Deduction modulo is an extension of first-order predicate logic where axioms are replaced by a congruence, modulo which deduction is performed. Like first-order predicate logic, Deduction modulo is a framework where many theories can be expressed, in particular predicative arithmetic [4] and impredicative arithmetic, usually called first-order and second-order arithmetic (terminology that we tr...

Deduction systems and graph rewriting systems are compared within a common categorical framework. This leads to an improved deduction method in diagrammatic logics.