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CATEGORICAL ABSTRACT LOGIC: HIDDEN MULTI-SORTED LOGICS AS MULTI-TERM π-INSTITUTIONS.
- Source :
-
Bulletin of the Section of Logic . 2016, Vol. 45 Issue 2, p111-124. 14p. - Publication Year :
- 2016
-
Abstract
- Babenyshev and Martins proved that two hidden multi-sorted deductive systems are deductively equivalent if and only if there exists an isomorphism between their corresponding lattices of theories that commutes with substitutions. We show that the π-institutions corresponding to the hidden multi-sorted deductive systems studied by Babenyshev and Martins satisfy the multi-term condition of Gil-Féerez. This provides a proof of the result of Babenyshev and Martins by appealing to the general result of Gil-Féerez pertaining to arbitrary multi-term π-institutions. The approach places hidden multi-sorted deductive systems in a more general framework and bypasses the laborious reuse of well-known proof techniques from traditional abstract algebraic logic by using "off the shelf" tools. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 01380680
- Volume :
- 45
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Bulletin of the Section of Logic
- Publication Type :
- Academic Journal
- Accession number :
- 122005723
- Full Text :
- https://doi.org/10.18778/0138-0680.45.2.04