A Foundational View on Integration Problems

TL;DR

This paper presents a foundational theoretical framework for integrating reasoning and computation systems across different logical foundations using the MMT language, addressing both safe and unsafe integration schemes.

Contribution

It introduces a formal framework based on theories and partial morphisms for system integration, including logic-agnostic and logic-specific approaches.

Findings

Develops a general model for system integration using theories and morphisms

Includes a discussion on safe versus unsafe integration schemes

Provides a formal foundation for logic-based system integration

Abstract

The integration of reasoning and computation services across system and language boundaries is a challenging problem of computer science. In this paper, we use integration for the scenario where we have two systems that we integrate by moving problems and solutions between them. While this scenario is often approached from an engineering perspective, we take a foundational view. Based on the generic declarative language MMT, we develop a theoretical framework for system integration using theories and partial theory morphisms. Because MMT permits representations of the meta-logical foundations themselves, this includes integration across logics. We discuss safe and unsafe integration schemes and devise a general form of safe integration.