  In the present paper, we propose Abstract Algebraic Logic (AAL) as a general
logical framework for Judgment Aggregation. Our main contribution is a
generalization of Herzberg's algebraic approach to characterization results in
on judgment aggregation and propositional-attitude aggregation, characterizing
certain Arrovian classes of aggregators as Boolean algebra and MV-algebra
homomorphisms, respectively. The characterization result of the present paper
applies to agendas of formulas of an arbitrary selfextensional logic. This
notion comes from AAL, and encompasses a vast class of logics, of which
classical, intuitionistic, modal, many-valued and relevance logics are special
cases. To each selfextensional logic $\Sm$, a unique class of algebras
$\Alg\Sm$ is canonically associated by the general theory of AAL. We show that
for any selfextensional logic $\Sm$ such that $\Alg\Sm$ is closed under direct
products, any algebra in $\Alg\Sm$ can be taken as the set of truth values on
which an aggregation problem can be formulated. In this way, judgment
aggregation on agendas formalized in classical, intuitionistic, modal,
many-valued and relevance logic can be uniformly captured as special cases.
This paves the way to the systematic study of a wide array of "realistic
agendas" made up of complex formulas, the propositional connectives of which
are interpreted in ways which depart from their classical interpretation. This
is particularly interesting given that, as observed by Dietrich, nonclassical
(subjunctive) interpretation of logical connectives can provide a strategy for
escaping impossibility results.
