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Halldén-Completeness in Super-Intuitionistic Predicate Logics

Nobu-Yuki Suzuki
Studia Logica: An International Journal for Symbolic Logic
Vol. 73, No. 1, Constructivism in Non-Classical Logics and Computer Science (Feb., 2003), pp. 113-130
Published by: Springer
Stable URL: http://www.jstor.org/stable/20016488
Page Count: 18
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Halldén-Completeness in Super-Intuitionistic Predicate Logics
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Abstract

One criterion of constructive logics is the disjunction property (DP). The Halldén-completeness is a weak DP, and is related to the relevance principle and variable separation. This concept is well-understood in the case of propositional logics. We extend this notion to predicate logics. Then three counterparts naturally arise. We discuss relationships between these properties and meet-irreducibility in the lattice of logics.

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