Paper Info
Title
Cantor's paradise regained: constructive mathematics from Brouwer to Kolmogorov to Gelfond
Abstract
Constructive mathematics, mathematics in which the existence of an object means that that we can actually construct this object, started as a heavily restricted version ofmathematics, a version in which many commonly used mathematical techniques (like the Law of Excluded Middle) were forbidden to maintain constructivity. Eventually, it turned out that not only constructive mathematics is not a weakened version of the classical one - as it was originally perceived - but that, vice versa, classical mathematics can be viewed as a particular (thus, weaker) case of the constructive one. Crucial results in this direction were obtained by M. Gelfond in the 1970s. In this paper, we mention the history of these results, and show how these results affected constructive mathematics, how they led to new algorithms, and how they affected the current activity in logic programming-related research.
Year
DOI
Venue
2011
10.1007/978-3-642-20832-4_12
Logic Programming, Knowledge Representation, and Nonmonotonic Reasoning
Keywords
Field
DocType
restricted version ofmathematics,mathematical technique,crucial result,classical mathematics,constructive mathematics,weakened version,new algorithm,current activity,m. gelfond,logic programming-related research,logic programming,algorithms
Constructive proof,Constructivism (mathematics),Law of excluded middle,Constructive,Classical mathematics,Pure mathematics,Intuitionism,Cantor's paradise,Calculus,Mathematics,Constructive analysis
Conference
Citations 
PageRank 
References 
0
0.34
4
Authors
1
Name
Order
Citations
PageRank
Vladik Kreinovich11091281.07