The ROMANS Action designs and implements systems for representing, storing, organizing and inferring scientific and technical knowledge described using both symbolics and numerics.

These knowledge-based systems rely on an explicit separation between the described knowledge and inference mechanisms in charge of exploiting this knowledge. This distinction enables, on the one hand, to make knowledge evolve more easily and, one the other hand, to trace the reasoning mechanism until the solution so that explanations can be given. These systems gather and structure knowledge of different kinds: descriptive knowledge (about the entities and concepts of the application domain), functional knowledge (about the behavior of these entities) and prescriptive knowledge (about the means to complete and characterize these descriptions). 

In this context, the research themes of the ROMANS Action concern both the design and the reuse of knowledge models well adapted to scientific and technical domains, as well as the study of the interactions with these models during their design and their use. In order to reduce the design cost of these models and to facilitate the reuse of existing models, it is our opinion that the numerical knowledge which usually composes the models has to be associated  with symbolic knowledge which will be in charge of informing about the context of use, the domain of validity, the modeling choices, or the accuracy of results. Classically, this symbolic knowledge can only be found, at best, in the specifications and documentations concerning the model and is rarely part of the model. This way, symbolic knowledge can be seen as the flesh of the model. It permits to reuse the model either for building a more complex model including it, or to use it in different conditions.

The approach chosen by the ROMANS Action in the development of knowledge representation tools supporting the coupling of numerics and symbolics is based on the integration of three paradigms for knowledge modeling and exploitation:

1. Object-Based Knowledge Representation
2. Relations
3. Algebraic Modeling Language

Object-Based Knowledge Representation: In this field of Knowledge Representation, the object is the central notion. Knowledge is here expressed by means of two kinds of objects: classes (which describe families of individuals) and instances (which describe the individuals). Classes are organized in hierarchies by a specialization relation upon which a inheritance mechanism is settled. This mechanism allows a more specific sub-class to inherit from all the properties of it super-class it does not redefine. Inference mechanisms are also proposed in order to complete knowledge: default value, classification, and procedural attachment. Classification is a central mechanism which determines for an instance the set of sub-classes of its current class to which it also could be linked. Procedural attachment consists in specifying a peace of code to be executed in order to obtain  the value of a property in a class, if needed. Through this approach, we extend the studies previously achieved in the Sherpa project from where the ROMANS Action stems.

Relations : In this approach, relations or associations between objects are considered as distinct representation entities  (like it is the case in entity/relationship models or in object-oriented design and conception methods), and are given in models a place as important as classes have. By doing so, it is possible to give associations a specific semantics and to handle in quite an easy way relations with an arity greater than two. Like classes, associations can be organized in hierarchies of specialization along which an inheritance mechanisms is in charge to broadcast knowledge from  super  to sub-classes. Thus, by distinguishing between classes and associations in models, the ROMANS Action brings closer object-based knowledge representation systems and  modeling methods used in software engineering, such as UML.

Algebraic Modeling Language: The goal here is to add to the  two central knowledge representation entities (i.e classes and associations) a language in charge of expressing operational knowledge (algebraic definitions of property values, constraints) as well as queries. First introduced in Operations Research, algebraic modeling languages enable the description of models or systems of equations and/or constraints in a formalism close to mathematical notations. In particular, they permit the use of indexed variables and  expressions, of quantifiers and iterated operators, in order to build expressions such as: 

Concerning algebraic modeling languages, the Romans Action has got a first experience through the design and development of the AMIA system, an environment for knowledge-based discrete-time modeling and simulation. 
Thus, coupled with algorithms for solving systems of equations and for constraint propagation, this unifying formalism opens now knowledge representation systems to simulation.

The integration of these three paradigms constitutes the approach chosen by the ROMANS Action to reach the fixed objective. This approach is tested and validated within the AROM platform.