Categorical abstract algebraic logic: truth-equational \(\pi\)-institutions (Q2354626)

The property of truth-equationality was studied, first, for protoalgebraic logics. Later, \textit{J. G. Raftery} [Rep. Math. Logic 41, 95--149 (2006; Zbl 1136.03011)] investigated the truth-equationality (that is the property that the truth predicate of the reduced matrix models definable by unary equations) for deductive systems, characterizing those systems, among others, which are truth-equational. This paper generalizes Raftery's results [loc. cit.] for \(\pi\)-institutions. \(\pi\)-institutions are basic structures in the formalization of those logical systems that can not be formalized in deductive systems.