Combining Logics: Parchments Revisited

• Authors: Carlos Caleiro;Paulo Mateus;Jaime Ramos;Amílcar Sernadas
• Venue: WADT '01 Selected papers from the 15th International Workshop on Recent Trends in Algebraic Development Techniques
• Year: 2001

In the general context of the theory of institutions, several notions of parchment and parchment morphism have been proposed as the adequate setting for combining logics. However, so far, they seem to lack one of the main advantages of the combination mechanism known as fibring: general results of transference of important logical properties from the logics being combined to the resulting fibred logic. Herein, in order to bring fibring to the institutional setting, we propose to work with the novel notion of c-parchment. We show how both free and constrained fibring can be characterized as colimits of c-parchments, and illustrate both the construction and its preservation capabilities by exploring the idea of obtaining partial equational logic by fibring equational logic with a suitable logic of partiality. Last but not least, in the restricted context of propositional based, we state and prove a collection of meaningful soundness and completeness preservation results for fibring, with respect to Hilbert-like proof-calculi.