Military Communications and Information Technology: A Trusted ...

Mathematical Foundations of Interoperability
and Composability
Andreas Tolk
Old Dominion University, Norfolk, Virginia, USA, atolk@odu.edu
Abstract: Based on the success stories of many engineering solutions, interoperability is often seen
as something that can be worked into a system after the fact. If two systems shall exchange information
with each other, system and software engineers are engaged to make these systems interoperable, often
using interface and protocol standards. Recent research results in relevant domains of mathematics,
in particular model theory and algorithmic information theory, show that such bottom-up engineering
approaches are limited for model-based applications. Such applications do not only require
the interoperability of implementations but also the composability of underlying conceptualizations.
As more and more applications in the Military Communications and Information Systems domains
are model-based applications, such as decision support systems and alternative course of action
analyses tools, these topics become increasingly relevant and may lead to a paradigm shift how we
look at federating our systems in support of international operations.
Introduction
The paper shares lessons-learned from interoperability work conducted in support
of integrating command and control systems with modeling and simulation
systems. It introduces the Levels of Conceptual Interoperability Model (LCIM)
as the current support method for interoperability engineering. It proposes the use
of more formal approaches utilizing the mathematical foundations of Model Theory
for future system developments based on interoperability design.
The underlying idea of most military interoperability efforts – even if new
forms of standards like those developed for the sematic web are applied – is still
to connect two already developed and often operational systems by engineering
interoperability. We are enabling information exchange solutions after the fact by
defining interfaces and protocols. This is the same idea that already supported
message exchange mechanisms as well as data replication mechanism: the participating
two systems exchange information via pre-defined interfaces. The systems
themselves don’t have to be modified as long as they are able to support the standard
interfaces. The underlying interoperability definition is captured by the IEEE as follows:
“Interoperability is the ability of two or more systems or components to exchange