In abstract algebraic logic the Leibniz operator is a tool used to classify deductive systems, which have a precise technical definition, and capture a large number of logics. The Leibniz operator was introduced by Willem Blok and Don Pigozzi, two of the founders of the field, as a means to abstract the well-known Lindenbaum-Tarski process, that leads to the association of Boolean algebras to classical propositional calculus, and make it applicable to as wide a variety of sentential logics as possible. It is an operator that assigns to a given theory of a given sentential logic, perceived as a free algebra with a consequence operation on its universe, the largest congruence on the algebra that is compatible with the theory.
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