The Experts below are selected from a list of 58782 Experts worldwide ranked by ideXlab platform
Gabriella Crocco - One of the best experts on this subject based on the ideXlab platform.
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Gödel, Leibniz and "Russell's Mathematical Logic
2013Co-Authors: Gabriella CroccoAbstract:This paper presents an overview of what is known about Kurt Gödel's reading Leibniz. The only published work in which Gödel explicitly mentions Leibniz's work is "Russell's Mathematical Logic" edited in 1944 by Schilpp for the Library of Living Philosophers. The author presents the available evidence (including the published and unpublished material of the Gödel archives and the transcriptions of Gödel's conversations with Hao Wang in 1970) which prove the deep influence of Leibniz on Gödel philosophical reflections and in his scientific work. The author shows how , on the basis of the unpublished material, the intricate structure of Gödel's paper on Russell reveals a every clear and Leibnizian conception of the nature of Logic and of the problems to be solved in order to achieve, in modern terms, Leibniz's program of the Characteristica .
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Gödel, Leibniz and “Russell’s Mathematical Logic”
New Essays on Leibniz Reception, 2012Co-Authors: Gabriella CroccoAbstract:Kurt Godel explicitly mentioned Leibniz in only one paper, “Russell’s Mathematical Logic”, which appeared in 1944 in the volume of the Library of Living Philosophers devoted to Bertrand Russell and edited by A. Schilpp.1 Nevertheless, the tribute paid by Godel to Leibniz in this text is so important that this alone suffices in attesting to the role that Leibniz’s work played in Godel’s thought.
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godel leibniz and russell s Mathematical Logic
2012Co-Authors: Gabriella CroccoAbstract:Kurt Godel explicitly mentioned Leibniz in only one paper, “Russell’s Mathematical Logic”, which appeared in 1944 in the volume of the Library of Living Philosophers devoted to Bertrand Russell and edited by A. Schilpp.1 Nevertheless, the tribute paid by Godel to Leibniz in this text is so important that this alone suffices in attesting to the role that Leibniz’s work played in Godel’s thought.
Jingde Cheng - One of the best experts on this subject based on the ideXlab platform.
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A Quantitative Analysis of Implicational Paradoxes in Classical Mathematical Logic
Electronic Notes in Theoretical Computer Science, 2007Co-Authors: Yuichi Goto, Jingde ChengAbstract:Classical Mathematical Logic includes a lot of ''implicational paradoxes'' as its Logic theorems. This paper uses the property of strong relevance as the criterion to identify implicational paradoxes in Logical theorems of classical Mathematical Logic, and enumerates Logical theorem schemata of classical Mathematical Logic that do not satisfy the strong relevance. This quantitative analysis shows that classical Mathematical Logic is by far not a suitable Logical basis for automated forward deduction.
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SAC - A quantitative analysis of implicational paradoxes in classical Mathematical Logic
Proceedings of the 2006 ACM symposium on Applied computing - SAC '06, 2006Co-Authors: Yuichi Goto, Jingde ChengAbstract:Classical Mathematical Logic includes a lot of "implicational paradoxes" as its Logic theorems. On the other hand, relevant Logics and strong relevant Logics have rejected those implicational paradoxes as their Logical theorems. This paper uses the property of strong relevance as the criterion to identify implicational paradoxes in Logical theorems of classical Mathematical Logic, and count the number of Logical theorem schemata of classical Mathematical Logic that do not satisfy the strong relevance. Our results quantitatively shows that classical Mathematical Logic is by far not a suitable Logical basis for automated forward deduction.
Yuichi Goto - One of the best experts on this subject based on the ideXlab platform.
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A Quantitative Analysis of Implicational Paradoxes in Classical Mathematical Logic
Electronic Notes in Theoretical Computer Science, 2007Co-Authors: Yuichi Goto, Jingde ChengAbstract:Classical Mathematical Logic includes a lot of ''implicational paradoxes'' as its Logic theorems. This paper uses the property of strong relevance as the criterion to identify implicational paradoxes in Logical theorems of classical Mathematical Logic, and enumerates Logical theorem schemata of classical Mathematical Logic that do not satisfy the strong relevance. This quantitative analysis shows that classical Mathematical Logic is by far not a suitable Logical basis for automated forward deduction.
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SAC - A quantitative analysis of implicational paradoxes in classical Mathematical Logic
Proceedings of the 2006 ACM symposium on Applied computing - SAC '06, 2006Co-Authors: Yuichi Goto, Jingde ChengAbstract:Classical Mathematical Logic includes a lot of "implicational paradoxes" as its Logic theorems. On the other hand, relevant Logics and strong relevant Logics have rejected those implicational paradoxes as their Logical theorems. This paper uses the property of strong relevance as the criterion to identify implicational paradoxes in Logical theorems of classical Mathematical Logic, and count the number of Logical theorem schemata of classical Mathematical Logic that do not satisfy the strong relevance. Our results quantitatively shows that classical Mathematical Logic is by far not a suitable Logical basis for automated forward deduction.
Vladimir Uspensky - One of the best experts on this subject based on the ideXlab platform.
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Mathematical Logic in the Former Soviet Union: Brief History and Current Trends
Logic and Scientific Methods, 1997Co-Authors: Vladimir UspenskyAbstract:Scientific life in the former Soviet Union (for short: fSU), as well as life in general, has changed drastically in recent years.1 Those changes are not specific for Mathematical Logic but without taking them into consideration, our situation in ML cannot be understood properly.
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KOLMOGOROV AND Mathematical Logic
Journal of Symbolic Logic, 1992Co-Authors: Vladimir UspenskyAbstract: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.
Angela D. Friederici - One of the best experts on this subject based on the ideXlab platform.
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Mathematical Logic in the Human Brain: Semantics
PLoS ONE, 2013Co-Authors: Roland M. Friedrich, Angela D. FriedericiAbstract:As a higher cognitive function in humans, mathematics is supported by parietal and prefrontal brain regions. Here, we give an integrative account of the role of the different brain systems in processing the semantics of Mathematical Logic from the perspective of macroscopic polysynaptic networks. By comparing algebraic and arithmetic expressions of identical underlying structure, we show how the different subparts of a fronto-parietal network are modulated by the semantic domain, over which the Mathematical formulae are interpreted. Within this network, the prefrontal cortex represents a system that hosts three major components, namely, control, arithmetic-Logic, and short-term memory. This prefrontal system operates on data fed to it by two other systems: a premotor-parietal top-down system that updates and transforms (external) data into an internal format, and a hippocampal bottom-up system that either detects novel information or serves as an access device to memory for previously acquired knowledge.
