A b s t r a c t. An analog of the strong version of a protoalgebraic logic, introduced by Font and Jansana, is presented for
\(N\)-protoalgebraic \(\pi\)-institutions. Some properties of this strong version of an
\(N\)-protoalgebraic \(\pi\)-institution are explored and they are related to the explicit definability of
\(N\)-Leibniz theory systems. \(N\)-Leibniz theory systems
were introduced in previous work by the author, also taking after the corresponding theory of Font and Jansana in the sentential framework.
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