Relevant bibliographies by topics / Mathematical Logic

Academic literature on the topic 'Mathematical Logic'

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Published: 4 June 2021
Last updated: 30 July 2024

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Journal articles on the topic "Mathematical Logic"

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Gehrke, Mai, Carol Walker, and Elbert Walker. "A Mathematical Setting for Fuzzy Logics." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 05, no. 03 (June 1997): 223–38. http://dx.doi.org/10.1142/s021848859700021x.

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The setup of a mathematical propositional logic is given in algebraic terms, describing exactly when two choices of truth value algebras give the same logic. The propositional logic obtained when the algebra of truth values is the real numbers in the unit interval equipped with minimum, maximum and -x=1-x for conjunction, disjunction and negation, respectively, is the standard propositional fuzzy logic. This is shown to be the same as three-valued logic. The propositional logic obtained when the algebra of truth values is the set {(a, b)|a≤ b and a,b∈[0,1]} of subintervals of the unit interval with component-wise operations, is propositional interval-valued fuzzy logic. This is shown to be the same as the logic given by a certain four element lattice of truth values. Since both of these logics are equivalent to ones given by finite algebras, it follows that there are finite algorithms for determining when two statements are logically equivalent within either of these logics. On this topic, normal forms are discussed for both of these logics.
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Austin, Keith, H. D. Ebbinghaus, J. Flum, W. Thomas, and A. S. Ferebee. "Mathematical Logic." Mathematical Gazette 69, no. 448 (June 1985): 147. http://dx.doi.org/10.2307/3616954.

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Bala, Romi, and Hemant Pandey. "Mathematical Logic: Foundations and Beyond." Turkish Journal of Computer and Mathematics Education (TURCOMAT) 9, no. 3 (December 17, 2018): 1405–11. http://dx.doi.org/10.61841/turcomat.v9i3.14599.

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Mathematical logic serves as the cornerstone of formal reasoning, providing precise tools for analyzing the structure and validity of arguments. This paper offers a comprehensive exploration of key topics in mathematical logic, spanning from classical propositional and predicate logic to modal logic and non-classical logics. It examines the syntactic and semantic aspects of various logical systems, delves into proof theory and computational complexity, and explores applications in diverse fields such as mathematics, computer science, philosophy, and linguistics. By elucidating the fundamental principles and practical implications of mathematical logic, this paper highlights its pivotal role in advancing knowledge and addressing complex challenges across disciplines.
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Bagaria, Joan. "On Turing’s legacy in mathematical logic and the foundations of mathematics." Arbor 189, no. 764 (December 30, 2013): a079. http://dx.doi.org/10.3989/arbor.2013.764n6002.

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Austin, Keith, and Elliott Mendelson. "Introduction to Mathematical Logic." Mathematical Gazette 71, no. 458 (December 1987): 325. http://dx.doi.org/10.2307/3617078.

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Sabbagh, G. "Conference on Mathematical Logic." Journal of Symbolic Logic 59, no. 1 (March 1994): 345. http://dx.doi.org/10.2307/2275271.

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Uspensky, Vladimir A. "Kolmogorov and mathematical logic." Journal of Symbolic Logic 57, no. 2 (June 1992): 385–412. http://dx.doi.org/10.2307/2275276.

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There are human beings whose intellectual power exceeds that of ordinary men. In my life, in my personal experience, there were three such men, and one of them was Andrei Nikolaevich Kolmogorov. I was lucky enough to be his immediate pupil. He invited me to be his pupil at the third year of my being student at the Moscow University. This talk is my tribute, my homage to my great teacher.Andrei Nikolaevich Kolmogorov was born on April 25, 1903. He graduated from Moscow University in 1925, finished his post-graduate education at the same University in 1929, and since then without any interruption worked at Moscow University till his death on October 20, 1987, at the age 84½.Kolmogorov was not only one of the greatest mathematicians of the twentieth century. By the width of his scientific interests and results he reminds one of the titans of the Renaissance. Indeed, he made prominent contributions to various fields from the theory of shooting to the theory of versification, from hydrodynamics to set theory. In this talk I should like to expound his contributions to mathematical logic.Here the term “mathematical logic” is understood in a broad sense. In this sense it, like Gallia in Caesarian times, is divided into three parts:(1) mathematical logic in the strict sense, i.e. the theory of formalized languages including deduction theory,(2) the foundations of mathematics, and(3) the theory of algorithms.
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Slater, Hartley. "Logic is not Mathematical." Polish Journal of Philosophy 6, no. 1 (2012): 69–86. http://dx.doi.org/10.5840/pjphil2012615.

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Harriss, E., and W. Hodges. "Logic for Mathematical Writing." Logic Journal of IGPL 15, no. 4 (July 25, 2007): 313–20. http://dx.doi.org/10.1093/jigpal/jzm022.

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Shapiro, Stewart. "Logic, ontology, mathematical practice." Synthese 79, no. 1 (April 1989): 13–50. http://dx.doi.org/10.1007/bf00873255.

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Dissertations / Theses on the topic "Mathematical Logic"

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Wedin, Hanna. "Mathematical Induction." Thesis, Uppsala universitet, Algebra och geometri, 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-414099.

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Moreno, Dávila Julio Moreno Davila Julio. "Mathematical programming for logic inference /." [S.l.] : [s.n.], 1990. http://library.epfl.ch/theses/?nr=784.

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Cerami, Marco. "Fuzzy Description Logics from a Mathematical Fuzzy Logic point of view." Doctoral thesis, Universitat de Barcelona, 2012. http://hdl.handle.net/10803/113374.

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Description Logic is a formalism that is widely used in the framework of Knowledge Representation and Reasoning in Artificial Intelligence. They are based on Classical Logic in order to guarantee the correctness of the inferences on the required reasoning tasks. It is indeed a fragment of First Order Predicate Logic whose language is strictly related to the one of Modal Logic. Fuzzy Description Logic is the generalization of the classical Description Logic framework thought for reasoning with vague concepts that often arise in practical applications. Fuzzy Description Logic has been investigated since the last decade of the 20th century. During the first fifteen years of investigation their semantics has been based on Fuzzy Set Theory. A semantics based on Fuzzy Set Theory, however, has been shown to have some counter-intuitive behavior, due to the fact that the truth function for the implication used is not the residuum of the truth function for the conjunction. In the meanwhile, Fuzzy Logic has been given a formal framework based on Many-valued Logic. This framework, called Mathematical Fuzzy Logic, has been proposed has the kernel of a mathematically well founded Fuzzy Logic. In this dissertation we propose a Fuzzy Description Logic whose semantics is based on Mathematical Fuzzy Logic as its mathematically well settled kernel. To this end we provide a novel notation that is strictly related to the notation that is used in Mathematical Fuzzy Logic. After having settled the notation, we investigate the hierarchies of description languages over different-“t” norm based semantics and the reductions that can be performed between reasoning tasks. The new framework that we establish gives us the possibility to systematically investigate the relation of Fuzzy Description Logic to Fuzzy First Order Logic and Fuzzy Modal Logic. Next we provide some (un)decidability results for the case of infinite “t”-norm based semantics with or without knowledge bases. Finally we investigate the complexity bounds of reasoning tasks without knowledge bases for basic Fuzzy Description Logics over finite “t”-norms.
El trabajo desarrollado en esta tesis es una propuesta de sistematizar la formalización de las Lógicas de la Descripción Fuzzy a partir de la Lógica Difusa Matemática. Para ello se define un lenguaje para las Lógicas de la Descripción Fuzzy que extiende el lenguaje de la primera tradición de esta disciplina para adaptarlo al lenguaje más propio de la Lógica Difusa Matemática. Desde el punto de vista semántico, la teoría de conjuntos borrosos cede el paso a una semántica algebraica, que es la que se utiliza en la Lógica Difusa Matemática y que resuelve las consecuencias poco intuitivas que tenía la semántica tradicional. A partir de esta formalización, se tratan temas que eran tradicionales en las Lógicas de la Descripción clásicas como son las jerarquías de inclusiones entre lenguajes de la descripción y la relación de las Lógicas de la Descripción Fuzzy con la Lógica Difusa de primer orden por un lado y la Lógica Difusa Multi-modal por el otro. En relación a problemas de decidibilidad se demuestra que la satisfacción y la subsunción de conceptos en el lenguaje ALE bajo una semántica basada en la Lógica del Producto son problemas decidibles. También se demuestra que la consistencia de bases de conocimiento en el lenguaje ALC bajo una semántica basada en la Lógica de Lukasiewicz es un problema indecidible. En relación a problemas de complejidad computacional se demuestra que satisfacción y validez de fórmulas en la Lógica Modal minimal de Lukasiewicz con valores finitos son problemas PSPACE-completos. También se demuestra que la satisfacción y subsunción de conceptos en el lenguaje IALCED bajo una semántica basada en cualquier lógica difusa con valores finitos son problemas PSPACE-completos. Otra contribución de nuestro trabajo es el estudio sistemático de algoritmos de decisión para la satisfacción y subsunción de conceptos en el lenguaje IALCED, respecto a modelos “witnessed", basados en una reducción de es- tos problemas a los problemas de satisfacción y consecuencia en la lógica proposicional correspondiente.
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Greer, Deirdre C. Silvern Steven B. "Logic-mathematical processes in beginning reading." Auburn, Ala., 2005. http://repo.lib.auburn.edu/2005%20Summer/doctoral/GREER_DEIRDRE_28.pdf.

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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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Collazo, Antonio. "The Mathematical Landscape." Scholarship @ Claremont, 2011. http://scholarship.claremont.edu/cmc_theses/116.

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The intent of this paper is to present the reader will enough information to spark a curiosity in to the subject. By no means is the following a complete formulation of any of the topics covered. I want to give the reader a tour of the mathematical landscape. There are plenty of further details to explore in each section, I have just touched the tip the iceberg. The work is basically in four sections: Numbers, Geometry, Functions, Sets and Logic, which are the basic building blocks of Math. The first sections are a exposition into the mathematical objects and their algebras. The last section dives into the foundation of math, sets and logic, and develops the ``language'' of Math. My hope is that after this, the reader will have the necessary (maybe not sufficient) information needed to talk the language of Math.
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Fors, Mikael. "Elementary Discrete Sets in Martin-Löf Type Theory." Thesis, Uppsala universitet, Algebra och geometri, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-175717.

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Wiklund, Tilo. "Locally cartesian closed categories, coalgebras, and containers." Thesis, Uppsala universitet, Algebra och geometri, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-197556.

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Yim, Austin Vincent. "On Galois correspondences in formal logic." Thesis, University of Oxford, 2012. http://ora.ox.ac.uk/objects/uuid:b47d1dda-8186-4c81-876c-359409f45b97.

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This thesis examines two approaches to Galois correspondences in formal logic. A standard result of classical first-order model theory is the observation that models of L-theories with a weak form of elimination of imaginaries hold a correspondence between their substructures and automorphism groups defined on them. This work applies the resultant framework to explore the practical consequences of a model-theoretic Galois theory with respect to certain first-order L-theories. The framework is also used to motivate an examination of its underlying model-theoretic foundations. The model-theoretic Galois theory of pure fields and valued fields is compared to the algebraic Galois theory of pure and valued fields to point out differences that may hold between them. The framework of this logical Galois correspondence is also applied to the theory of pseudoexponentiation to obtain a sketch of the Galois theory of exponential fields, where the fixed substructure of the complex pseudoexponential field B is an exponential field with the field Qrab as its algebraic subfield. This work obtains a partial exponential analogue to the Kronecker-Weber theorem by describing the pure field-theoretic abelian extensions of Qrab, expanding upon work in the twelfth of Hilbert’s problems. This result is then used to determine some of the model-theoretic abelian extensions of the fixed substructure of B. This work also incorporates the principles required of this model-theoretic framework in order to develop a model theory over substructural logics which is capable of expressing this Galois correspondence. A formal semantics is developed for quantified predicate substructural logics based on algebraic models for their propositional or nonquantified fragments. This semantics is then used to develop substructural forms of standard results in classical first-order model theory. This work then uses this substructural model theory to demonstrate the Galois correspondence that substructural first-order theories can carry in certain situations.
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Eliasson, Jonas. "Ultrasheaves." Doctoral thesis, Uppsala : Matematiska institutionen, Univ. [distributör], 2003. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-3762.

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Books on the topic "Mathematical Logic"

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

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Ebbinghaus, Heinz-Dieter, Jörg Flum, and Wolfgang Thomas. Mathematical Logic. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-73839-6.

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Csirmaz, Laszlo, and Zalán Gyenis. Mathematical Logic. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-79010-3.

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Li, Wei. Mathematical Logic. Basel: Springer Basel, 2014. http://dx.doi.org/10.1007/978-3-0348-0862-0.

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Ebbinghaus, H. D., J. Flum, and W. Thomas. Mathematical Logic. New York, NY: Springer New York, 1994. http://dx.doi.org/10.1007/978-1-4757-2355-7.

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Tourlakis, George. Mathematical Logic. Hoboken, NJ, USA: John Wiley & Sons, Inc., 2008. http://dx.doi.org/10.1002/9781118032435.

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Petkov, Petio Petrov, ed. Mathematical Logic. Boston, MA: Springer US, 1990. http://dx.doi.org/10.1007/978-1-4613-0609-2.

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Kossak, Roman. Mathematical Logic. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-97298-5.

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Li, Wei. Mathematical Logic. Basel: Birkhäuser Basel, 2010. http://dx.doi.org/10.1007/978-3-7643-9977-1.

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

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Book chapters on the topic "Mathematical Logic"

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Šikić, Zvonimir. "Mathematical Logic: Mathematics of Logic or Logic of Mathematics." In Guide to Deep Learning Basics, 1–6. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-37591-1_1.

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Kolmogorov, A. N., and A. P. Yushkevich. "Mathematical Logic." In Mathematics of the 19th Century, 1–34. Basel: Birkhäuser Basel, 2001. http://dx.doi.org/10.1007/978-3-0348-8293-4_1.

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Kuzicheva, Z. A. "Mathematical Logic." In Mathematics of the 19th Century, 1–34. Basel: Birkhäuser Basel, 1992. http://dx.doi.org/10.1007/978-3-0348-5112-1_1.

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Lavrov, Igor, Larisa Maksimova, and Giovanna Corsi. "Mathematical logic." In Problems in Set Theory, Mathematical Logic and the Theory of Algorithms, 51–134. Boston, MA: Springer US, 2003. http://dx.doi.org/10.1007/978-1-4615-0185-5_2.

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Lavrov, Igor, Larisa Maksimova, and Giovanna Corsi. "Mathematical logic." In Problems in Set Theory, Mathematical Logic and the Theory of Algorithms, 203–47. Boston, MA: Springer US, 2003. http://dx.doi.org/10.1007/978-1-4615-0185-5_5.

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Weik, Martin H. "mathematical logic." In Computer Science and Communications Dictionary, 985. Boston, MA: Springer US, 2000. http://dx.doi.org/10.1007/1-4020-0613-6_11175.

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Jebril, Iqbal H., Hemen Dutta, and Ilwoo Cho. "Mathematical Logic." In Concise Introduction to Logic and Set Theory, 1–28. Boca Raton: CRC Press, 2021. http://dx.doi.org/10.1201/9780429022838-1.

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Yadav, Santosh Kumar. "Mathematical Logic." In Discrete Mathematics with Graph Theory, 115–79. Cham: Springer International Publishing, 2023. http://dx.doi.org/10.1007/978-3-031-21321-2_3.

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Clarke, Barry R. "Logic." In Mathematical Conundrums, 135–61. New York: A K Peters/CRC Press, 2023. http://dx.doi.org/10.1201/9781003358275-7.

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Visser, Albert. "Interpretability Logic." In Mathematical Logic, 175–209. Boston, MA: Springer US, 1990. http://dx.doi.org/10.1007/978-1-4613-0609-2_13.

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Conference papers on the topic "Mathematical Logic"

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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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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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Durcheva, Mariana, and Elena Nikolova. "Modeling mathematical logic using MAPLE." In PROCEEDINGS OF THE 44TH INTERNATIONAL CONFERENCE ON APPLICATIONS OF MATHEMATICS IN ENGINEERING AND ECONOMICS: (AMEE’18). Author(s), 2018. http://dx.doi.org/10.1063/1.5082125.

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Aagaard, Frederik Lerbjerg, Jonathan Sterling, and Lars Birkedal. "A denotationally-based program logic for higher-order store." In Conference on the Mathematical Foundations of Programming Semantics. Electronic Notes in Theoretical Informatics and Computer Science, 2023. http://dx.doi.org/10.46298/entics.12232.

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Separation logic is used to reason locally about stateful programs. State of the art program logics for higher-order store are usually built on top of untyped operational semantics, in part because traditional denotational methods have struggled to simultaneously account for general references and parametric polymorphism. The recent discovery of simple denotational semantics for general references and polymorphism in synthetic guarded domain theory has enabled us to develop TULIP, a higher-order separation logic over the typed equational theory of higher-order store for a monadic version of System F{mu,ref}. The Tulip logic differs from operationally-based program logics in two ways: predicates range over the meanings of typed terms rather than over the raw code of untyped terms, and they are automatically invariant under the equational congruence of higher-order store, which applies even underneath a binder. As a result, "pure" proof steps that conventionally require focusing the Hoare triple on an operational redex are replaced by a simple equational rewrite in Tulip. We have evaluated Tulip against standard examples involving linked lists in the heap, comparing our abstract equational reasoning with more familiar operational-style reasoning. Our main result is the soundness of Tulip, which we establish by constructing a BI-hyperdoctrine over the denotational semantics of F{mu,ref} in an impredicative version of synthetic guarded domain theory.
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Doz, Daniel, Darjo Felda, and Mara Cotič. "Using Fuzzy Logic to Assess Studentsʼ Mathematical Knowledge." In Nauka i obrazovanje – izazovi i perspektive. University of Kragujevac, Faculty of Edaucatin in Uzice, 2022. http://dx.doi.org/10.46793/noip.263d.

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Assessing students’ mathematical knowledge informs students, educators, and parents about students’ mathematical competencies. In Italy, some students receive both written and oral grades in mathematics at the end of the first semester, which are then averaged for a final grade. The possibility of applying fuzzy logic, which has been widely used to deal with uncertain or verbal descriptions, to this process has not yet been explored extensively. In the present contribution, we consider a sample of N = 47 Italian high school students, and analyze two fuzzy combinations of their mathematics grades. Students’ hypothetical grades produced with the center-of-gravity defuzzification method are lower than students’ grades in their report cards, while the mean-of-maxima defuzzification method produced grades that are statistically higher than the students’ original grades. Implications are discussed, leading to suggestions for assessment research.
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Badia, Guillermo, and Carles Noguera. "Saturated Models in Mathematical Fuzzy Logic." In 2018 IEEE 48th International Symposium on Multiple-Valued Logic (ISMVL). IEEE, 2018. http://dx.doi.org/10.1109/ismvl.2018.00034.

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Gottwald, S. "Toward Problems for Mathematical Fuzzy Logic." In 2006 IEEE International Conference on Fuzzy Systems. IEEE, 2006. http://dx.doi.org/10.1109/fuzzy.2006.1681928.

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Le, Van-Hung, Fei Liu, and Dinh-Khang Tran. "Mathematical fuzzy logic with many dual hedges." In the Fifth Symposium. New York, New York, USA: ACM Press, 2014. http://dx.doi.org/10.1145/2676585.2676619.

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Le, Van-Hung. "First-Order Mathematical Fuzzy Logic with Hedges." In The Fourth International Conference on Database and Data Mining. Academy & Industry Research Collaboration Center (AIRCC), 2016. http://dx.doi.org/10.5121/csit.2016.60509.

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Hendel, Russell Jay. "A Mathematical-Logic Technique Facilitating Good Teaching." In 17th International Multi-Conference on Society, Cybernetics and Informatics. Winter Garden, Florida, United States: International Institute of Informatics and Cybernetics, 2023. http://dx.doi.org/10.54808/imsci2023.01.105.

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Reports on the topic "Mathematical Logic"

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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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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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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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5

Obua, Steven. Philosophy of Abstraction Logic. Steven Obua (trading as Recursive Mind), December 2021. http://dx.doi.org/10.47757/pal.1.

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Abstraction Logic has been introduced in a previous, rather technical article. In this article we take a step back and look at Abstraction Logic from a conceptual point of view. This will make it easier to appreciate the simplicity, elegance, and pragmatism of Abstraction Logic. We will argue that Abstraction Logic is the best logic for serving as a foundation of mathematics.
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6

Obua, Steven. Philosophy of Abstraction Logic. Steven Obua (trading as Recursive Mind), December 2021. http://dx.doi.org/10.47757/pal.2.

Full text
Abstract:
Abstraction Logic has been introduced in a previous, rather technical article. In this article we take a step back and look at Abstraction Logic from a conceptual point of view. This will make it easier to appreciate the simplicity, elegance, and pragmatism of Abstraction Logic. We will argue that Abstraction Logic is the best logic for serving as a foundation of mathematics.
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