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1

Many-Valued Logic in the Jewish Short Stories

100%
Levin V. I.
Studia Humana
|
2014
|
vol. 3
|
issue 4
3-6
EN
Jewish short stories (parables, tales, jokes, etc.) are explained from the viewpoint of many-valued logic. On the basis of some examples, we show, how their contents may be logically interpreted.
2

The Logic of Self-Organized Criticality

100%
Bakhtiyarov K. I.
Studia Humana
|
2015
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vol. 4
|
issue 3
37-40
EN
A consideration of non-classical logic in terms of classical one allows us to show a role of designated truth values. In this way we show that our version of non-classical many-valued logic can be based on the structure of genetic code.
3

A simple Henkin-style completeness proof for Gödel 3-valued logic G3

100%
Robles G.
Logic and Logical Philosophy
|
2014
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vol. 23
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issue 4
371–390
EN
A simple Henkin-style completeness proof for Gödel 3-valued propositional logic G3 is provided. The idea is to endow G3 with an under-determined semantics (u-semantics) of the type defined by Dunn. The key concept in u-semantics is that of “under-determined interpretation” (u-interpretation). It is shown that consistent prime theories built upon G3 can be understood as (canonical) u-interpretations. In order to prove this fact we follow Brady by defining G3 as an extension of Anderson and Belnap’s positive fragment of First Degree Entailment Logic.
4

On Two-Valued and Multiple-Valued Logic and on Paradoxes of Verity

75%
Tajsin E. A.
Dialogue and Universalism
|
2023
|
issue 1
143-161
EN
This article is dedicated to the centenary of the Russian philosopher and logician Alexander Alexandrovich Zinov’ev (1922–2006). The phenomena of truth, truthfulness, veracity and “truthiness” discussed widely in logic, epistemology as theory of science and gnoseology as general theory of knowledge, have received many interpretations—and not a single one to be generally accepted. Discussions continue not only upon narrow technical, operational questions of the predicate calculus and/or propositions calculus, but also on logic-gnoseological problems, one of which casts doubt on the maxim “logic is the house of truth,” and the other highlights the laxity of the opposition of “truth—falsehood” meanings as the main categories of the two-valued logic. These evaluations of proposition do not in fact op[1]pose each other in the sense of a contradiction. Verity and falsity are controversial (op[1]posite), but not contradictory (antithetical) concepts; it is truth and non-truth that are contradictory. Therefore, there is not only the possibility, but also the reality of the existence of a field, or zone, of transition between the values “true—false.”
5
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Krata podwójna: próba opisu wydarzeń przyszłych za pomocą narzędzi logicznych

71%
Bażyk A. P.
Semina Scientiarum
|
2012
|
vol. 11
EN
An unflagging interest in describing future events has continuously motivated investigations, particularly in the field of logic.Aristotle, universally acknowledged as the father of logic, proposed a set of certain bases from which we could depart with our investigations. However, these are tools in which, despite their great value, one can perceive certain shortcomings.Over the centuries many attempts have been made to discover a means of describing any sentence, expressed in any grammatical form. One of these attempts is bilattice theory, through which it has been attempted to describe future events. This theory makes use of tools such as vagueness and different forms of semantics including subvaluationism and supervaluationism.In lattice theory itself, the double lattice known as the FOUR lattice (four-valued bilattice logic) is directly employed.After analyzing the structure of a given theory one may easily make use of it in practice, providing examples of its usage.
6

The critics of paraconsistency and of many-valuedness and the geometry of oppositions

51%
Moretti A.
Logic and Logical Philosophy
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2010
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vol. 19
|
issue 1-2
63–94
EN
In 1995 Slater argued both against Priest’s paraconsistent system LP (1979) and against paraconsistency in general, invoking the fundamental opposition relations ruling the classical logical square. Around 2002 Béziau constructed a double defence of paraconsistency (logical and philosophical), relying, in its philosophical part, on Sesmat’s (1951) and Blanche’s (1953) “logical hexagon”, a geometrical, conservative extension of the logical square, and proposing a new (tridimensional) “solid of opposition”, meant to shed new light on the point raised by Slater. By using n-opposition theory (NOT) we analyse Beziau’s anti-Slater move and show both its right intuitions and its technical limits. Moreover, we suggest that Slater’s criticism is much akin to a well-known one by Suszko (1975) against the conceivability of many-valued logics. This last criticism has been addressed by Malinowski (1990) and Shramko and Wansing (2005), who developed a family of tenable logical counter-examples to it: trans-Suszkian systems are radically many-valued. This family of new logics has some strange logical features, essentially: each system has more than one consequence operator. We show that a new, deeper part of the aforementioned geometry of logical oppositions (NOT), the “logical poly-simplexes of dimension m”, generates new logical-geometrical structures, essentially many-valued, which could be a very natural (and intuitive) geometrical counterpart to the “strange”, new, non-Suszkian logics of Malinowski, Shramko and Wansing. By a similar move, the geometry of opposition therefore sheds light both on the foundations of paraconsistent logics and on those of many-valued logics.
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