y& Elsevier]

An extension principle for fuzzy logic is considered to obtain a Boolean logic able to manage incomplete and partially inconsistent information. Such a logic is strictly related with an extended notion of belief measure. This gives tools to design expert systems able to manage information probabilistic in nature. [ABSTRACT FROM AUTHOR]