Separations of non-monotonic randomness notions
نویسندگان
چکیده
منابع مشابه
Separations of Non-monotonic Randomness Notions
In the theory of algorithmic randomness, several notions of random sequence are defined via a game-theoretic approach, and the notions that received most attention are perhaps Martin-Löf randomness and computable randomness. The latter notion was introduced by Schnorr and is rather natural: an infinite binary sequence is computably random if no total computable strategy succeeds on it by bettin...
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This paper explores the role of some basic notions in the study of non-monotonic reasoning, such as validity, logical consequence, context, rules and assumptions. It offers some considerations about the relation between non-monotonicity and the ideal of perfect validity in logical inference and the pertinence of taking into account human limitations. I propose that work on non-monotonic reasoni...
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It is an open problem in the area of computable randomness whether Kolmogorov-Loveland randomness coincides with Martin-Löf randomness. Joe Miller and André Nies suggested some variations of Kolmogorov-Loveland randomness to approach this problem and to provide a partial solution. We show that their proposed notion of partial permutation randomness is still weaker than Martin-Löf randomness.
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Schnorr famously proved that Martin-Löf-randomness of a sequence A can be characterised via the complexity of A’s initial segments. Nies, Stephan and Terwijn as well as independently Miller showed that Kolmogorov randomness coincides with Martin-Löf randomness relative to the halting problem K; that is, a set A is Martin-Löf random relative to K iff there is no function f such that for all m an...
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ژورنال
عنوان ژورنال: Journal of Logic and Computation
سال: 2010
ISSN: 0955-792X,1465-363X
DOI: 10.1093/logcom/exq037