Abstract

The integration of reasoning and computation services across system and language boundaries has been mostly treated from an engineering perspective. In this paper we take a foundational point of view. We identify the following form of integration problems: an informal (mathematical; i.e, logically underspecified) specification has multiple concrete formal implementations between which queries and results have to be transported. The integration challenge consists in dealing with the implementation-specific details such as additional constants and properties. We pinpoint their role in safe and unsafe integration schemes and propose a proof-theoretic solution based on modular theory-graphs that include the meta-logical foundations. This also gives a clean conceptual basis for earlier attempts that explain integration via “content/semantic markup”.