Geodesic
Categorical Abstract Logic: Hidden Multi-Sorted Logics as Multi-Term π-Institutions
Bulletin of the Section of Logic, Tome 45 (2016) no. 2.

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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-F´erez. This provides a proof of the result of Babenyshev and Martins by appealing to the general result of Gil-F´erez 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.
Keywords: Behavioral Equivalence, Hidden Logic, Multi-Sorted Logic, Multi-term π-Institutions, Interpretability, Deductive Equivalence 
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     author = {Voutsadakis, George},
     title = {Categorical {Abstract} {Logic:} {Hidden} {Multi-Sorted} {Logics} as {Multi-Term} {\ensuremath{\pi}-Institutions}},
     journal = {Bulletin of the Section of Logic},
     publisher = {mathdoc},
     volume = {45},
     number = {2},
     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BSL_2016_45_2_a2/}
}
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Voutsadakis, George. Categorical Abstract Logic: Hidden Multi-Sorted Logics as Multi-Term π-Institutions. Bulletin of the Section of Logic, Tome 45 (2016) no. 2. http://geodesic.mathdoc.fr/item/BSL_2016_45_2_a2/