Categorical abstract algebraic logic: Gentzen π -institutions and the deduction-detachment property
✍ Scribed by George Voutsadakis
- Publisher
- John Wiley and Sons
- Year
- 2005
- Tongue
- English
- Weight
- 134 KB
- Volume
- 51
- Category
- Article
- ISSN
- 0044-3050
No coin nor oath required. For personal study only.
✦ Synopsis
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.