Log in

Relevant bibliographies by topics / Mathematical Logic / Journal articles

Journal articles on the topic 'Mathematical Logic'

To see the other types of publications on this topic, follow the link: Mathematical Logic.

Author: Grafiati

Published: 4 June 2021

Last updated: 30 July 2024

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles

Select a source type:

Consult the top 50 journal articles for your research on the topic 'Mathematical Logic.'

Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.

You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.

Browse journal articles on a wide variety of disciplines and organise your bibliography correctly.

1

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.

Full text

Abstract:

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.

APA, Harvard, Vancouver, ISO, and other styles

2

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.

Full text

APA, Harvard, Vancouver, ISO, and other styles

3

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.

Full text

Abstract:

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.

APA, Harvard, Vancouver, ISO, and other styles

4

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.

Full text

APA, Harvard, Vancouver, ISO, and other styles

5

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

Full text

APA, Harvard, Vancouver, ISO, and other styles

6

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

Full text

APA, Harvard, Vancouver, ISO, and other styles

7

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.

Full text

Abstract:

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.

APA, Harvard, Vancouver, ISO, and other styles

8

Slater, Hartley. "Logic is not Mathematical." Polish Journal of Philosophy 6, no. 1 (2012): 69–86. http://dx.doi.org/10.5840/pjphil2012615.

Full text

APA, Harvard, Vancouver, ISO, and other styles

9

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.

Full text

APA, Harvard, Vancouver, ISO, and other styles

10

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

Full text

APA, Harvard, Vancouver, ISO, and other styles

11

HUET, GÉRARD. "Special issue on ‘Logical frameworks and metalanguages’." Journal of Functional Programming 13, no. 2 (March 2003): 257–60. http://dx.doi.org/10.1017/s0956796802004549.

Full text

Abstract:

There is both a great unity and a great diversity in presentations of logic. The diversity is staggering indeed – propositional logic, first-order logic, higher-order logic belong to one classification; linear logic, intuitionistic logic, classical logic, modal and temporal logics belong to another one. Logical deduction may be presented as a Hilbert style of combinators, as a natural deduction system, as sequent calculus, as proof nets of one variety or other, etc. Logic, originally a field of philosophy, turned into algebra with Boole, and more generally into meta-mathematics with Frege and Heyting. Professional logicians such as Gödel and later Tarski studied mathematical models, consistency and completeness, computability and complexity issues, set theory and foundations, etc. Logic became a very technical area of mathematical research in the last half century, with fine-grained analysis of expressiveness of subtheories of arithmetic or set theory, detailed analysis of well-foundedness through ordinal notations, logical complexity, etc. Meanwhile, computer modelling developed a need for concrete uses of logic, first for the design of computer circuits, then more widely for increasing the reliability of sofware through the use of formal specifications and proofs of correctness of computer programs. This gave rise to more exotic logics, such as dynamic logic, Hoare-style logic of axiomatic semantics, logics of partial values (such as Scott's denotational semantics and Plotkin's domain theory) or of partial terms (such as Feferman's free logic), etc. The first actual attempts at mechanisation of logical reasoning through the resolution principle (automated theorem proving) had been disappointing, but their shortcomings gave rise to a considerable body of research, developing detailed knowledge about equational reasoning through canonical simplification (rewriting theory) and proofs by induction (following Boyer and Moore successful integration of primitive recursive arithmetic within the LISP programming language). The special case of Horn clauses gave rise to a new paradigm of non-deterministic programming, called Logic Programming, developing later into Constraint Programming, blurring further the scope of logic. In order to study knowledge acquisition, researchers in artificial intelligence and computational linguistics studied exotic versions of modal logics such as Montague intentional logic, epistemic logic, dynamic logic or hybrid logic. Some others tried to capture common sense, and modeled the revision of beliefs with so-called non-monotonic logics. For the careful crafstmen of mathematical logic, this was the final outrage, and Girard gave his anathema to such “montres à moutardes”.

APA, Harvard, Vancouver, ISO, and other styles

12

Wong, Bertrand. "Logic in general and mathematical logic in particular*." Bulletin of Pure & Applied Sciences- Mathematics and Statistics 40e, no. 2 (2021): 172–76. http://dx.doi.org/10.5958/2320-3226.2021.00020.5.

Full text

APA, Harvard, Vancouver, ISO, and other styles

13

Hintikka, Jaakko. "Which Mathematical Logic is the Logic of Mathematics?" Logica Universalis 6, no. 3-4 (August 31, 2012): 459–75. http://dx.doi.org/10.1007/s11787-012-0065-6.

Full text

APA, Harvard, Vancouver, ISO, and other styles

14

Nisa, Khairun, Eri Saputra, and M. Mursalin. "Development of Mathematical Logic Pipeline Tools (Pilogmath) for Learning Mathematical on Logic Material." International Journal of Trends in Mathematics Education Research 6, no. 4 (December 30, 2023): 345–52. http://dx.doi.org/10.33122/ijtmer.v6i4.285.

Full text

Abstract:

This development research aims to determine the feasibility of using Mathematical Logic Pipe teaching aid (Pilogmath) on mathematical logic material at SMA Negeri 1 Tanah Luas in terms of validity, practicality, and attractiveness. The development model used is the ADDIE development model which consists of the stages of analysis (analysis), design (design), development (development), implementation (implementation), evaluation (eveluation). The subjects of this research are class X SMA Negeri 1 Tanah Luas. The feasibility of learning media refers to the results of the assessment of teaching aids by experts, teachers and small group students. Feasibility can be seen from the results of the validator's assessment where all validators stated very valid, the results of the percentage of product ratings by media experts were 81% in the “Very Valid” category, the results of the percentage of product ratings by material experts were 87% in the “Very Valid” category, the results of the percentage of product assessment by the teacher were 92% in the “Very Practical” category, and the results of the percentage of product assessment by 6 small group students were 93 .6 % in the “Very Interesting” category. Based on product assessment by all validators who stated that it was very valid, the teachers assessment stated that it was very practical, and student assessment stated that it was very interesting, the Mathematical Logic Pipe teaching aid (Pilogmath) that was developed meeting the criteria of being very feasible to use for class X students of SMA Negeri 1 Tanah Luas.

APA, Harvard, Vancouver, ISO, and other styles

15

Khlebalin, Aleksandr. "MATHEMATICAL PRACTICE AND MATHEMATICAL LOGIC: TO THE HISTORY OF RELATIONSHIP." Respublica literaria, RL. 2021. Vol. 2. No. 4 (November 29, 2021): 93–99. http://dx.doi.org/10.47850/rl.2021.2.4.93-99.

Full text

Abstract:

The article annuls the role of practice in the development of mathematics in the 19th century in the formation of mathematical logic. It is shown that the revolutionary transformations of mathematics of the 19th century, which led to an increase in the abstractness of mathematical theories and concepts, was accompanied by an increase in uncertainty regarding the standards of proof, which led to the universal spread of anxiety (J. Gray) as an element of mathematical practice. It is argued that this element of practice was one of the sources of the emergence of mathematical logic, which claims to give rigor and accuracy to mathematics. The article argues that the socio- epistemological analysis of the practice of mathematics and the formation of mathematical logic will clarify the specifics of the development of relations between mathematics and mathematical logic.

APA, Harvard, Vancouver, ISO, and other styles

16

Garrido, Angel. "Another Journal on Mathematical Logic and Mathematical Physics?" Axioms 1, no. 1 (September 1, 2011): 1–3. http://dx.doi.org/10.3390/axioms1010001.

Full text

APA, Harvard, Vancouver, ISO, and other styles

17

Jin, Chen. "A review on multiple-valued logic circuits." Applied and Computational Engineering 43, no. 1 (February 26, 2024): 322–26. http://dx.doi.org/10.54254/2755-2721/43/20230857.

Full text

Abstract:

Since the traditional binary logic has several disadvantages including inaccuracy, high complexity, and limited applications. Multiple-Valued Logic (MVL), which can store more information in one digit than binary logics, require less number of logic gates and take the third value in practical logic problems, is developed and introduced. More information stored per digit leads to higher computational efficiency. Less logic gates results in more spaces on the circuit board. Considering the third value means higher accuracy. In this research, some examples of different MVL circuit are designed to give a rough picture of current research in this domain. These designs are based on ternary and quaternary logics rather than binary logics. Besides, reliability evaluation through mathematical approach is presented in order to prove that the new design is more preferable. This can be carried out with mathematical analysis such as calculating a matrix that reflects its reliability, and simulating different designs to obtain certain values and comparing them with each other. Despite facing various challenges, including complicated physical implementation and difficulty to modulate the signals. This means that there is still potential of further research in this domain of logic circuits. This result in the conclusion that the MVL logic circuits will replace the conventional binary logic circuits in the future, and probably that decimal logic would be developed and no binary-to-decimal conversion unit will be required.

APA, Harvard, Vancouver, ISO, and other styles

18

Hikmah, Rezkiyana, Sri Rejeki, and Bayu Jaya Tama. "Effect of Student Attitudes on Mathematical Understanding Ability in Mathematical Logic in Hybrid Learning." Journal of Instructional Mathematics 4, no. 2 (November 29, 2023): 98–105. http://dx.doi.org/10.37640/jim.v4i2.1887.

Full text

Abstract:

This studi aims to determine the effect of students’ attitudes on learning outcomes of mathematical logic and to determine how much influence students’ attitudes have on learning outcomes of mathematical logic The research sample consisted of third semester students of the computer science engineering program who took the mathematical logic course. The result obtained are that there is an effect of attitude on the learning outcomes of student mathematical logic. The result of the regression model obtained with the value of F count = 7.055 with a significance level of 0.009 < 0,005 with indicates that there is an effect of attitude on the learning outcomes of mathematical logic. The result of the correlation value r is 0.231 and the coefficient of determination (R square) is 0.053 which shows that the effect of the independent variable (attitude) on the dependent variable (learning outcomes of mathematical logic) is 5.3%. This shows that there is a positive influence of students’ attitudes on students’ learning outcomes in mathematical logic.

APA, Harvard, Vancouver, ISO, and other styles

19

Rizza, Davide. "Magicicada, Mathematical Explanation and Mathematical Realism." Erkenntnis 74, no. 1 (November 20, 2010): 101–14. http://dx.doi.org/10.1007/s10670-010-9261-z.

Full text

APA, Harvard, Vancouver, ISO, and other styles

20

Scott, D. "Letter: Well-Structured Mathematical Logic." Choice Reviews Online 52, no. 10 (May 20, 2015): 1611. http://dx.doi.org/10.5860/choice.52.10.1611d.

Full text

APA, Harvard, Vancouver, ISO, and other styles

21

Adamowicz, Zofia. "Diagonal reasonings in mathematical logic." Banach Center Publications 34, no. 1 (1995): 9–18. http://dx.doi.org/10.4064/-34-1-9-18.

Full text

APA, Harvard, Vancouver, ISO, and other styles

22

Dogan, Hamide. "Mathematical induction: deductive logic perspective." European Journal of Science and Mathematics Education 4, no. 3 (July 15, 2016): 315–30. http://dx.doi.org/10.30935/scimath/9473.

Full text

APA, Harvard, Vancouver, ISO, and other styles

23

耿, 佳丽. "Teaching Logic on Mathematical Beauty." Advances in Education 11, no. 06 (2021): 2183–90. http://dx.doi.org/10.12677/ae.2021.116339.

Full text

APA, Harvard, Vancouver, ISO, and other styles

24

Beeson, Michael, and Robert S. Wolf. "A Tour through Mathematical Logic." American Mathematical Monthly 113, no. 3 (March 1, 2006): 275. http://dx.doi.org/10.2307/27641911.

Full text

APA, Harvard, Vancouver, ISO, and other styles

25

Welch, P. "CONSTRUCTIBILITY (Perspectives in Mathematical Logic)." Bulletin of the London Mathematical Society 18, no. 1 (January 1986): 81–82. http://dx.doi.org/10.1112/blms/18.1.81.

Full text

APA, Harvard, Vancouver, ISO, and other styles

26

Gardies, Jean Louis. "Do Mathematical Constructions Escape Logic?" Synthese 134, no. 1/2 (January 2003): 273–88. http://dx.doi.org/10.1023/a:1022148016910.

Full text

APA, Harvard, Vancouver, ISO, and other styles

27

Hájek, Petr. "What is mathematical fuzzy logic." Fuzzy Sets and Systems 157, no. 5 (March 2006): 597–603. http://dx.doi.org/10.1016/j.fss.2005.10.004.

Full text

APA, Harvard, Vancouver, ISO, and other styles

28

Mundy, Brent. "Mathematical Physics and Elementary Logic." PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1990, no. 1 (January 1990): 289–301. http://dx.doi.org/10.1086/psaprocbienmeetp.1990.1.192711.

Full text

APA, Harvard, Vancouver, ISO, and other styles

29

Garrido, Angel. "Fuzzy Logic and Mathematical Education." Journal of Educational System 2, no. 4 (2018): 1–5. http://dx.doi.org/10.22259/2637-5877.0204001.

Full text

APA, Harvard, Vancouver, ISO, and other styles

30

KIKUCHI, Makoto. "Preface to the Symposium : Mathematical Logic and Its Applications(Mathematical Logic and Its Applications)." Annals of the Japan Association for Philosophy of Science 19 (2011): 27. http://dx.doi.org/10.4288/jafpos.19.0_27.

Full text

APA, Harvard, Vancouver, ISO, and other styles

31

Wang, Hongguang, and Guoping Du. "Chinese Research on Mathematical Logic and the Foundations of Mathematics." Asian Studies 10, no. 2 (May 9, 2022): 243–66. http://dx.doi.org/10.4312/as.2022.10.2.243-266.

Full text

Abstract:

This paper outlines the Chinese research on mathematical logic and the foundations of mathematics. Firstly, it presents the introduction and spread of mathematical logic in China, especially the teaching and translation of mathematical logic initiated by Bertrand Russell’s lectures in the country. Secondly, it outlines the Chinese research on mathematical logic after the founding of the People’s Republic of China. The research in this period experienced a short revival under the criticism of the Soviet Union, explorations under the heavy influence of the Cultural Revolution, and the vigorous development of mathematical logic teaching and research after the period of “Reform and Opening Up” that started in the late 1970s, and the full integration of Chinese mathematical logic research into the international academic circle in the new century after 2000. In the third part, it focuses on the unique and original results of the Chinese mathematical logic research teams from the following three aspects: medium logic, lattice implication algebras and their lattice-valued systems of logic, and Chinese notation of logical constants, which can be used as a substantive supplement to the relevant literature on the history of mathematical logic in China. The last part is a reflection on the shortcomings of contemporary Chinese research on mathematical logic and the foundations of mathematics.

APA, Harvard, Vancouver, ISO, and other styles

32

C, Swathi, Jenifer Ebienazer, Swathi M, and Suruthipriya S. "Fuzzy Logic." International Journal of Innovative Research in Information Security 09, no. 03 (June 23, 2023): 147–52. http://dx.doi.org/10.26562/ijiris.2023.v0903.19.

Full text

Abstract:

Fuzzy logic is a mathematical framework for reasoning about ambiguous or inaccurate information. It is founded on the idea that truth can be stated as a degree of membership in a fuzzy set rather than as a binary value of true or untrue. Fuzzy logic is used in control systems, artificial intelligence, and decision-making. This paper defines fuzzy logic and discusses its key concepts, mathematical underpinnings, and applications. We look at the benefits and drawbacks.

APA, Harvard, Vancouver, ISO, and other styles

33

Aristidou, Michael. "Is Mathematical Logic Really Necessary in Teaching Mathematical Proofs?" ATHENS JOURNAL OF EDUCATION 7, no. 1 (December 6, 2019): 99–122. http://dx.doi.org/10.30958/aje.7-1-5.

Full text

APA, Harvard, Vancouver, ISO, and other styles

34

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.

Full text

Abstract:

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?

APA, Harvard, Vancouver, ISO, and other styles

35

Maddy, Penelope. "Mathematical Existence." Bulletin of Symbolic Logic 11, no. 3 (September 2005): 351–76. http://dx.doi.org/10.2178/bsl/1122038992.

Full text

Abstract:

Despite some discomfort with this grandly philosophical topic, I do in fact hope to address a venerable pair of philosophical chestnuts: mathematical truth and existence. My plan is to set out three possible stands on these issues, for an exercise in compare and contrast. A word of warning, though, to philosophical purists (and perhaps of comfort to more mathematical readers): I will explore these philosophical positions with an eye to their interconnections with some concrete issues of set theoretic method.Let me begin with a brief look at what to count as ‘philosophy’. To some extent, this is a matter of usage, and mathematicians sometimes classify as ‘philosophical’ any considerations other than outright proofs. So, for example, discussions of the propriety of particular mathematical methods would fall under this heading: should we prefer analytic or synthetic approaches in geometry? Should elliptic functions be treated in terms of explicit representations (as in Weierstrass) or geometrically (as in Riemann)? Should we allow impredicative definitions? Should we restrict ourselves to a logic without bivalence or the law of the excluded middle? Also included in this category would be the trains of thought that shaped our central concepts: should a function always be defined by a formula? Should a group be required to have an inverse for every element? Should ideal divisors be defined contextually or explicitly, treated computationally or abstractly? In addition, there are more general questions concerning mathematical values, aims and goals: Should we strive for powerful theories or low-risk theories? How much stress should be placed on the fact or promise of physical applications? How important are interconnections between the various branches of mathematics? These philosophical questions of method naturally include several peculiar to set theory: should set theorists focus their efforts on drawing consequences for areas of interest to mathematicians outside mathematical logic? Should exploration of the standard axioms of ZFC be preferred to the exploration and exploitation of new axioms? How should axioms for set theory be chosen? What would a solution to the Continuum Problem look like?

APA, Harvard, Vancouver, ISO, and other styles

36

Winczewski, Damian. "Dialektyka wiedzy logikomatematycznej w ujęciu Jarosława Ładosza." Studia Philosophica Wratislaviensia 15, no. 4 (March 31, 2021): 27–47. http://dx.doi.org/10.19195/1895-8001.15.4.2.

Full text

Abstract:

The aim of the article is an analysis of the early works of Jarosław Ładosz, a Polish philosopher and mathematician, who in the 1960s conducted a thorough examination of the most important scientiﬁc accomplishments in the ﬁeld of logic and mathematics from the perspective of Marxist philosophy. Being nowadays assessed as a symbol of dogmatism and orthodoxy in Polish Marxism, Ładosz revised most of the superstitions on the relationship between mathematical logic and dialectics, which have been legitimized in oﬃcial Marxist philosophy since the times of Marx and Engels, in his early works. Having rejected the claims of some Marxists for the formalization of dialectics, he presented the original concept of dialectics as a methodological tool for studying the sources of logical knowledge. Combining dialectical materialism with Jean Piaget’s epistemology, he formulated an elaborate, original hypothesis of the social construction of logico-mathematical knowledge, while at the same time transcending the subject-object division as-sumed in Marxist dogmatic epistemology.

APA, Harvard, Vancouver, ISO, and other styles

37

Kilakos, Dimitris. "Sofia A. Yanovskaya: The Marxist Pioneer of Mathematical Logic in the Soviet Union." Transversal: International Journal for the Historiography of Science, no. 6 (June 30, 2019): 49. http://dx.doi.org/10.24117/2526-2270.2019.i6.06.

Full text

Abstract:

K. Marx’s 200th jubilee coincides with the celebration of the 85 years from the first publication of his “Mathematical Manuscripts” in 1933. Its editor, Sofia Alexandrovna Yanovskaya (1896–1966), was a renowned Soviet mathematician, whose significant studies on the foundations of mathematics and mathematical logic, as well as on the history and philosophy of mathematics are unduly neglected nowadays. Yanovskaya, as a militant Marxist, was actively engaged in the ideological confrontation with idealism and its influence on modern mathematics and their interpretation. Concomitantly, she was one of the pioneers of mathematical logic in the Soviet Union, in an era of fierce disputes on its compatibility with Marxist philosophy. Yanovskaya managed to embrace in an originally Marxist spirit the contemporary level of logico-philosophical research of her time. Due to her highly esteemed status within Soviet academia, she became one of the most significant pillars for the culmination of modern mathematics in the Soviet Union. In this paper, I attempt to trace the influence of the complex socio-cultural context of the first decades of the Soviet Union on Yanovskaya’s work. Among the several issues I discuss, her encounter with L. Wittgenstein is striking.

APA, Harvard, Vancouver, ISO, and other styles

38

LARSON, Paul B. "Three Days of Ω-logic(Mathematical Logic and Its Applications)." Annals of the Japan Association for Philosophy of Science 19 (2011): 57–86. http://dx.doi.org/10.4288/jafpos.19.0_57.

Full text

APA, Harvard, Vancouver, ISO, and other styles

39

Basti, Gianfranco. "The Philosophy of Nature of the Natural Realism. The Operator Algebra from Physics to Logic." Philosophies 7, no. 6 (October 26, 2022): 121. http://dx.doi.org/10.3390/philosophies7060121.

Full text

Abstract:

This contribution is an essay of formal philosophy—and more specifically of formal ontology and formal epistemology—applied, respectively, to the philosophy of nature and to the philosophy of sciences, interpreted the former as the ontology and the latter as the epistemology of the modern mathematical, natural, and artificial sciences, the theoretical computer science included. I present the formal philosophy in the framework of the category theory (CT) as an axiomatic metalanguage—in many senses “wider” than set theory (ST)—of mathematics and logic, both of the “extensional” logics of the pure and applied mathematical sciences (=mathematical logic), and the “intensional” modal logics of the philosophical disciplines (=philosophical logic). It is particularly significant in this categorical framework the possibility of extending the operator algebra formalism from (quantum and classical) physics to logic, via the so-called “Boolean algebras with operators” (BAOs), with this extension being the core of our formal ontology. In this context, I discuss the relevance of the algebraic Hopf coproduct and colimit operations, and then of the category of coalgebras in the computations over lattices of quantum numbers in the quantum field theory (QFT), interpreted as the fundamental physics. This coalgebraic formalism is particularly relevant for modeling the notion of the “quantum vacuum foliation” in QFT of dissipative systems, as a foundation of the notion of “complexity” in physics, and “memory” in biological and neural systems, using the powerful “colimit” operators. Finally, I suggest that in the CT logic, the relational semantics of BAOs, applied to the modal coalgebraic relational logic of the “possible worlds” in Kripke’s model theory, is the proper logic of the formal ontology and epistemology of the natural realism, as a formalized philosophy of nature and sciences.

APA, Harvard, Vancouver, ISO, and other styles

40

Florio, Salvatore, and Øystein Linnebo. "Critical Plural Logic†." Philosophia Mathematica 28, no. 2 (June 1, 2020): 172–203. http://dx.doi.org/10.1093/philmat/nkaa020.

Full text

Abstract:

Abstract What is the relation between some things and the set of these things? Mathematical practice does not provide a univocal answer. On the one hand, it relies on ordinary plural talk, which is implicitly committed to a traditional form of plural logic. On the other hand, mathematical practice favors a liberal view of definitions which entails that traditional plural logic must be restricted. We explore this predicament and develop a “critical” alternative to traditional plural logic.

APA, Harvard, Vancouver, ISO, and other styles

41

Hannula, Miika, Juha Kontinen, and Jonni Virtema. "Polyteam semantics." Journal of Logic and Computation 30, no. 8 (September 23, 2020): 1541–66. http://dx.doi.org/10.1093/logcom/exaa048.

Full text

Abstract:

Abstract Team semantics is the mathematical framework of modern logics of dependence and independence in which formulae are interpreted by sets of assignments (teams) instead of single assignments as in first-order logic. In order to deepen the fruitful interplay between team semantics and database dependency theory, we define Polyteam Semantics in which formulae are evaluated over a family of teams. We begin by defining a novel polyteam variant of dependence atoms and give a finite axiomatization for the associated implication problem. We relate polyteam semantics to team semantics and investigate in which cases logics over the former can be simulated by logics over the latter. We also characterize the expressive power of poly-dependence logic by properties of polyteams that are downwards closed and definable in existential second-order logic ($\textsf{ESO}$). The analogous result is shown to hold for poly-independence logic and all $\textsf{ESO}$-definable properties. We also relate poly-inclusion logic to greatest fixed point logic.

APA, Harvard, Vancouver, ISO, and other styles

42

Buss, Samuel, Ulrich Kohlenbach, and Michael Rathjen. "Mathematical Logic: Proof Theory, Constructive Mathematics." Oberwolfach Reports 8, no. 4 (2011): 2963–3002. http://dx.doi.org/10.4171/owr/2011/52.

Full text

APA, Harvard, Vancouver, ISO, and other styles

43

Buss, Samuel, Ulrich Kohlenbach, and Michael Rathjen. "Mathematical Logic: Proof Theory, Constructive Mathematics." Oberwolfach Reports 11, no. 4 (2014): 2933–86. http://dx.doi.org/10.4171/owr/2014/52.

Full text

APA, Harvard, Vancouver, ISO, and other styles

44

Buss, Samuel, Rosalie Iemhoff, Ulrich Kohlenbach, and Michael Rathjen. "Mathematical Logic: Proof Theory, Constructive Mathematics." Oberwolfach Reports 14, no. 4 (December 18, 2018): 3121–83. http://dx.doi.org/10.4171/owr/2017/53.

Full text

APA, Harvard, Vancouver, ISO, and other styles

45

Buss, Samuel, Rosalie Iemhoff, Ulrich Kohlenbach, and Michael Rathjen. "Mathematical Logic: Proof Theory, Constructive Mathematics." Oberwolfach Reports 17, no. 4 (September 13, 2021): 1693–757. http://dx.doi.org/10.4171/owr/2020/34.

Full text

APA, Harvard, Vancouver, ISO, and other styles

46

Cowen, Robert. "A Beginner's Guide to Mathematical Logic." American Mathematical Monthly 125, no. 2 (January 30, 2018): 188–92. http://dx.doi.org/10.1080/00029890.2018.1401883.

Full text

APA, Harvard, Vancouver, ISO, and other styles

47

Rota, Gian-Carlo. "Mathematical logic and theoretical computer science." Advances in Mathematics 72, no. 1 (November 1988): 168. http://dx.doi.org/10.1016/0001-8708(88)90023-0.

Full text

APA, Harvard, Vancouver, ISO, and other styles

48

Cintula, P., G. Metcalfe, and C. Noguera. "Special Issue on Mathematical Fuzzy Logic." Journal of Logic and Computation 21, no. 5 (September 22, 2011): 715–16. http://dx.doi.org/10.1093/logcom/exp057.

Full text

APA, Harvard, Vancouver, ISO, and other styles

49

UYHAN, Ramazan, and Zülfiye GÖK. "Mathematical Success with Fuzzy Logic Modeling." Erzincan Üniversitesi Fen Bilimleri Enstitüsü Dergisi 15, no. 3 (December 30, 2022): 862–72. http://dx.doi.org/10.18185/erzifbed.1131694.

Full text

Abstract:

In this paper, the effect of high school students on mathematics achievement by taking active participation and absent of high school students was investigated by using fuzzy logic modeling. The questionnaire prepared by the researcher is applied to the students to determine the active participation of the students. These written exam scores are used in order to evaluate the absences and achievements of the students until the end of the 1st semester written exam. In this study, inputs are active participation and absent, and output is mathematics achievement. These data were tabulated, graded and transferred to Matlab and the model is obtained by using fuzzy logic toolbox. The actual results obtained from this model with the output values R^2 review by making the similarity rate is found to be 80%.

APA, Harvard, Vancouver, ISO, and other styles

50

Selden, John, and Annie Selden. "Unpacking the logic of mathematical statements." Educational Studies in Mathematics 29, no. 2 (September 1995): 123–51. http://dx.doi.org/10.1007/bf01274210.

Full text

APA, Harvard, Vancouver, ISO, and other styles

We offer discounts on all premium plans for authors whose works are included in thematic literature selections. Contact us to get a unique promo code!