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Shore, Richard A. "The Bulletin of Symbolic Logic." Bulletin of Symbolic Logic 1, no. 1 (March 1995): 1–3. http://dx.doi.org/10.1017/s107989860000826x.
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At the 1993 Annual meeting of the Association for Symbolic Logic, the Council of the association voted to establish a new journal to be called The Bulletin of Symbolic Logic. The intended goal of the Council was to produce a journal that would be both accessible and of interest to as wide an audience as possible, with the stated purpose of keeping the logic community abreast of important developments in all parts of our discipline. The first issue was to appear in March of 1995 and you now have it in your hands.In accordance with the Council resolution, we intend to publish primarily two types of papers. The first section of The Bulletin, Articles, will usually be devoted to works of an expository or survey nature. These papers will generally present topics of broad interest in a way that should be accessible to a large majority of the members of the Association. Topics will be drawn from all areas of logic including mathematical or philosophical logic, logic in computer science or linguistics, the history or philosophy of logic, logic education and applications of logic to other fields. One view of a role that this section of The Bulletin will play is as an ongoing handbook of logic.
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Peckhaus, Volker. "19th Century Logic Between Philosophy and Mathematics." Bulletin of Symbolic Logic 5, no. 4 (December 1999): 433–50. http://dx.doi.org/10.2307/421117.
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AbstractThe history of modern logic is usually written as the history of mathematical or, more general, symbolic logic. As such it was created by mathematicians. Not regarding its anticipations in Scholastic logic and in the rationalistic era, its continuous development began with George Boole's The Mathematical Analysis of Logic of 1847, and it became a mathematical subdiscipline in the early 20th century. This style of presentation cuts off one eminent line of development, the philosophical development of logic, although logic is evidently one of the basic disciplines of philosophy. One needs only to recall some of the standard 19th century definitions of logic as, e.g., the art and science of reasoning (Whateley) or as giving the normative rules of correct reasoning (Herbart).In the paper the relationship between the philosophical and the mathematical development of logic will be discussed. Answers to the following questions will be provided:1. What were the reasons for the philosophers' lack of interest in formal logic?2. What were the reasons for the mathematicians' interest in logic?3. What did “logic reform” mean in the 19th century? Were the systems of mathematical logic initially regarded as contributions to a reform of logic?4. Was mathematical logic regarded as art, as science or as both?
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Kim, S. H., and N. P. Suh. "Mathematical Foundations for Manufacturing." Journal of Engineering for Industry 109, no. 3 (August 1, 1987): 213–18. http://dx.doi.org/10.1115/1.3187121.
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For the field of manufacturing to become a science, it is necessary to develop general mathematical descriptions for the analysis and synthesis of manufacturing systems. Standard analytic models, as used extensively in the past, are ineffective for describing the general manufacturing situation due to their inability to deal with discontinuous and nonlinear phenomena. These limitations are transcended by algebraic models based on set structures. Set-theoretic and algebraic structures may be used to (1) express with precision a variety of important qualitative concepts such as hierarchies, (2) provide a uniform framework for more specialized theories such as automata theory and control theory, and (3) provide the groundwork for quantitative theories. By building on the results of other fields such as automata theory and computability theory, algebraic structures may be used as a general mathematical tool for studying the nature and limits of manufacturing systems. This paper shows how manufacturing systems may be modeled as automatons, and demonstrates the utility of this approach by discussing a number of theorems concerning the nature of manufacturing systems. In addition symbolic logic is used to formalize the Design Axioms, a set of generalized decision rules for design. The application of symbolic logic allows for the precise formulation of the Axioms and facilitates their interpretation in a logical programming language such as Prolog. Consequently, it is now possible to develop a consultive expert system for axiomatic design.
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Davis, Martin. "American Logic in the 1920s." Bulletin of Symbolic Logic 1, no. 3 (September 1995): 273–78. http://dx.doi.org/10.2307/421156.
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In 1934 Alonzo Church, Kurt Gödei, S. C. Kleene, and J. B. Rosser were all to be found in Princeton, New Jersey. In 1936 Church founded The Journal of Symbolic Logic. Shortly thereafter Alan Turing arrived for a two year visit. The United States had become a world center for cutting-edge research in mathematical logic. In this brief survey1 we shall examine some of the writings of American logicians during the 1920s, a period of important beginnings and remarkable insights as well as of confused gropings.The publication of Whitehead and Russell's monumental Principia Mathematica [18] during the years 1910-1913 provided the basis for much of the research that was to follow. It also provided the basis for confusion that remained a factor during the period we are discussing. In 1908, Henri Poincaré, a famous skeptic where mathematical logic was concerned, wrote pointedly ([13]):It is difficult to admit that the word if acquires, when written ⊃, a virtue it did not possess when written if.Principia provided no very convincing answer to Poincaré. Indeed the fact that the authors of Principia saw fit to place their first two “primitive propositions”*1.1: Anything implied by a true proposition is true.*1.2: ⊢ p ⋁ p ⊃ punder one and the same heading suggest that they had thought of what they were doing as just such a translation as Poincare had derided.
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Sato, T., and Y. Kameya. "Parameter Learning of Logic Programs for Symbolic-Statistical Modeling." Journal of Artificial Intelligence Research 15 (December 1, 2001): 391–454. http://dx.doi.org/10.1613/jair.912.
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We propose a logical/mathematical framework for statistical parameter learning of parameterized logic programs, i.e. definite clause programs containing probabilistic facts with a parameterized distribution. It extends the traditional least Herbrand model semantics in logic programming to distribution semantics, possible world semantics with a probability distribution which is unconditionally applicable to arbitrary logic programs including ones for HMMs, PCFGs and Bayesian networks. We also propose a new EM algorithm, the graphical EM algorithm, that runs for a class of parameterized logic programs representing sequential decision processes where each decision is exclusive and independent. It runs on a new data structure called support graphs describing the logical relationship between observations and their explanations, and learns parameters by computing inside and outside probability generalized for logic programs. The complexity analysis shows that when combined with OLDT search for all explanations for observations, the graphical EM algorithm, despite its generality, has the same time complexity as existing EM algorithms, i.e. the Baum-Welch algorithm for HMMs, the Inside-Outside algorithm for PCFGs, and the one for singly connected Bayesian networks that have been developed independently in each research field. Learning experiments with PCFGs using two corpora of moderate size indicate that the graphical EM algorithm can significantly outperform the Inside-Outside algorithm.
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Firnanda, Dwi Tri Fresti, and Indah Wahyuni. "Semiotic Mathematics Representation Ability Based on Symbolic in Solving SPLSV Problems in Class VII Students." Ta'dib 27, no. 1 (June 13, 2024): 205. http://dx.doi.org/10.31958/jt.v27i1.11562.
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Mathematical semiotic representation is the ability to analyze and express mathematical ideas or notions of a phenomenon and everyday problem situations into the form of signs, images, symbols, and symbols that represent them and provide meaning and explanation to a package of verbal sign messages. The symbolic stage is the stage where students have understood the symbols and concepts and have ideas that are strongly influenced by language and logic skills and students are able to manipulate symbols or symbols of a particular object. The purpose of this study was to determine the representation of symbolic-based mathematical semiotics in seventh grade students of MTS Al Barokah Ajung Jember on SPLSV material using qualitative descriptive method. The instrument used by researchers in the form of written test questions consisting of two questions tailored to the symbolic representation that has two indicators that use mathematical symbols to solve problems and interpret mathematical symbols. From the results of research that has been done obtained the error of representation on indicators using mathematical symbols to solve the problem of 100% and error of representation on indicators interpreting mathematical symbols of 0%. Several studies have been carried out to explain the mistakes that students make in representation skills. This paper presents the ability of mathematical symbolic semiotic representation of students who are more specific in solving SPLSV problems that can be considered by teachers in designing learning about the ability of mathematical semiotic representation and information for observers of mathematics education.
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Ashok, Dhananjay, Joseph Scott, Sebastian J. Wetzel, Maysum Panju, and Vijay Ganesh. "Logic Guided Genetic Algorithms (Student Abstract)." Proceedings of the AAAI Conference on Artificial Intelligence 35, no. 18 (May 18, 2021): 15753–54. http://dx.doi.org/10.1609/aaai.v35i18.17873.
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We present a novel Auxiliary Truth enhanced Genetic Algorithm (GA) that uses logical or mathematical constraints as a means of data augmentation as well as to compute loss (in conjunction with the traditional MSE), with the aim of increasing both data efficiency and accuracy of symbolic regression (SR) algorithms. Our method, logic-guided genetic algorithm (LGGA), takes as input a set of labelled data points and auxiliary truths (AT) (mathematical facts known a priori about the unknown function the regressor aims to learn) and outputs a specially generated and curated dataset that can be used with any SR method. We evaluate LGGA against state-of-the-art SR tools, namely, Eureqa and TuringBot and find that using these SR tools in conjunction with LGGA results in them solving up to 30% more equations, needing only a fraction of the amount of data compared to the same tool without LGGA, i.e., resulting in up to a 61.9% improvement in data efficiency.
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Lobovikov, Vladimir O. "A wonderful analogy between Augustine’s definition of moral-value- functional sense of response-action and Philo’s definition of truth-functional sense of implication in logic." CIENCIA ergo sum 27, no. 3 (August 12, 2020): e94. http://dx.doi.org/10.30878/ces.v27n3a4.
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The paper is dvoted to interdisciplinary research at the intersection of symbolic logic, mathematical ethics, and philosophical theology. By comparing definitions of relevant functions, a surprising analogy is discovered between the well-known Philo’s precise definition of implication in logic (classical one) and Augustine’s precise definition of God’s morally good reaction to human actions. The moral-value-table-representation of Augustinian doctrine is compared with moral-value-table-representations of Pelagius’ and Leo Tolstoy’s views of adequate moral-response-actions.
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Riede, U. N., Joh Kensuke, and G. William Moore. "Symbolic logic model of cellular adaptation." Mathematical Modelling 7, no. 9-12 (1986): 1301–23. http://dx.doi.org/10.1016/0270-0255(86)90082-5.
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RAHEEM Tunde Rasheed and SAM-KAYODE Christianah Olajumoke (Ph. D). "The Use of Truth Table, Logical Reasoning and Logic Gate in Teaching and Learning Process." International Journal of Latest Technology in Engineering Management & Applied Science 13, no. 6 (June 28, 2024): 1–12. http://dx.doi.org/10.51583/ijltemas.2024.130601.
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The concept of truth table is based on the content to analyze in teaching and learning logical reasoning and logic gate, which is a visual representation of possible combination of input and output information of Boolean prepositions in logical reasoning and Boolean functions in logic gate plotted into a table. It adopts Boolean algebra for problem solving as a method or science of reasoning, or ability to argue and convince. In the teaching and learning processes of logic, formal and informal reasoning tasks are used in a variety of ways, including using symbols and entirely in plain language without symbols where symbolic logics are commonly referred to as mathematical logic. This paper therefore considers the Use of Truth Table, Logical Reasoning and Logic Gate in Teaching and Learning Process It highlighted the benefits of using the truth table and compared logical reasoning and logic gate connectives and concluded that, there exist similarities, differences and peculiarities in the interactive features of the content of the truth table. The paper suggested that teachers should vividly state the similarities, differences and peculiarities in the interactive features of truth table in logical reasoning and logic gate while incorporating thought in teaching and learning process to avoid confusion.
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Mosser, Kurt. "The Grammatical Background of Kant's General Logic." Kantian Review 13, no. 1 (March 2008): 116–40. http://dx.doi.org/10.1017/s1369415400001114.
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In theCritique of Pure Reason, Kant conceives of general logic as a set of universal and necessary rules for the possibility of thought, or as a set of minimal necessary conditions for ascribing rationality to an agent (exemplified by the principle of non-contradiction). Such a conception, of course, contrasts with contemporary notions of formal, mathematical or symbolic logic. Yet, in so far as Kant seeks to identify those conditions that must hold for the possibility of thought in general, such conditions must holda fortiorifor any specific model of thought, including axiomatic treatments of logic and standard natural deduction models of first-order predicate logic. Kant's general logic seeks to isolate those conditions by thinking through – or better, reflecting on – those conditions that themselves make thought possible.
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Miguel Tomé, Sergio. "Towards a model-theoretic framework for describing the semantic aspects of cognitive processes." ADCAIJ: Advances in Distributed Computing and Artificial Intelligence Journal 8, no. 4 (April 22, 2020): 83–96. http://dx.doi.org/10.14201/adcaij2019848396.
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Semantics is one of the most challenging aspects of cognitive architectures. Mathematical logic, or linguistics, highlights that semantics is essential to human cognition. The Cognitive Theory of True Conditions (CTTC) is a proposal to implement cognitive abilities and to describe the semantics of symbolic cognitive architectures based on model-theoretic semantics. This article focuses on the concepts supporting the mathematical formulation of the CTTC, its relationship to other proposals, and how it can be used as a framework for designing cognitive abilities in agents.
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Ferreirós, José. "La lógica matemática: una disciplina en busca de encuadre." THEORIA 25, no. 3 (September 27, 2010): 279–99. http://dx.doi.org/10.1387/theoria.717.
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We offer an analysis of the disciplinary transformations underwent by mathematical or symbolic logic since its emergence in the late 19th century. Examined are its origins as a hybrid of philosophy and mathematics, the maturity and institutionalisation attained under the label "logic and foundations," a second wave of institutionalisation in the Postwar period, and the institutional developments since 1975 in connection with computer science and with the study of language and informatics. Although some "internal history" is discussed, the main focus is on the emergence, consolidation and convolutions of logic as a discipline, through various professional associations and journals, in centers such as Torino, Göttingen, Warsaw, Berkeley, Princeton, Carnegie Mellon, Stanford, and Amsterdam.
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Scott, Joseph, Maysum Panju, and Vijay Ganesh. "LGML: Logic Guided Machine Learning (Student Abstract)." Proceedings of the AAAI Conference on Artificial Intelligence 34, no. 10 (April 3, 2020): 13909–10. http://dx.doi.org/10.1609/aaai.v34i10.7227.
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We introduce Logic Guided Machine Learning (LGML), a novel approach that symbiotically combines machine learning (ML) and logic solvers to learn mathematical functions from data. LGML consists of two phases, namely a learning-phase and a logic-phase with a corrective feedback loop, such that, the learning-phase learns symbolic expressions from input data, and the logic-phase cross verifies the consistency of the learned expression with known auxiliary truths. If inconsistent, the logic-phase feeds back "counterexamples" to the learning-phase. This process is repeated until the learned expression is consistent with auxiliary truth. Using LGML, we were able to learn expressions that correspond to the Pythagorean theorem and the sine function, with several orders of magnitude improvements in data efficiency compared to an approach based on an out-of-the-box multi-layered perceptron (MLP).
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Zhang, Hehua, Yu Jiang, William N. N. Hung, Xiaoyu Song, Ming Gu, and Jiaguang Sun. "Symbolic Analysis of Programmable Logic Controllers." IEEE Transactions on Computers 63, no. 10 (October 2014): 2563–75. http://dx.doi.org/10.1109/tc.2013.124.
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Mezhoud, Salim. "Language Mathematics and Mathematics Language, Reading from Computational Linguistics." Mathematical Linguistics 1, no. 1 (December 31, 2021): 7–24. http://dx.doi.org/10.58205/ml.v1i1.140.
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The language of mathematics is the system used by mathematicians to communicate mathematical ideas among themselves. This language consists of a substrate of some natural language using technical terms and grammatical conventions that are peculiar to mathematical discourse, supplemented by a highly specialized symbolic notation for mathematical formulas.
mathematical characterizations of various notions of linguistic complexity include also computational linguistics, philosophical logic, knowledge representation as a branch of artificial intelligence, theoretical computer science, and computational psychology. Mathematical linguistics has initially served as a foundation for computational linguistics, though its research agenda of designing machines to simulate natural language understanding is clearly more applied. Inductive methods have gained the upper hand in applied computational linguistics
The question is whether mathematics is a language, or that language is mathematical, and how computational linguistics employs language as mathematics.
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Amendola, Giovanni. "Special Issue on Logic-Based Artificial Intelligence." Algorithms 16, no. 2 (February 13, 2023): 106. http://dx.doi.org/10.3390/a16020106.
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Since its inception, research in the field of Artificial Intelligence (AI) has had a fundamentally logical approach; therefore, discussions have taken place to establish a way of distinguishing symbolic AI from sub-symbolic AI, basing the approach instead on the statistical approaches typical of machine learning, deep learning or Bayesian networks [...]
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Hellman, Geoffrey. "Stewart Shapiro. Second-order languages and mathematical practice. The journal of symbolic logic, vol. 50 (1985), pp. 714–742." Journal of Symbolic Logic 54, no. 1 (March 1989): 291–93. http://dx.doi.org/10.2307/2275038.
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Zach, Richard. "Completeness Before Post: Bernays, Hilbert, and the Development of Propositional Logic." Bulletin of Symbolic Logic 5, no. 3 (September 1999): 331–66. http://dx.doi.org/10.2307/421184.
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AbstractSome of the most important developments of symbolic logic took place in the 1920s. Foremost among them are the distinction between syntax and semantics and the formulation of questions of completeness and decidability of logical systems. David Hilbert and his students played a very important part in these developments. Their contributions can be traced to unpublished lecture notes and other manuscripts by Hilbert and Bernays dating to the period 1917–1923. The aim of this paper is to describe these results, focussing primarily on propositional logic, and to put them in their historical context. It is argued that truth-value semantics, syntactic (“Post-”) and semantic completeness, decidability, and other results were first obtained by Hilbert and Bernays in 1918, and that Bernays's role in their discovery and the subsequent development of mathematical logic is much greater than has so far been acknowledged.
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Patel, Usha, Parita Rajiv Oza, Riya Revdiwala, Utsav Mukeshchandra Haveliwala, Smita Agrawal, and Preeti Kathiria. "Fuzzy Logic Inference-Based Automated Water Irrigation System." International Journal of Ambient Computing and Intelligence 13, no. 1 (January 1, 2022): 1–15. http://dx.doi.org/10.4018/ijaci.304726.
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To fulfill the food interest of consistently expanding populace of our planet, it is important to do essential in the field of agribusiness. Traditional techniques for water systems like trench, wells, and precipitation are tedious and occasional. With the help of an automated water irrigation system the water, energy, and time can be moderated. This paper presents fuzzy rule logic inference-based automated water system framework. The soil moisture, weather forecast, crop status, and water-tank level are taken as input parameters. Soil moisture and water tank level can be recorded by utilizing sensors. The fuzzy logic-based system uses eighty-one rules to identify the amount of time to irrigate the fields. The emphasis is to solve agricultural problems by employing symbolic logic and to develop a system using computer science and mathematical logic. The use of such an automated system will decline costs, water prerequisite, and give power streamlining, with expanded proficiency.
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Roberts, Alexander. "Relative Necessity and Propositional Quantification." Journal of Philosophical Logic 49, no. 4 (December 28, 2019): 703–26. http://dx.doi.org/10.1007/s10992-019-09534-8.
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AbstractFollowing Smiley’s (The Journal of Symbolic Logic, 28, 113–134 1963) influential proposal, it has become standard practice to characterise notions of relative necessity in terms of simple strict conditionals. However, Humberstone (Reports on Mathematical Logic, 13, 33–42 1981) and others have highlighted various flaws with Smiley’s now standard account of relative necessity. In their recent article, Hale and Leech (Journal of Philosophical Logic, 46, 1–26 2017) propose a novel account of relative necessity designed to overcome the problems facing the standard account. Nevertheless, the current article argues that Hale & Leech’s account suffers from its own defects, some of which Hale & Leech are aware of but underplay. To supplement this criticism, the article offers an alternative account of relative necessity which overcomes these defects. This alternative account is developed in a quantified modal propositional logic and is shown model-theoretically to meet several desiderata of an account of relative necessity.
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Demidov, Valery Anatolyevich. "Corrigendum to: V. A. Sokolov, “On the Existence Problem of Finite Bases of Identities in the Algebras of Recursive Functions”, Modeling and analysis of information systems, vol. 27, no. 3, pp. 304-315, 2020. DOI: https://doi.org/10.18255/1818-1015-2020-3-304-315." Modeling and Analysis of Information Systems 27, no. 4 (December 20, 2020): 510–11. http://dx.doi.org/10.18255/1818-1015-2020-4-510-511.
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The author regrets that in the original list the references [3] and [4] are in the wrong places and they should be rearranged. In addition, [3] has the wrong article title. The corrected reference list is shown below.The author would like to apologize for an inconvenience caused.References[1] A. I. Mal'tsev, “Constructive algebras I”, Russian Mathematical Surveys, vol. 16, no. 3, pp. 77-129, 1961.[2] A. I. Mal'tsev, Algoritmy i rekursivnye funktsii. Moscow: Nauka, 1965, In Russian.[3] R. M. Robinson, “Primitive recursive functions”, Bulletin of the American Mathematical Society, vol. 53, no. 10,pp. 925-942, 1947.[4] J. Robinson, “General recursive functions”, Proceedings of the American Mathematical Society, vol. 1, no. 6,pp. 703-718, 1950.[5] V. A. Sokolov, “Ob odnom klasse tozhdestv v algebre Robinsona”, in 14-ya Vsesoyuznaya algebraicheskaya konferentsiya: tezisy dokladov, In Russian, vol. 2, Novosibirsk, 1977, pp. 123-124.[6] P. M. Cohn, Universal Algebra. New York, Evanston, and London: Harper & Row, 1965.[7] A. Robinson, “Equational logic for partial functions under Kleene equality: a complete and an incomplete set of rules”, The Journal of Symbolic Logic, vol. 54, no. 2, pp. 354-362, 1989.
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Nadweh, Rama Asad. "On The Fusion of Neural Networks and Fuzzy Logic, Membership Functions and Weights." Galoitica: Journal of Mathematical Structures and Applications 7, no. 1 (2023): 18–25. http://dx.doi.org/10.54216/gjmsa.070102.
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Fuzzy logic plays a huge role in the symbolic inference and causality associated with modern cognitive human systems. In this paper, we present a mathematical method that defines the mechanism of forming a hybrid structure in which neural networks and expert systems are connected so that one forms a primary processing stage for the other, where the neural network can act as a primary processor that processes low-level information, or as an internal Subsystem for learning tasks or generalization and classification. Where neural networks can be used to generate rules using training data and then submit these rules to be used by a fuzzy system to give the final results.
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Kim, Steven H., and Nam P. Suh. "Application of symbolic logic to the design axioms." Robotics and Computer-Integrated Manufacturing 2, no. 1 (January 1985): 55–64. http://dx.doi.org/10.1016/0736-5845(85)90008-0.
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Harrod, James B. "A post-structuralist revised Weil–Lévi-Strauss transformation formula for conceptual value-fields." Sign Systems Studies 46, no. 2/3 (November 19, 2018): 255–81. http://dx.doi.org/10.12697/sss.2018.46.2-3.03.
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The structuralist André-Weil–Claude-Lévi-Strauss transformation formula (CF), initially applied to kinship systems, mythology, ritual, artistic design and architecture, was rightfully criticized for its rationalism and tendency to reduce complex transformations to analogical structures. I present a revised non-mathematical revision of the CF, a general transformation formula (rCF) applicable to networks of complementary semantic binaries in conceptual value-fields of culture, including comparative religion and mythology, ritual, art, literature and philosophy. The rCF is a rule-guided formula for combinatorial conceptualizing in non-representational, presentational mythopoetics and other cultural symbolizations. I consider poststructuralist category-theoretic and algebraic mathematical interpretations of the CF as themselves only mathematical analogies, which serve to stimulate further revision of the logic model of the rCF. The rCF can be used in hypothesis-making to advance understanding of the evolution and prehistory of human symbolic behaviour in cultural space, philosophical ontologies and categories, definitions and concepts in art, religion, psychotherapy, and other cultural-value forms.
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Parisi, Luciana. "Interactive Computation and Artificial Epistemologies." Theory, Culture & Society 38, no. 7-8 (October 19, 2021): 33–53. http://dx.doi.org/10.1177/02632764211048548.
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What is algorithmic thought? It is not possible to address this question without first reflecting on how the Universal Turing Machine transformed symbolic logic and brought to a halt the universality of mathematical formalism and the biocentric speciation of thought. The article draws on Sylvia Wynter’s discussion of the sociogenic principle to argue that both neurocognitive and formal models of automated cognition constitute the epistemological explanations of the origin of the human and of human sapience. Wynter’s argument will be related to Gilbert Simondon’s reflections on ‘technical mentality’ to consider how socio-techno-genic assemblages can challenge the biocentricism and the formalism of modern epistemology. This article turns to ludic logic as one possible example of techno-semiotic languages as a speculative overturning of sociogenic programming. Algorithmic rules become technique-signs coinciding not with classic formalism but with interactive localities without re-originating the universality of colonial and patriarchal cosmogony.
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d'Avila Garcez, Artur, Dov M. Gabbay, Steffen Hölldobler, and John G. Taylor. "Journal of Applied Logic Special Volume on Neural-Symbolic Systems." Journal of Applied Logic 2, no. 3 (September 2004): 241–43. http://dx.doi.org/10.1016/j.jal.2004.03.001.
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de Mol, Liesbeth. "Closing the Circle: An Analysis of Emil Post's Early Work." Bulletin of Symbolic Logic 12, no. 2 (June 2006): 267–89. http://dx.doi.org/10.2178/bsl/1146620062.
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AbstractIn 1931 Kurt Gödel published his incompleteness results, and some years later Church and Turing showed that the decision problem for certain systems of symbolic logic has a negative solution. However, already in 1921 the young logician Emil Post worked on similar problems which resulted in what he called an “anticipation” of these results. For several reasons though he did not submit these results to a journal until 1941. This failure ‘to be the first’, did not discourage him: his contributions to mathematical logic and its foundations should not be underestimated. It is the purpose of this article to show that an interest in the early work of Emil Post should be motivated not only by this historical fact, but also by the fact that Post's approach and method differs substantially from those offered by Gödel, Turing and Church. In this paper it will be shown how this method evolved in his early work and how it finally led him to his results.
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Monk, J. Donald. "Joseph R. Shoenfield. Mathematical logic. Republication of JSL XL 234. Association for Symbolic Logic, Urbana, and A K Peters, Natick, Mass., 2001, viii + 344 pp." Bulletin of Symbolic Logic 7, no. 3 (September 2001): 376. http://dx.doi.org/10.2307/2687755.
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Filgueira Arias, Cándida, and Maria del Carmen Escribano Ródenas. "Mathematical Narrations and Poetry. A Mathematical Resilience Tool." Multidisciplinary Journal of School Education 11, no. 2 (22) (December 28, 2022): 357–81. http://dx.doi.org/10.35765/mjse.2022.1122.18.
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Mathematics frequently appear in stories, poetry, stories, literary narratives, in general in different literary genres.
Numbers and Mathematics usually appear in the stories, poems and narratives of children's and youth literature. Likewise, in these literary genres spatial relationships, shapes, sizes, quantities, numbers are verified, and it is that in Mathematics the pillars of logic and creativity underlie (Cervera, 1983).
Thus, it is intended to develop an analysis and reflection through a bibliographic review of children's and youth literature related to Mathematics as a resilient tool for coping with the teaching of this discipline, creating new learning situations to develop significant links between literature. “mathematics” and resilience.
The results of the research have revealed theoretical and practical tools (stories, tales, poetry, literary narratives, stories) that will accompany and promote resilient mathematical processes through the construction of symbolic spaces of refuge and socio-emotional acceptance through reading and creative expression motivated by children's and youth literature.
Las Matemáticas aparecen frecuentemente en cuentos, poesías, relatos, narraciones literarias, en general en distintos géneros literarios.
Los números y las Matemáticas aparecen habitualmente en los cuentos, poemas y narraciones de la literatura infantil y juvenil. Así mismo, en estos géneros literarios se constatan relaciones espaciales, formas, tamaños, cantidades, números, y es que en las “Matemáticas subyacen los pilares de la lógica y la creatividad” (Cervera, 1983, p. 32).
Así pues, se pretende desarrollar un análisis y reflexión a través de una revisión bibliográfica de la literatura infantil y juvenil relacionada con las “Matemáticas como herramienta resiliente para el afrontamiento de la enseñanza de esta disciplina creando nuevas situaciones de aprendizaje para desarrollar vínculos significativos entre la literatura matemática y la resiliencia” (Cervera, 1983, p. 22).
Los resultados de la investigación han dado a conocer herramientas teóricas y prácticas (relatos, cuentos, poesías, narraciones literarias, relatos) que acompañarán y favorecerán los procesos resilientes matemáticos a través de “la construcción de espacios simbólicos de refugio y acogimiento socioemocional mediante la lectura y la expresión creativa motivada por la literatura infantil y juvenil” (Pavón, 2015, p. 15)
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Cooper, Mark S., and Adam S. Przebinda. "Synaptic Conversion of Chloride-Dependent Synapses in Spinal Nociceptive Circuits: Roles in Neuropathic Pain." Pain Research and Treatment 2011 (May 30, 2011): 1–12. http://dx.doi.org/10.1155/2011/738645.
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Electrophysiological conversion of chloride-dependent synapses from inhibitory to excitatory function, as a result of aberrant neuronal chloride homeostasis, is a known mechanism for the genesis of neuropathic pain. This paper examines theoretically how this type of synaptic conversion can disrupt circuit logic in spinal nociceptive circuits. First, a mathematical scaling factor is developed to represent local aberration in chloride electrochemical driving potential. Using this mathematical scaling factor, electrophysiological symbols are developed to represent the magnitude of synaptic conversion within nociceptive circuits. When inserted into a nociceptive circuit diagram, these symbols assist in understanding the generation of neuropathic pain associated with the collapse of transmembrane chloride gradients. A more generalized scaling factor is also derived to represent the interplay of chloride and bicarbonate driving potentials on the function of GABAergic and glycinergic synapses. These mathematical and symbolic representations of synaptic conversion help illustrate the critical role that anion driving potentials play in the transduction of pain. Using these representations, we discuss ramifications of glial-mediated synaptic conversion in the genesis, and treatment, of neuropathic pain.
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Mewada, Shivlal. "Perspectives of Fuzzy Logic and Their Applications." International Journal of Data Analytics 2, no. 1 (January 2021): 99–145. http://dx.doi.org/10.4018/ijda.2021010105.
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Fuzzy logic is a highly suitable and applicable basis for developing knowledge-based systems in engineering and applied sciences. The concepts of a fuzzy number plays a fundamental role in formulating quantitative fuzzy variable. These are variable whose states are fuzzy numbers. When in addition, the fuzzy numbers represent linguistic concepts, such as very small, small, medium, and so on, as interpreted in a particular contest, the resulting constructs are usually called linguistic variables. Each linguistic variable the states of which are expressed by linguistic terms interpreted as specific fuzzy numbers is defined in terms of a base variable, the value of which are real numbers within a specific range. A base variable is variable in the classical sense, exemplified by the physical variable (e.g., temperature, pressure, speed, voltage, humidity, etc.) as well as any other numerical variable (e.g., age, interest rate, performance, salary, blood count, probability, reliability, etc.). Logic is the science of reasoning. Symbolic or mathematical logic is a powerful computational paradigm. Just as crisp sets survive on a 2-state membership (0/1) and fuzzy sets on a multistage membership [0 - 1], crisp logic is built on a 2-state truth-value (true or false) and fuzzy logic on a multistage truth-value (true, false, very true, partly false and so on). The author now briefly discusses the crisp logic and fuzzy logic. The aim of this paper is to explain the concept of classical logic, fuzzy logic, fuzzy connectives, fuzzy inference, fuzzy predicate, modifier inference from conditional fuzzy propositions, generalized modus ponens, generalization of hypothetical syllogism, conditional, and qualified propositions. Suitable examples are given to understand the topics in brief.
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Ott, Natalie, Roland Brünken, Markus Vogel, and Sarah Malone. "Multiple symbolic representations: The combination of formula and text supports problem solving in the mathematical field of propositional logic." Learning and Instruction 58 (December 2018): 88–105. http://dx.doi.org/10.1016/j.learninstruc.2018.04.010.
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Simpson, Stephen G. "Partial realizations of Hilbert's program." Journal of Symbolic Logic 53, no. 2 (June 1988): 349–63. http://dx.doi.org/10.1017/s0022481200028309.
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§0. Introduction. What follows is a write-up of my contribution to the symposium “Hilbert's Program Sixty Years Later” which was sponsored jointly by the American Philosophical Association and the Association for Symbolic Logic. The symposium was held on December 29,1985 in Washington, D. C. The panelists were Solomon Feferman, Dag Prawitz and myself. The moderator was Wilfried Sieg. The research which I discuss here was partially supported by NSF Grant DMS-8317874.I am grateful to the organizers of this timely symposium on an important topic. As a mathematician I particularly value the opportunity to address an audience consisting largely of philosophers. It is true that I was asked to concentrate on the mathematical aspects of Hilbert's program. But since Hilbert's program is concerned solely with the foundations of mathematics, the restriction to mathematical aspects is really no restriction at all.Hilbert assigned a special role to a certain restricted kind of mathematical reasoning known as finitistic. The essence of Hilbert's program was to justify all of set-theoretical mathematics by means of a reduction to finitism. It is now well known that this task cannot be carried out. Any such possibility is refuted by Gödel's theorem. Nevertheless, recent research has revealed the feasibility of a significant partial realization of Hilbert's program. Despite Gödel's theorem, one can give a finitistic reduction for a substantial portion of infinitistic mathematics including many of the best-known nonconstructive theorems. My purpose here is to call attention to these modern developments.
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Chernoskutov, Yu Yu. "On the Syllogistic of G. Boole." Discourse 7, no. 2 (April 29, 2021): 5–15. http://dx.doi.org/10.32603/2412-8562-2021-7-2-5-15.
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Introduction. This article focuses on the investigation of Boole’s theory of categorical syllogism, exposed in his book “The Mathematical analysis of Logic”. That part of Boolean legacy has been neglected in the prevailed investigations on the history of logic; the latter provides the novelty of the work presented.Methodology and sources. The formal reconstruction of the methods of algebraic presentation of categorical syllogism, as it is exposed in the original work of Boole, is conducted. The character of Boolean methods is investigated in the interconnections with the principles of symbolic algebra on the one hand, and with the principles of signification, taken from R. Whately, on the other hand. The approaches to signification, grounding the syllogistic theories of Boole and Brentano, are analyzed in comparison, wherefrom we explain the reasons why the results of those theories are different so much.Results and discussion. It is demonstrated here that Boole has borrowed the principles of signification from the Whately’s book “The Elements of Logic”. The interpreting the content of the terms as classes, being combined with methods of symbolic algebra, has determined the core features of Boolean syllogism theory and its unexpected results. In contrast to Whately, Boole conduct the approach to ultimate ends, overcoming the restrictions imposed by Aristotelean doctrine. In particular, he neglects the distinction of subject and predicate among the terms of proposition, the order of premises, and provide the possibility to draw conclusions with negative terms. At the same time Boole missed that the forms of inference, parallel to Bramantip and Fresison, are legitimate forms in his system. In spite of the apparent affinities between the Boolean and Brentanian theories of judgment, the syllogistics of Boole appeared to be more flexible. The drawing of particular conclusion from universal premises is allowable in Boolean theory, but not in Brentanian one; besides, in his theory is allowable the drawing of conclusion from two negative premises, which is prohibited in Aristotelian syllogistic.Conclusion. Boole consistently interpreted signification of terms as classes; being combine with methods symbolic algebra it led to very flexible syllogism theory with rich results.
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Kilmister, C. W. "Mathematical logic, by J. R. Shoenfield. Pp. 344. £24. 2001. ISBN 1 56881 135 7 (Association for Symbolic Logic, in collaboration with A. K. Peters Ltd.)." Mathematical Gazette 87, no. 509 (July 2003): 407. http://dx.doi.org/10.1017/s0025557200173474.
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WHITEN, BILL. "A SIMPLE ALGORITHM FOR DEDUCTION." ANZIAM Journal 51, no. 1 (July 2009): 102–22. http://dx.doi.org/10.1017/s1446181109000352.
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AbstractIt is shown that a simple deduction engine can be developed for a propositional logic that follows the normal rules of classical logic in symbolic form, but the description of what is known about a proposition uses two numeric state variables that conveniently describe unknown and inconsistent, as well as true and false. Partly true and partly false can be included in deductions. The multi-valued logic is easily understood as the state variables relate directly to true and false. The deduction engine provides a convenient standard method for handling multiple or complicated logical relations. It is particularly convenient when the deduction can start with different propositions being given initial values of true or false. It extends Horn clause based deduction for propositional logic to arbitrary clauses. The logic system used has potential applications in many areas. A comparison with propositional logic makes the paper self-contained.
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BEGGS, EDWIN, JOSÉ FÉLIX COSTA, DIOGO POÇAS, and JOHN V. TUCKER. "Computations with oracles that measure vanishing quantities." Mathematical Structures in Computer Science 27, no. 8 (June 23, 2016): 1315–63. http://dx.doi.org/10.1017/s0960129516000219.
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We consider computation with real numbers that arise through a process of physical measurement. We have developed a theory in which physical experiments that measure quantities can be used as oracles to algorithms and we have begun to classify the computational power of various forms of experiment using non-uniform complexity classes. Earlier, in Beggs et al. (2014 Reviews of Symbolic Logic7(4) 618–646), we observed that measurement can be viewed as a process of comparing a rational number z – a test quantity – with a real number y – an unknown quantity; each oracle call performs such a comparison. Experiments can then be classified into three categories, that correspond with being able to return test results $$\begin{eqnarray*} z < y\text{ or }z > y\text{ or }\textit{timeout},\\ z < y\text{ or }\textit{timeout},\\ z \neq y\text{ or }\textit{timeout}. \end{eqnarray*} $$ These categories are called two-sided, threshold and vanishing experiments, respectively. The iterative process of comparing generates a real number y. The computational power of two-sided and threshold experiments were analysed in several papers, including Beggs et al. (2008 Proceedings of the Royal Society, Series A (Mathematical, Physical and Engineering Sciences)464 (2098) 2777–2801), Beggs et al. (2009 Proceedings of the Royal Society, Series A (Mathematical, Physical and Engineering Sciences)465 (2105) 1453–1465), Beggs et al. (2013a Unconventional Computation and Natural Computation (UCNC 2013), Springer-Verlag 6–18), Beggs et al. (2010b Mathematical Structures in Computer Science20 (06) 1019–1050) and Beggs et al. (2014 Reviews of Symbolic Logic, 7 (4):618-646). In this paper, we attack the subtle problem of measuring physical quantities that vanish in some experimental conditions (e.g., Brewster's angle in optics). We analyse in detail a simple generic vanishing experiment for measuring mass and develop general techniques based on parallel experiments, statistical analysis and timing notions that enable us to prove lower and upper bounds for its computational power in different variants. We end with a comparison of various results for all three forms of experiments and a suitable postulate for computation involving analogue inputs that breaks the Church–Turing barrier.
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Becker, Howard. "Greg Hjorth. Classification and orbit equivalence relations. Mathematical Surveys and Monographs, vol. 75. American Mathematical Society, Providence, RI, 2000, xviii + 195 pp. - Greg Hjorth. A dichotomy theorem for turbulence. The Journal of Symbolic Logic, vol. 67 no. 4 (2002), pp. 1520–1540." Bulletin of Symbolic Logic 16, no. 3 (September 2010): 403–5. http://dx.doi.org/10.2178/bsl/1286284560.
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Roanes-Lozano, E., Luis M. Laita, and E. Roanes-Macias. "A Symbolic-Numeric Approach to MPL Continuous Logic and to Rule Based Expert Systems whose Underlying Logic is MPL." Open Applied Mathematics Journal 2, no. 1 (October 23, 2008): 126–33. http://dx.doi.org/10.2174/1874114200802010126.
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Wang, Rui, Wanwei Liu, Tun Li, Xiaoguang Mao, and Ji Wang. "Bounded Model Checking of ETL Cooperating with Finite and Looping Automata Connectives." Journal of Applied Mathematics 2013 (2013): 1–12. http://dx.doi.org/10.1155/2013/462532.
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As a complementary technique of the BDD-based approach, bounded model checking (BMC) has been successfully applied to LTL symbolic model checking. However, the expressiveness of LTL is rather limited, and some important properties cannot be captured by such logic. In this paper, we present a semantic BMC encoding approach to deal with the mixture ofETLfandETLl. Since such kind of temporal logic involves both finite and looping automata as connectives, all regular properties can be succinctly specified with it. The presented algorithm is integrated into the model checker ENuSMV, and the approach is evaluated via conducting a series of imperial experiments.
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ALPUENTE, MARÍA, SANTIAGO ESCOBAR, JULIA SAPIÑA, and DEMIS BALLIS. "Symbolic Analysis of Maude Theories with Narval." Theory and Practice of Logic Programming 19, no. 5-6 (September 2019): 874–90. http://dx.doi.org/10.1017/s1471068419000243.
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AbstractConcurrent functional languages that are endowed with symbolic reasoning capabilities such as Maude offer a high-level, elegant, and efficient approach to programming and analyzing complex, highly nondeterministic software systems. Maude’s symbolic capabilities are based on equational unification and narrowing in rewrite theories, and provide Maude with advanced logic programming capabilities such as unification modulo user-definable equational theories and symbolic reachability analysis in rewrite theories. Intricate computing problems may be effectively and naturally solved in Maude thanks to the synergy of these recently developed symbolic capabilities and classical Maude features, such as: (i) rich type structures with sorts (types), subsorts, and overloading; (ii) equational rewriting modulo various combinations of axioms such as associativity, commutativity, and identity; and (iii) classical reachability analysis in rewrite theories. However, the combination of all of these features may hinder the understanding of Maude symbolic computations for non-experienced developers. The purpose of this article is to describe how programming and analysis of Maude rewrite theories can be made easier by providing a sophisticated graphical tool called Narval that supports the fine-grained inspection of Maude symbolic computations.
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ШКАРБАН, Інна. "LINGUISTIC ASPECT OF MODALITY IN MODERN MATH DISCOURSE IN ENGLISH." Проблеми гуманітарних наук. Серія Філологія, no. 49 (June 8, 2022): 231–36. http://dx.doi.org/10.24919/2522-4565.2022.49.33.
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The article reveals linguistic aspect of modality in modern math discourse in English, critically outlines a number of actual problematic issues in the area, such as the distinction between epistemic modality and evidentiality marked by formal logics philosophical grounding. General reference to previous scholarly activity in math modality research proves that it is largely based on propositional aspects of meaning. The math text corpus analysis aims to extract a set of modalities that are indispensable for formulating modal deductive reasoning. However, from a linguistic perspective academic math discourse requires natural language premise selection in the processes of mathematical reasoning and argumentation. It is presumed that two different self-attention cognition layers are focused at the same time on the proper classical symbolic logic and mathematical elements (formal language), while the other attends to natural language. Defining the semantic meanings of math discourse modality markers involves the interpretation phase. Thus, objectivity is generally associated with evidential adverbs which are markers of the evidence verification concerning the speaker’s assessment of the truth value of the proposition. Modal auxiliaries of high, medium and low modality, semimodal verbs and conditionals involve ascribing a justification value in the set of possible logical inference making. The formal logical structure of mathematical reasoning explains the non-intuitive possibility of a deductive proof. It has been grounded that a linguistic category of modality in math discourse indispensably presupposes the universal truth of knowledge, high level of logical formalization in propositional verification status, formulaic nature of the argumentation, i.e. synthesis of hypothetical preconditions, theoretical knowledge and subjectivity of reasoning leading to a new hypothesis verification and visual exemplification of the empirical deductive processes in particular by linguistic means of modality expression.
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Gao, Yuan, Yueling Guo, Nurul Atiqah Romli, Mohd Shareduwan Mohd Kasihmuddin, Weixiang Chen, Mohd Asyraf Mansor, and Ju Chen. "GRAN3SAT: Creating Flexible Higher-Order Logic Satisfiability in the Discrete Hopfield Neural Network." Mathematics 10, no. 11 (June 1, 2022): 1899. http://dx.doi.org/10.3390/math10111899.
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One of the main problems in representing information in the form of nonsystematic logic is the lack of flexibility, which leads to potential overfitting. Although nonsystematic logic improves the representation of the conventional k Satisfiability, the formulations of the first, second, and third-order logical structures are very predictable. This paper proposed a novel higher-order logical structure, named G-Type Random k Satisfiability, by capitalizing the new random feature of the first, second, and third-order clauses. The proposed logic was implemented into the Discrete Hopfield Neural Network as a symbolic logical rule. The proposed logic in Discrete Hopfield Neural Networks was evaluated using different parameter settings, such as different orders of clauses, different proportions between positive and negative literals, relaxation, and differing numbers of learning trials. Each evaluation utilized various performance metrics, such as learning error, testing error, weight error, energy analysis, and similarity analysis. In addition, the flexibility of the proposed logic was compared with current state-of-the-art logic rules. Based on the simulation, the proposed logic was reported to be more flexible, and produced higher solution diversity.
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Brkić, Dejan, Pavel Praks, Renáta Praksová, and Tomáš Kozubek. "Symbolic Regression Approaches for the Direct Calculation of Pipe Diameter." Axioms 12, no. 9 (August 31, 2023): 850. http://dx.doi.org/10.3390/axioms12090850.
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This study provides novel and accurate symbolic regression-based solutions for the calculation of pipe diameter when flow rate and pressure drop (head loss) are known, together with the length of the pipe, absolute inner roughness of the pipe, and kinematic viscosity of the fluid. PySR and Eureqa, free and open-source symbolic regression tools, are used for discovering simple and accurate approximate formulas. Three approaches are used: (1) brute force of computing power, which provides results based on raw input data; (2) an improved method where input parameters are transformed through the Lambert W-function; (3) a method where the results are based on inputs and the Colebrook equation transformed through new suitable dimensionless groups. The discovered models were simplified by the WolframAlpha simplify tool and/or the equivalent Matlab Symbolic toolbox. Novel models make iterative calculus redundant; they are simple for computer coding while the relative error remains lower compared with the solution through nomograms. The symbolic-regression solutions discovered by brute force computing power discard the kinematic viscosity of the fluid as an input parameter, implying that it has the least influence.
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Qudrat-I Elahi, Khandakar. "A difficulty in Arrow’s impossibility theorem." International Journal of Social Economics 44, no. 12 (December 4, 2017): 1609–21. http://dx.doi.org/10.1108/ijse-02-2016-0065.
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Purpose The purpose of this paper is twofold. First, it evaluates the impossibility proposition, called the “Arrow impossibility theorem” (AIT), which is widely attributed to Arrow’s social choice theory. This theorem denies the possibility of arriving at any collective majority resolution in any group voting system if the social choice function must satisfy “certain natural conditions”. Second, it intends to show the reasons behind the proliferation of this impossibility impression. Design/methodology/approach Theoretical and philosophical. Findings Arrow’s mathematical model does not seem to suggest or support his impossibility thesis. He has considered only one voting outcome, well known by the phrase “the Condorcet paradox”. However, other voting results are equally likely from his model, which might suggest unambiguous majority choice. This logical dilemma has been created by Arrow’s excessive dependence on the language of mathematics and symbolic logic. Research limitations/implications The languages of mathematics and symbolic logic – numbers, letters and signs – have definite advantages in scientific argumentation and reasoning. These numbers and letters being invented however do not have any behavioural characteristics, which suggests that conclusions drawn from the model merely reflect the author’s opinions. The AIT is a good example of this logical dilemma. Social implications The modern social choice theory, which is founded on the AIT, seems to be an academic assault to the system of democratic governance that is dominating current global village. By highlighting weaknesses in the AIT, this paper attempts to discredit this intellectual omission. Originality/value The paper offers a counter example to show that the impossibility of social choice is not necessarily implied by the Arrow’s model. Second, it uses Locke’s theory of human understanding to explain why the concerned social scientists are missing this point. This approach is probably entirely novel in this area of research.
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Riesco, Adrián, Beatriz Santos-Buitrago, Javier De Las Rivas, Merrill Knapp, Gustavo Santos-García, and Carolyn Talcott. "Epidermal Growth Factor Signaling towards Proliferation: Modeling and Logic Inference Using Forward and Backward Search." BioMed Research International 2017 (2017): 1–11. http://dx.doi.org/10.1155/2017/1809513.
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In biological systems, pathways define complex interaction networks where multiple molecular elements are involved in a series of controlled reactions producing responses to specific biomolecular signals. These biosystems are dynamic and there is a need for mathematical and computational methods able to analyze the symbolic elements and the interactions between them and produce adequate readouts of such systems. In this work, we use rewriting logic to analyze the cellular signaling of epidermal growth factor (EGF) and its cell surface receptor (EGFR) in order to induce cellular proliferation. Signaling is initiated by binding the ligand protein EGF to the membrane-bound receptor EGFR so as to trigger a reactions path which have several linked elements through the cell from the membrane till the nucleus. We present two different types of search for analyzing the EGF/proliferation system with the help of Pathway Logic tool, which provides a knowledge-based development environment to carry out the modeling of the signaling. The first one is a standard (forward) search. The second one is a novel approach based onnarrowing, which allows us to trace backwards the causes of a given final state. The analysis allows the identification of critical elements that have to be activated to provoke proliferation.
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Bylieva, D. S. "Word in technogenic multidimensional space." Philosophical Problems of IT & Cyberspace (PhilIT&C), no. 1 (August 2, 2022): 18–33. http://dx.doi.org/10.17726/philit.2022.1.2.
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Today, artificial intelligence is actively mastering natural languages, becoming an interlocutor and partner of human in various aspects of activity. However, the symbolic approach, which implies the transfer of rules and logic, has failed, the number of rules and exceptions of the language does not allow its formalization, so modern «deep learning» of artificial neural networks involves an independent search for patterns in extensive databases. During training, artificial intelligence puts a word into a sentence so that the syntagmatic relationships are as close as possible to those of the target word in the base, taking into account both the semantic relationships of words and the relationships between words in the sequence of presentation. The «language» of information technologies is digital. During natural language processing, words are represented in vector form as a sequence of numbers. The idea of representing words mathematically is familiar to people and is usually associated with logical consistency. Visualization of the position of words in a multidimensional space created by artificial intelligence demonstrates a number of patterns, obvious semantic and syntactic relationships, but the essence of other relationships between words is not obvious. The mathematical representation of words, created by artificial intelligence, can allow you to look at the language from a new non-human point of view.
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García, Víctor, Santiago Escobar, Kazuhiro Ogata, Sedat Akleylek, and Ayoub Otmani. "Modelling and verification of post-quantum key encapsulation mechanisms using Maude." PeerJ Computer Science 9 (September 19, 2023): e1547. http://dx.doi.org/10.7717/peerj-cs.1547.
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Communication and information technologies shape the world’s systems of today, and those systems shape our society. The security of those systems relies on mathematical problems that are hard to solve for classical computers, that is, the available current computers. Recent advances in quantum computing threaten the security of our systems and the communications we use. In order to face this threat, multiple solutions and protocols have been proposed in the Post-Quantum Cryptography project carried on by the National Institute of Standards and Technologies. The presented work focuses on defining a formal framework in Maude for the security analysis of different post-quantum key encapsulation mechanisms under assumptions given under the Dolev-Yao model. Through the use of our framework, we construct a symbolic model to represent the behaviour of each of the participants of the protocol in a network. We then conduct reachability analysis and find a man-in-the-middle attack in each of them and a design vulnerability in Bit Flipping Key Encapsulation. For both cases, we provide some insights on possible solutions. Then, we use the Maude Linear Temporal Logic model checker to extend the analysis of the symbolic system regarding security, liveness and fairness properties. Liveness and fairness properties hold while the security property does not due to the man-in-the-middle attack and the design vulnerability in Bit Flipping Key Encapsulation.
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Zhu, Xixi, Bin Liu, Cheng Zhu, Zhaoyun Ding, and Li Yao. "Approximate Reasoning for Large-Scale ABox in OWL DL Based on Neural-Symbolic Learning." Mathematics 11, no. 3 (January 17, 2023): 495. http://dx.doi.org/10.3390/math11030495.
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The ontology knowledge base (KB) can be divided into two parts: TBox and ABox, where the former models schema-level knowledge within the domain, and the latter is a set of statements of assertions or facts about instances. ABox reasoning is a process of discovering implicit knowledge in ABox based on the existing KB, which is of great value in KB applications. ABox reasoning is influenced by both the complexity of TBox and scale of ABox. The traditional logic-based ontology reasoning methods are usually designed to be provably sound and complete but suffer from long algorithm runtimes and do not scale well for ontology KB represented by OWL DL (Description Logic). In some application scenarios, the soundness and completeness of reasoning results are not the key constraints, and it is acceptable to sacrifice them in exchange for the improvement of reasoning efficiency to some extent. Based on this view, an approximate reasoning method for large-scale ABox in OWL DL KBs was proposed, which is named the ChunfyReasoner (CFR). The CFR introduces neural-symbolic learning into ABox reasoning and integrates the advantages of symbolic systems and neural networks (NNs). By training the NN model, the CFR approximately compiles the logic deduction process of ontology reasoning, which can greatly improve the reasoning speed while ensuring higher reasoning quality. In this paper, we state the basic idea, framework, and construction process of the CFR in detail, and we conduct experiments on two open-source ontologies built on OWL DL. The experimental results verify the effectiveness of our method and show that the CFR can support the applications of large-scale ABox reasoning of OWL DL KBs.