Revisiting the Institutional Approach to Herbrand's Theorem

More than a decade has passed since Herbrand’s theorem was first generalized to arbitrary institutions, enabling in this way the development of the logic-programming paradigm over formalisms beyond the conventional framework of relational first-order logic. Despite the mild assumptions of the original theory, recent developments have shown that the institution-based approach cannot capture constructions that arise when service-oriented computing is presented as a form of logic programming, thus prompting the need for a new perspective on Herbrand’s theorem founded instead upon a concept of generalized substitution system. In this paper, we formalize the connection between the institution- and the substitution-system-based approach to logic programming by investigating a number of features of institutions, like the existence of a quantification space or of representable substitutions, under which they give rise to suitable generalized substitution systems. Building on these resu...

• Type: Journal
• Year: 2015
• Where: CALCO
• Authors: Ionut Tutu, José Luiz Fiadeiro
• Keywords: CALCO 2015, Mathematics