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Categorical abstract algebraic logic: Gentzen π -institutions and the deduction-detachment property.
- Source :
-
Mathematical Logic Quarterly . Nov2005, Vol. 51 Issue 6, p570-578. 9p. - Publication Year :
- 2005
-
Abstract
- Given a π -institution I , a hierarchy of π -institutions I(n ) is constructed, for n ≥ 1. We call I(n ) the n-th order counterpart of I . The second-order counterpart of a deductive π -institution is a Gentzen π -institution, i.e. a π -institution associated with a structural Gentzen system in a canonical way. So, by analogy, the second order counterpart I(2) of I is also called the “Gentzenization” of I . In the main result of the paper, it is shown that I is strongly Gentzen , i.e. it is deductively equivalent to its Gentzenization via a special deductive equivalence, if and only if it has the deduction-detachment property . (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 09425616
- Volume :
- 51
- Issue :
- 6
- Database :
- Academic Search Index
- Journal :
- Mathematical Logic Quarterly
- Publication Type :
- Academic Journal
- Accession number :
- 18522844
- Full Text :
- https://doi.org/10.1002/malq.200310132