منابع مشابه
Gödel Homomorphisms as Gödel Modal Operators
We extend propositional Gödel logic by a unary modal operator, which we interpret as 5 Gödel homomorphisms, i.e. functions [0, 1] → [0, 1] that distribute over the interpretations of the 6 binary connectives of Gödel logic. We show that validity in the propositional fragment has a simple 7 superintuitionistic Hilbert-type proof system, which is not structurally complete, and that validity 8 doe...
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Entailment in propositional Gödel logics can be defined in a natural way. While all infinite sets of truth values yield the same sets of tautologies, the entailment relations differ. It is shown that there is a rich structure of infinite-valued Gödel logics, only one of which is compact. It is also shown that the compact infinite-valued Gödel logic is the only one which interpolates, and the on...
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The identification of an informal concept of “effective calculability”with a rigorous mathematical notion like “recursiveness” or “Turingcomputability” is still viewed as problematic, and I think rightly so. I analyzethree different and conflicting perspectives Gödel articulated in the three decadesfrom 1934 to 1964. The significant shifts in Gödel's position underline thedi...
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Visualization of general relativity illustrates aspects of Einstein's insights into the curved nature of space and time to the expert as well as the layperson. One of the most interesting models which came up with Einstein's theory was developed by Kurt Gödel in 1949. The Gödel universe is a valid solution of Einstein's field equations, making it a possible physical description of our universe....
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We discuss the influence of Gödel and his results on the surfacing of the rigorous notion of computability afforded by Turing. We also address the debate about the limits of Artificial Intelligence spurned by Roger Penrose, on the basis of Gödel's theorems, and the views of Gödel himself. We conclude by touching upon the use of logic as a tool with which to approach the description of mind.
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ژورنال
عنوان ژورنال: Nature
سال: 1986
ISSN: 0028-0836,1476-4687
DOI: 10.1038/323766b0