Deduction Graphs with Universal Quantification

Deduction Graphs are meant to generalise both Gentzen-Prawitz style natural deductions and Fitch style flag deductions. They have the structure of acyclic directed graphs with boxes. In [Herman Geuvers and Iris Loeb. Natural Deduction via Graphs: Formal Definition and Computation Rules. Mathematical Structures in Computer Science (Special Issue on Theory and Applications of Term Graph Rewriting), Volume 17(03):485–526, 2007.] we have investigated the deduction graphs for minimal proposition logic. This paper studies the extension with first-order universal quantification, showing the robustness of the concept of deduction graphs.