Coproduct and amalgamation of deductive systems by means of ordered algebras

TL;DR

This paper introduces methods for combining propositional languages and deductive systems using algebraic structures like quantales, highlighting the relationships between algebraic, order-theoretic, and logical approaches.

Contribution

It develops new techniques for amalgamating deductive systems via ordered algebras, expanding on prior algebraic and logical frameworks.

Findings

Methods for amalgamating propositional languages and deductive systems

Extensive analysis of algebraic and order-theoretic relationships

Application of quantales and modules in logical system combination

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.