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An Arithmetical Hierarchy of the Law of Excluded Middle and Related Principles
Turku, Finland July 13-July 17
DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/LICS.2004.131961319th Annual IEEE Symposium on Logic i ...
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Yohji Akama, Tohoku University, Sendai, Japan
Stefano Berardi, University of Turin, Italy
Susumu Hayashi, Kobe University, Japan
Ulrich Kohlenbach, Darmstadt University of Technology, Germany
The topic of this paper is Relative Constructivism. We are concerned with classifying non-constructive principles from the constructive viewpoint. We compare, up to provability in Intuitionistic Arithmetic, sub-classical principles like Markov's Principle, (a function-free version of) Weak K?nig's Lemma, Post's Theorem, Excluded Middle for simply Existential and simply Universal statements, and many others. Our motivations are rooted in the experience of one of the authors with an extended program extraction and of another author with bound extraction from classical proofs.
Citation:
Yohji Akama, Stefano Berardi, Susumu Hayashi, Ulrich Kohlenbach, "An Arithmetical Hierarchy of the Law of Excluded Middle and Related Principles," lics, pp.192-201, 19th Annual IEEE Symposium on Logic in Computer Science (LICS'04), 2004
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