Conceptual interoperability is a concept in simulation theory.
From the early ideas of Harkrider and Lunceford, simulation composability has been studied in more detail. Petty and Weisel formulated the current working definition: "Composability is the capability to select and assemble simulation components in various combinations into simulation systems to satisfy specific user requirements. The defining characteristic of composability is the ability to combine and recombine components into different simulation systems for different purposes." A recent RAND study provided a coherent overview of the state of composability for military simulation systems within the U.S. Department of Defense; many of its findings have much broader applicability.
Levels of conceptual interoperability
The resulting challenges have produced layered views. Petty and Weisel distinguish between the idea of interoperability, coping with the technical challenges, and composability, dealing with modeling issues. Research at the Virginia Modeling, Analysis and Simulation Center (VMASC) refined these layers to define the "Levels of Conceptual Interoperability Model (LCIM)," This definition has undergone gradual improvement since the first discussion in. The current version of LCIM was first documented by Turnitsa in.
The different levels are characterized as follows:
- Level 0: Stand-alone systems have No Interoperability.
- Level 1: On the level of Technical Interoperability, a communication protocol exists for exchanging data between participating systems. On this level, a communication infrastructure is established allowing systems to exchange bits and bytes, and the underlying networks and protocols are unambiguously defined.
- Level 2: The Syntactic Interoperability level introduces a common structure to exchange information; i.e., a common data format is applied. On this level, a common protocol to structure the data is used; the format of the information exchange is unambiguously defined. This layer defines structure.
- Level 3: If a common information exchange reference model is used, the level of Semantic Interoperability is reached. On this level, the meaning of the data is shared; the content of the information exchange requests are unambiguously defined. This layer defines (word) meaning. There is a related but slightly different interpretation of the phrase semantic interoperability, which is closer to what is here termed Conceptual Interoperability, i.e. information in a form whose meaning is independent of the application generating or using it.
- Level 4: Pragmatic Interoperability is reached when the interoperating systems are aware of the methods and procedures that each system is employing. In other words, the use of the data – or the context of its application – is understood by the participating systems; the context in which the information is exchanged is unambiguously defined. This layer puts the (word) meaning into context.
- Level 5: As a system operates on data over time, the state of that system will change, and this includes the assumptions and constraints that affect its data interchange. If systems have attained Dynamic Interoperability, they are able to comprehend the state changes that occur in the assumptions and constraints that each is making over time, and they are able to take advantage of those changes. When interested specifically in the effects of operations, this becomes increasingly important; the effect of the information exchange within the participating systems is unambiguously defined.
- Level 6: Finally, if the conceptual model – i.e. the assumptions and constraints of the meaningful abstraction of reality – are aligned, the highest level of interoperability is reached: Conceptual Interoperability. This requires that conceptual models are documented based on engineering methods enabling their interpretation and evaluation by other engineers. In essence, this requires a “fully specified, but implementation independent model” as requested by Davis and Anderson; this is not simply text describing the conceptual idea.
The LCIM shows that a layered approach to support composable services is necessary. The WS standards described earlier are not able to manage all levels, in particular not with the M&S specific upper layers. It is worth mentioning, however, that the LCIM focuses on technical support by information systems, such as command and control information systems in the military context. As Alberts and Hayes point out in, the organizational and social aspects are often even more important. Tolk proposes such a layered framework for measures of merits dealing with questions like tactical or strategic alignment of objectives or even political will of coalition partners in. Within this contribution, however, the focus will be on the information system aspects.
Page et al. suggest defining composability as the realm of the model and interoperability as the realm of the software implementation of the model. In addition, their research introduces integratability coping with the hardware-side and configuration side of connectivity. The author supports this categorization and recommends the following distinction when dealing with issues of simulation system interoperability, to include meaningful simulation-to-simulation system interoperation:
- Integratability contends with the physical/ technical realms of connections between systems, which include hardware and firmware, protocols, etc.
- Interoperability contends with the software- and implementation details of interoperations, including exchange of data elements based on a common data interpretation, etc.
- Composability contends with the alignment of issues on the modeling level. The underlying models are purposeful abstractions of reality used for the conceptualization being implemented by the resulting simulation systems.
This ideas complement the LCIM. The LCIM has been successfully applied not only in the domain of Modeling & Simulation, but generally in model-based interoperability challenges. It should be pointed out that the LCIM can be used in descriptive and in prescriptive mode. It was recently recommended to extend the LCIM to an Interoperability Maturity Matrix. 
Composability as a Great Challenge
During an ACM SIGSIM and SCS sponsored expert discussion during the SCS Spring Simulation Multiconference in San Diego, CA, on April 11, 2013, Professor Tolk addressed Composability as a Grand Challenge of Modeling & Simulation when we are thinking about M&S and Cloud-based Simulation. He proposed the following two definitions:
- Interoperability: the ability to exchange usable data between two systems and to invoke their services using the appropriate input parameters!
- Composability: the consistent representation of truth regarding the same objects as represented in the participating systems!
He referred to the latest work of his research team that utilizes Model Theory 
The LCIM in this form or slightly variants thereof has been applied not only in simulation, but in many other domains as well. Examples are
Health and Human Sciences (http://aspe.hhs.gov/sp/reports/2010/erpreqlim/report.shtml);
Department of Energy SmartGrid (http://www.gridwiseac.org/pdfs/interopframework_v1_1.pdf);
Enterprise Interoperability (http://www.sciencedirect.com/science/article/pii/S0166361508000353);
Geographic Information Systems (http://onlinelibrary.wiley.com/doi/10.1111/j.1749-8198.2009.00241.x/abstract),
- Harkrider, S. M. and Lunceford, W. H. (1999). Modeling and Simulation Composability. Proceedings Interservice/Industry Training, Simulation and Education Conference (I/ITSEC)
- Petty, M.D. and Weisel, E.W. (2003). A Composability Lexicon. Proceedings IEEE Spring Simulation Interoperability Workshop, IEEE CS Press
- Davis, P.K. and Anderson, R.H. (2003). Improving the Composability of Department of Defense Models and Simulations. RAND Corporation
- Tolk, A. and Muguira, J.A. (2003). The Levels of Conceptual Interoperability Model (LCIM). Proceedings IEEE Fall Simulation Interoperability Workshop, IEEE CS Press
- Turnitsa, C.D. (2005). Extending the Levels of Conceptual Interoperability Model. Proceedings IEEE Summer Computer Simulation Conference, IEEE CS Press
- Alberts, D.S. and Hayes, R.E. (2003). Power to the Edge, Command and Control in the Information Age. Information Age Transformation Series, CCRP Press
- Tolk, A. (2003). Beyond Technical Interoperability - Introducing a Reference Model for Measures of Merit for Coalition Interoperability. Proceedings of the Command and Control Research and Technology Symposium (CCRTS), CCRP Press
- Page, E.H., Briggs, R., and Tufarolo, J.A. (2004). Toward a Family of Maturity Models for the Simulation Interconnection Problem. Proceedings of the Spring 2004 Simulation Interoperability Workshop, IEEE CS Press
- Wenguang Wang, Andreas Tolk, and Weiping Wang. 2009. The levels of conceptual interoperability model: applying systems engineering principles to M&S. In Proceedings of the 2009 Spring Simulation Multiconference (SpringSim '09). Society for Computer Simulation International, San Diego, CA, USA, , Article 168 , 9 pages.
- Tolk, A., L.J. Bair, and S.Y. Diallo (2013). Supporting Network Enabled Capability by extending the Levels of Conceptual Interoperability Model to an interoperability maturity model The Journal of Defense Modeling and Simulation: Applications, Methodology, Technology 10:145-160
- Tolk, A., S.Y. Diallo, H. Herencia-Zapana, and J.J. Padilla (2013). Reference modelling in support of M&S—foundations and applications. Journal of Simulation (2013) 7, 69–82. doi:10.1057/jos.2013.3
This information is based on Tolk A (2006) "What Comes After the Semantic Web - PADS Implications for the Dynamic Web," PADS, pp. 55-62, 20th Workshop on Principles of Advanced and Distributed Simulation (PADS'06), http://doi.ieeecomputersociety.org/10.1109/PADS.2006.39 and Tolk A, Diallo SY, Turnitsa CD, Winters LS (2006) "Composable M&S Web Services for Net-centric Applications," Journal for Defense Modeling & Simulation (JDMS), Volume 3 Number 1, pp. 27-44, January 2006