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Categorical abstract algebraic logic: more on protoalgebraicity. (English) Zbl 1134.03044

\(\pi\)-institutions arose within formal specification theory as a meta-theory for multi-signature deductive systems, independently of the actual details of the logic involved.
This paper is part of the great programme undertaken by the same author to generalize algebraization of deductive systems resp. sentential logic (as developed by Blok, Pigozzi, Font, Jansana, etc.) to the level of \(\pi\)-institutions.
Protoalgebraic \(\pi\)-institutions have been introduced recently by the same author as an analog of protoalgebraic sentential logics with the intention of extending the Leibniz hierarchy from the concrete sentential framework to the abstract \(\pi\)-institutions framework. The current work is a continuation of previous work by the author by advancing the lifting of properties of protoalgebraic logics from the sentential to the \(\pi\)-institutions level.

MSC:

03G30 Categorical logic, topoi
18C15 Monads (= standard construction, triple or triad), algebras for monads, homology and derived functors for monads
68N30 Mathematical aspects of software engineering (specification, verification, metrics, requirements, etc.)
08C05 Categories of algebras
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