Coproduct and amalgamation of deductive systems by means of ordered algebras

Abstract

We propose various methods for combining or amalgamating propositional languages and deductive systems. We make heavy use of quantales and quantale modules in the wake of previous works by the present and other authors. We also describe quite extensively the relationships among the algebraic and order-theoretic constructions and the corresponding ones based on a purely logical approach.

This paper has been awarded the 2021 Newton da Costa Prize from the Brazilian Logic Society. 27 pages, to appear on Logica Universalis