Gödel on Many-Valued Logic

Lethen, Tim

doi:10.1017/s1755020321000034

Cited by 3 publications

(3 citation statements)

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“…The problem of applicability of multivalued logics to the reflection of laws of thought is most closely related to the problem of interpreting the variables of multivalued logic, which remains relevant at present 9 , 10 . Whereas within binary logic, its variables can be uniquely associated with the notion of truth, such uniqueness is lost for multivalued logics, which determines the relevance of research in the philosophy of multivalued logics, which is currently being actively pursued 11 , 12 .…”

Section: Introductionmentioning

confidence: 99%

“…In a famous monograph on the history of mathematics 3 the following passage from one of J. Boole's main works, "Investigation of the laws of thought", is given to illustrate exactly this approach, which prevailed then in the field of logic creation: "In the treatise before us we intend to investigate the fundamental laws of those operations of the mind by which thinking is effected, in order to express them in the symbolic language of calculus, and on this basis to construct the science of logic and its method. "Obviously, most modern works on multivalued logics have departed far enough from this tradition, otherwise the problem of interpretation of multivalued logics and their classification would not be so acute.The problem of applicability of multivalued logics to the reflection of laws of thought is most closely related to the problem of interpreting the variables of multivalued logic, which remains relevant at present 9,10 . Whereas…”

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Improving the efficiency of using multivalued logic tools

Сулейменов

Vitulyova

Kabdushev

et al. 2023

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Multivalued logics are becoming one of the most important tools of information technology. They are in great demand for creation of artificial intelligence systems that are close to human intelligence, since the functioning of the latter cannot be reduced to the operations of binary logic. At the same time, the problem of improving the efficiency of using the results of research in multivalued logics, as well as the problem of interpreting variables of multivalued logic, is acute. These problems create certain interdisciplinary barriers and make it difficult to implement the results of research in the field of multivalued logics in other fields of knowledge. It is shown that the problem of interpreting multivalued logic variables can be removed by establishing correspondence with fuzzy logic variables. Improving the efficiency of using of operations of multivalued logics and their variables can be provided by using their close connection to Galois fields. This connection, among other things, makes it possible to reduce any operations of multivalued logics, the number of variables in which is equal to a prime number, to algebraic functions whose arguments take values in Galois fields. This allows, among other things, to eliminate the very cumbersome constructions used in works on multivalued logic and make its apparatus convenient for use in related scientific disciplines in information technology. Direct verification of the adequacy of algorithms based on the use of Galois fields can be carried out by means of radio-electronic circuits, examples of which are presented in the present paper.

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Section: Introductionmentioning

confidence: 99%

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confidence: 99%

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Improving the efficiency of using multivalued logic tools

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Vitulyova

Kabdushev

et al. 2023

Sci Rep

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How much Time Does a Logical Inference Take?

Lethen

2023

On Gödel and the Nonexistence of Time – Gödel Und Die Nichtexistenz Der Zeit

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A Talmudic norms approach to many-valued logic

Lethen

2021

Journal of Logic and Computation

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In three-valued logic, the third truth-value is often interpreted as undefined. However, the value of a logical term may be well defined if its ‘history’ is taken into account. Following this approach, the analogy to the Sorites paradox meets the eye, which in turn has recently been addressed by means of a ‘Talmudic Norms’ approach. This paper thus lays bare a religious contribution to the field of many-valued logic and implements a simplified dynamic model for the theory of Talmudic mixtures—and, thus, for the outlined Sorites logic—using standard AI search and planning techniques.

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Gödel on Many-Valued Logic

Abstract: This paper collects and presents unpublished notes of Kurt Gödel concerning the field of many-valued logic. In order to get a picture as complete as possible, both formal and philosophical notes, transcribed from the Gabelsberger shorthand system, are included.

Cited by 3 publications

References 16 publications

Improving the efficiency of using multivalued logic tools

Improving the efficiency of using multivalued logic tools

How much Time Does a Logical Inference Take?

A Talmudic norms approach to many-valued logic

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