Relevant bibliographies by topics / Logic (symbolic and mathematical)

Academic literature on the topic 'Logic (symbolic and mathematical)'

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Published: 4 June 2021
Last updated: 29 July 2024

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Journal articles on the topic "Logic (symbolic and mathematical)"

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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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Dissertations / Theses on the topic "Logic (symbolic and mathematical)"

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Friend, Michèle Indira. "Second-order logic is logic." Thesis, University of St Andrews, 1997. http://hdl.handle.net/10023/14753.

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"Second-order logic" is the name given to a formal system. Some claim that the formal system is a logical system. Others claim that it is a mathematical system. In the thesis, I examine these claims in the light of some philosophical criteria which first motivated Frege in his logicist project. The criteria are that a logic should be universal, it should reflect our intuitive notion of logical validity, and it should be analytic. The analysis is interesting in two respects. One is conceptual: it gives us a purchase on where and how to draw a distinction between logic and other sciences. The other interest is historical: showing that second-order logic is a logical system according to the philosophical criteria mentioned above goes some way towards vindicating Frege's logicist project in a contemporary context.
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Lindroth, Olof. "A random formula lower bound for ordered DLL extended with local symmetry recognition /." Uppsala, 2004. http://www.math.uu.se/research/pub/Lindroth1.pdf.

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Gorman, Judith A. "Aspects of coherent logic." Thesis, McGill University, 1987. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=63868.

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Bishop, Joyce Wolfer Otto Albert D. Lubinski Cheryl Ann. "Middle school students' understanding of mathematical patterns and their symbolic representations." Normal, Ill. Illinois State University, 1997. http://wwwlib.umi.com/cr/ilstu/fullcit?p9803721.

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Thesis (Ph. D.)--Illinois State University, 1997.
Title from title page screen, viewed June 1, 2006. Dissertation Committee: Albert D. Otto, Cheryl A. Lubinski (co-chairs), John A. Dossey, Cynthia W. Langrall, George Padavil. Includes bibliographical references (leaves 119-123) and abstract. Also available in print.
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Boskovitz, Agnes. "Data editing and logic : the covering set method from the perspective of logic /." View thesis entry in Australian Digital Theses, 2008. http://thesis.anu.edu.au/public/adt-ANU20080314.163155/index.html.

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Baysal, Onur Alizde Rarail. "Lower-top and upper-bottom points for any formula in temporal logic/." [s.l.]: [s.n.], 2006. http://library.iyte.edu.tr/tezler/master/matematik/T000549.pdf.

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Horsfall, Benjamin Robert. "The logic of bunched implications : a memoir /." Connect to thesis, 2007. http://eprints.unimelb.edu.au/archive/00002633.

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Rossberg, Marcus. "Second-order logic : ontological and epistemological problems." Thesis, University of St Andrews, 2006. http://hdl.handle.net/10023/6407.

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In this thesis I provide a survey over different approaches to second-order logic and its interpretation, and introduce a novel approach. Of special interest are the questions whether (a particular form of) second-order logic can count as logic in some (further to be specified) proper sense of logic, and what epistemic status it occupies. More specifically, second-order logic is sometimes taken to be mathematical, a mere notational variant of some fragment of set theory. If this is the case, it might be argued that it does not have the "epistemic innocence" which would be needed for, e.g., foundational programmes in (the philosophy of) mathematics for which second-order logic is sometimes used. I suggest a Deductivist conception of logic, that characterises logical consequence by means of inference rules, and argue that on this conception second-order logic should count as logic in the proper sense.
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Weiss, Bernhard. "Intuitionistic semantics and the revision of logic." Thesis, University of St Andrews, 1992. http://hdl.handle.net/10023/14755.

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In this thesis I investigate the implications, for one's account of mathematics, of holding an anti-realist view. The primary aim is to appraise the scope of revision imposed by anti-realism on classical inferential practice in mathematics. That appraisal has consequences both for our understanding of the nature of mathematics and for our attitude towards anti-realism itself. If an anti-realist position seems inevitably to be absurdly revisionary then we have grounds for suspecting the coherence of arguments canvassed in favour of anti-realism. I attempt to defend the anti-realist position by arguing, i) that it is not internally incoherent for anti-realism to be a potentially revisionary position, and ii) that an anti-realist position can, plausibly, be seen to result in a stable intuitionistic position with regard to the logic it condones. The use of impredicative methods in classical mathematics is a site of traditional intuitionistic attacks. I undertake an examination of what the anti-realist attitude towards such methods should be. This question is of interest both because such methods are deeply implicated in classical mathematical theory of analysis and because intuitionistic semantic theories make use of impredicative methods. I attempt to construct the outlines of a set theory which is anti-realistically acceptable but which, although having no antecedent repugnance for impredicative methods as such, appears to be too weak to offer an anti-realistic vindication of impredicative methods in general. I attempt to exonerate intuitionistic semantic theories in their use of impredicative methods by showing that a partial order relying on the nature of our grasp of the intuitionistic meaning stipulations for the logical constants precludes a possible circularity.
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Brierley, William. "Undecidability of intuitionistic theories." Thesis, McGill University, 1985. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=66016.

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Books on the topic "Logic (symbolic and mathematical)"

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Klenk, Virginia. Understanding symbolic logic. 3rd ed. Englewood Cliffs, N.J: Prentice Hall, 1994.

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Klenk, Virginia. Understanding symbolic logic. 3rd ed. Upper Saddle River, N.J: Prentice Hall, 1994.

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Smith, Karl J. Introduction to symbolic logic. 2nd ed. Pacific Grove, Calif: Brooks/Cole Pub. Co., 1991.

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Ebbinghaus, Heinz-Dieter. Mathematical logic. 2nd ed. New York: Springer, 1996.

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Klenk, Virginia. Understanding symbolic logic. 2nd ed. Englewood Cliffs, N.J: Prentice Hall, 1989.

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Jörg, Flum, and Thomas Wolfgang 1947-, eds. Mathematical logic. 2nd ed. New York: Springer-Verlag, 1994.

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Martin, Robert M. Introducing symbolic logic. Peterborough, Ont: Broadview Press, 2004.

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Tourlakis, George J. Mathematical logic. Hoboken, N.J: Wiley, 2008.

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Gustason, William. Elementary symbolic logic. 2nd ed. Prospect Heights, Ill: Waveland Press, 1989.

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Summer School and Conference on Mathematical Logic (1988 Chaĭka, Varnenski okrŭg, Bulgaria). Mathematical logic. New York: Plenum Press, 1990.

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Book chapters on the topic "Logic (symbolic and mathematical)"

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Scott, Dana S. "Computational Logic needs Symbolic Mathematics." In Computational Logic, 210–11. Berlin, Heidelberg: Springer Berlin Heidelberg, 1990. http://dx.doi.org/10.1007/978-3-642-76274-1_15.

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Buchberger, Bruno. "Computational Mathematics, Computational Logic, and Symbolic Computation." In Computer Science Logic, 98–99. Berlin, Heidelberg: Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/978-3-540-45220-1_10.

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Bryant, Randal E. "Verification of synchronous circuits by symbolic logic simulation." In Hardware Specification, Verification and Synthesis: Mathematical Aspects, 14–24. New York, NY: Springer New York, 1990. http://dx.doi.org/10.1007/0-387-97226-9_21.

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Roanes-Lozano, Eugenio, Luis M. Laita, and Eugenio Roanes-Macías. "An inference engine for propositional two-valued logic based on the radical membership problem." In Artificial Intelligence and Symbolic Mathematical Computation, 71–86. Berlin, Heidelberg: Springer Berlin Heidelberg, 1996. http://dx.doi.org/10.1007/3-540-61732-9_51.

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Jumpertz, Pierre. "Linear logic and real closed fields: A way to handle situations dynamically." In Integrating Symbolic Mathematical Computation and Artificial Intelligence, 93–114. Berlin, Heidelberg: Springer Berlin Heidelberg, 1995. http://dx.doi.org/10.1007/3-540-60156-2_8.

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Isaac, Manuel Gustavo. "Symbolic Knowledge in Husserlian Pure Logic." In Peirce and Husserl: Mutual Insights on Logic, Mathematics and Cognition, 77–96. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-25800-9_5.

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Moreno, Ginés, Jaime Penabad, and José Antonio Riaza. "Symbolic Unfolding of Multi-adjoint Logic Programs." In Trends in Mathematics and Computational Intelligence, 43–51. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-030-00485-9_5.

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Grattan-Guinness, Ivor. "Giuseppe Peano: a Revolutionary in Symbolic Logic?" In Giuseppe Peano between Mathematics and Logic, 135–41. Milano: Springer Milan, 2011. http://dx.doi.org/10.1007/978-88-470-1836-5_7.

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Kovásznai, Gergely, Helmut Veith, Andreas Fröhlich, and Armin Biere. "On the Complexity of Symbolic Verification and Decision Problems in Bit-Vector Logic." In Mathematical Foundations of Computer Science 2014, 481–92. Berlin, Heidelberg: Springer Berlin Heidelberg, 2014. http://dx.doi.org/10.1007/978-3-662-44465-8_41.

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Zeilberger, Doron. "Towards a Symbolic Computational Philosophy (and Methodology!) for Mathematics." In Mathematics, Computer Science and Logic - A Never Ending Story, 101–13. Cham: Springer International Publishing, 2013. http://dx.doi.org/10.1007/978-3-319-00966-7_4.

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Conference papers on the topic "Logic (symbolic and mathematical)"

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Huang, Kung-Shiuh, B. K. Jenkins, and A. A. Sawchuk. "Binary image algebra representations of optical cellular logic and symbolic substitution." In OSA Annual Meeting. Washington, D.C.: Optica Publishing Group, 1987. http://dx.doi.org/10.1364/oam.1987.tha4.

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Binary image algebra (BIA) provides a systematic mathematical formalism for both digital optical cellular logic and symbolic substitution processors, in addition to being a unified theory of parallel binary image processing.1 Cellular logic operations and symbolic substitution rules are proved to be special cases of image transformations in BIA; and BIA serves as an algebraic theory for developing and analyzing parallel algorithms of both cellular logic and symbolic substitution.
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Dimarogonas, Andrew D. "Interval Analysis of Neural Net Adaptive Expert Systems for Diagnosis of Machinery Incipient Failure." In ASME 1993 Design Technical Conferences. American Society of Mechanical Engineers, 1993. http://dx.doi.org/10.1115/detc1993-0279.

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Abstract Interval calculus is a tool to evaluate a mathematical expression for ranges of values of its parameters. The basic mathematical operations are defined in the interval algebra. Neural networks is an approach leading to engineering expert systems that are capable of learning, self adapting to particular engineering applications and handling fuzzy and interval input information. In traditional machine learning, symbolic representations, such as first order predicate calculus, are used to represent knowledge. The resulting algorithms are specific to the selected representation and presume an ad-hoc knowledge of the system represented. In the neural network representation, knowledge is distributed to a large number of weighted synapses that facilitates learning by experience, realized through modification of the synapses weights according to a chosen learning rule. Traditional classification systems use binary logic. This assumes a clear distinction between two and only two possible states of an event. However, key elements in the human thinking are not numbers but labels of fuzzy sets, that is, classes of objects in which the transition from non-membership to membership is gradual rather than abrupt and ranges of key parameters involved. A heteroassociative neural network is used to map the existing knowledge and acquire new knowledge in learning sessions. The inputs can be binary, fuzzy and interval variables. To process the diagnosis in a back-propagation mode, interval calculus is utilized in algebraic and matrix operations and the diagnosis results in interval output parameters, the identification scores. Interval calculus was programmed in a software package to allow for interval computations. The package includes arithmetic, function and matrix operations. Available experience for failure diagnosis in turbomachinery was utilized to initially teach the system. Additional diagnoses from the author’s experience were taught to the system and additional features and diagnoses defined. Convergence of the procedure depends on the monotonicity of the functions used. For usual networks and threshold functions, convergence is warranted.
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Gerges, Nader, Gennady Makarychev, Luisa Ana Barillas, Christophe Darous, Alaa Maarouf, Midhun Madhavan, Sushmitha Kuruba, Lulwa Almarzooqi, Chakib Kada Kloucha, and Hussein Mustapha. "Novel Approach for Automated Pore Network Characterization and Machine Learning Assisted Capillary Pressure Modeling for an Improved Water Saturation Modelling in Carbonate Reservoirs." In SPE Reservoir Characterisation and Simulation Conference and Exhibition. SPE, 2023. http://dx.doi.org/10.2118/212612-ms.

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Abstract Capillary pressure (Pc) measurements, together with conventional core analysis, are typically used for reservoir characterization and saturation height modeling (SHM). Workflows involving Pc data are time consuming and interpretively biased. We aim to enhance these workflows’ efficiency and reduce the interpretation bias by automating the Pc-based pore network characterization and applying machine learning (ML) to capillary pressure modeling. We have also built advanced analytics dashboards to allow for QC and interactive adjustments by the user. The solution defines the pore system modality based on the automated peak(s) detection of the pore throat radius (PTR) distribution and computes an absolute porosity distribution and its porosity partition. Next, it builds the SHF per rock type at special core analysis (SCAL) level using a novel approach based on a symbolic regressor logic. This automatically defines the best correlation of the extracted fitting coefficients to core porosity and permeability while honoring the physical reservoir constraints. Furthermore, the system applies analytical equations with fitting coefficients replaced by defined correlations to capillary pressure data and automatically identifies the equation and correlations that provide lower relative error to the input capillary pressure curves. We developed and tested the proposed algorithms on a real data from a large carbonate oil field in the Middle East. The input dataset is rich, consisting of around 600 good to excellent quality mercury injection capillary pressure (MICP) samples. Parent-plug porosity and permeability is also available for all samples. Initial experiments demonstrated that the proposed workflow significantly improves the Pc-based pore network characterization workflow. Initial QA/QC algorithms based on advanced data science outliers’ detection logic allows us to automatically identify poor quality data and outlier samples. These outlier samples are filtered out eliminating data-quality-artifacts in the interpretation. The automated pore network characterization solution allows a clear understanding of the porosity partition and modality in few steps. This characterization will be the foundation of the petrophysical grouping at MICP level. We present a thorough comparison between results from petrophysical rock typing using traditional approaches compared to results obtained using the newly proposed pore network characterization methodology. Although the focus of this study is to improve the petrophysical grouping component of the rock-typing, further integration with geology and diagenetic overprints is required to improve the over-all workflow. Moreover, we automatically define the best Pc analytical model and compute the final saturation height functions using ML algorithms. This novel workflow allows more complex mathematical modelling compared to the currently available traditional approaches in commercial petrophysical packages. The overall results provide an enhanced mathematical solution constrained to the petrophysical model for the Core Build Model (CBM).
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Cathey, W. Thomas. "Optical symbolic logic." In OSA Annual Meeting. Washington, D.C.: Optica Publishing Group, 1987. http://dx.doi.org/10.1364/oam.1987.tuq1.

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Optical systems for implementing optical expert systems have been designed and simulated. Components of the system have been built and tested. The concept, optical system used, and types of Al problem that can be solved with the current system are described. The current research results are reviewed, and future plans are outlined. Results of other optical symbolic logic experiments are also presented. These experiments are based on the use of polarization to carry the information through the system.
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McAulay, Alastair D. "Digital optical pipeline cellular automata arithmetic unit." In Optical Computing. Washington, D.C.: Optica Publishing Group, 1995. http://dx.doi.org/10.1364/optcomp.1995.omc3.

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The arithmetic unit presents a substantial challenge to those interested in the long term goal of ultrafast all-optical general purpose computers (1 Ch. 10). Previously we demonstrated an optical adder using electron trapping materials for which the speed seems to be limited to hundreds of nanseconds (2). The multiplication of images in 160 fs was recently demonstrated by means of four-wave mixing in a new polymer material (3). We present a conceptual method of using such a material in a loop to perform pipeline digital arithmetic operations such as addition and multiplication. Only the word operands are entered at each cycle while the loop performs 2-D operations so that the rate of computation in the polymer is several orders of magnitude higher than that for data entry and removal. The method uses a modification of the transition function proposed previously for computation with cellular automata or symbolic substitution (4), (1 Ch. 15). Cellular automata on an infinite plane were shown by Dr. Von Neuman to provide universal-constructor machines capable of endlessly self reproducing new Turing machines, each of which can compute anything that can be computed by logical or mathematical reasoning (5,6). Others have subsequently provided rules for such mappings (7). Flexibility is achieved because the operation performed may be changed by replacing an optical control image. This idea of treating control information optically in the same manner as data has been highly developed in pattern logic which has been experimentally demonstrated for an optical ripple-carry adder (8, 1 Ch 9 and 10). The correlation operation required for the cellular automata is performed by four wave mixing and is independent of the control information, the data, and their locations on the array. The mapping of a full adder and a 3-bit multiplier onto such a computer are shown. The problems of achieving short pipelines for small latency are discussed and alternative possible improvements mentioned. A proposed optical set up is shown which includes a loop around a four wave mixing experiment such as that in paper (3). Some difficulties anticipated in performing such an experiment are considered.
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Ludwig, Simone A., Omer F. Rana, William Naylor, and Julian Padget. "Mathematical matchmaker for numeric and symbolic services." In the fourth international joint conference. New York, New York, USA: ACM Press, 2005. http://dx.doi.org/10.1145/1082473.1082819.

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7

Habiballa, Hashim, and Radek Jendryscik. "Constructivistic mathematical logic education." In INTERNATIONAL CONFERENCE OF COMPUTATIONAL METHODS IN SCIENCES AND ENGINEERING 2018 (ICCMSE 2018). Author(s), 2018. http://dx.doi.org/10.1063/1.5079069.

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8

Tiunova, M. "ONLINE MATHEMATICAL LOGIC TOOLS." In Modern problems of physics education. Baskir State University, 2021. http://dx.doi.org/10.33184/mppe-2021-11-10.154.

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9

Zhao, Siang, Zhongyang Li, Zhenbang Chen, and Ji Wang. "Symbolic Verification of Fuzzy Logic Models." In 2023 38th IEEE/ACM International Conference on Automated Software Engineering (ASE). IEEE, 2023. http://dx.doi.org/10.1109/ase56229.2023.00087.

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Kasihmuddin, Mohd Shareduwan Mohd, Saratha Sathasivam, and Mohd Asyraf Mansor. "Artificial bee colony in neuro - Symbolic integration." In PROCEEDINGS OF THE 24TH NATIONAL SYMPOSIUM ON MATHEMATICAL SCIENCES: Mathematical Sciences Exploration for the Universal Preservation. Author(s), 2017. http://dx.doi.org/10.1063/1.4995912.

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Reports on the topic "Logic (symbolic and mathematical)"

1

Bezhanishvili, Guram, and Wesley Fussner. An Introduction to Symbolic Logic. Washington, DC: The MAA Mathematical Sciences Digital Library, June 2013. http://dx.doi.org/10.4169/loci003990.

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2

Obua, Steven. Practal — Practical Logic: A Bicycle for Your Mathematical Mind. Recursive Mind, July 2021. http://dx.doi.org/10.47757/practal.1.

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3

Prokaznikova, E. N. The distance learning course «The Mathematical Logic and Theory of Algorithms». OFERNIO, December 2018. http://dx.doi.org/10.12731/ofernio.2018.23531.

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4

Frantseva, Anastasiya. The video lectures course "Elements of Mathematical Logic" for students enrolled in the Pedagogical education direction, profile Primary education. Frantseva Anastasiya Sergeevna, April 2021. http://dx.doi.org/10.12731/frantseva.0411.14042021.

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The video lectures course is intended for full-time and part-time students enrolled in "Pedagogical education" direction, profile "Primary education" or "Primary education - Additional education". The course consists of four lectures on the section "Elements of Mathematical Logic" of the discipline "Theoretical Foundations of the Elementary Course in Mathematics" on the profile "Primary Education". The main lecture materials source is a textbook on mathematics for students of higher pedagogical educational institutions Stoilova L.P. (M.: Academy, 2014.464 p.). The content of the considered mathematics section is adapted to the professional needs of future primary school teachers. It is accompanied by examples of practice exercises from elementary school mathematics textbooks. The course assumes students productive learning activities, which they should carry out during the viewing. The logic’s studying contributes to the formation of the specified profile students of such professional skills as "the ability to carry out pedagogical activities for the implementation of primary general education programs", "the ability to develop methodological support for programs of primary general education." In addition, this section contributes to the formation of such universal and general professional skills as "the ability to perform searching, critical analysis and synthesis of information, to apply a systematic approach to solving the assigned tasks", "the ability to participate in the development of basic and additional educational programs, to design their individual components". The video lectures course was recorded at Irkutsk State University.
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Striuk, Andrii M. Software engineering: first 50 years of formation and development. [б. в.], December 2018. http://dx.doi.org/10.31812/123456789/2880.

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The article analyzes the main stages of software engineering (SE) development. Based on the analysis of materials from the first SE conferences (1968-1969), it was determined how the software crisis prompted scientists and practitioners to join forces to form an engineering approach to programming. Differences in professional training for SE are identified. The fundamental components of the training of future software engineers are highlighted. The evolution of approaches to the design, implementation, testing and documentation of software is considered. The system scientific, technological approaches and methods for the design and construction of computer programs are highlighted. Analysis of the historical stages of the development of SE showed that despite the universal recognition of the importance of using the mathematical apparatus of logic, automata theory and linguistics when developing software, it was created empirically without its use. The factor that led practitioners to turn to the mathematical foundations of an SE is the increasing complexity of software and the inability of empirical approaches to its development and management to cope with it. The training of software engineers highlighted the problem of the rapid obsolescence of the technological content of education, the solution of which lies in its fundamentalization through the identification of the basic foundations of the industry. It is determined that mastering the basics of computer science is the foundation of vocational training in SE.
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