Journal of Pure and Applied Mathematics: Advances and ApplicationsAuthor's: George Voutsadakis
Pages: [27] - [73]
Received Date: March 23, 2015
Submitted by:
DOI: http://dx.doi.org/10.18642/jsata_7100121472
A general notion of a congruence system is introduced for 
Congruence systems in this sense are
collections of equivalence relations on the sets of sentences of the
that are preserved both by signature
morphisms and by fixed collections of natural transformations from
finite tuples of sentences to sentences. Based on this notion of a
congruence system, the notion of a Tarski congruence system,
generalizing the notion of a Tarski congruence from sentential logics,
is considered. Logical and bilogical morphisms are introduced for
also generalizing similar concepts from the
theory of sentential logics, and their relationship with the familiar
translations and interpretations of institutions is discussed.
Finally, the interplay between these logical maps and the formation of
logical quotients of 
and the way they transform the Tarski
congruence systems is investigated.
abstract algebraic logic, deductive systems, institutions, equivalent deductive systems, algebraizable deductive systems, adjunctions, equivalent institutions, algebraizable institutions, Leibniz congruence, Tarski congruence, algebraizable sentential logics.
