## Section: Scientific Foundations

### Transformations and properties

A transformation ( ) is an algorithmic manner to generate a representation ((o) ) from another one (o ), not necessarily in the same language. We focus on transformations made by composition of more elementary transformations for which we only know the input, output and assumed properties. These transformations may have been generated from an alignment or by any other means.

A transformation system is characterised by a set of elementary transformations and a set of composition operators. A transformation flow is the composition of elementary transformation instances whose input/output are connected by channels. A transformation flow is itself a transformation.

The design of information systems like transformation flows requires the ability to express such flows and to determine their properties. A property is a boolean predicate about the transformation, e.g., "preserving information" is such a predicate - it is true or false of a transformation - which is satisfied if there exists an algorithmic mean to recover o from (o) .

We consider more closely preservation properties that can allow the preservation (or anti-preservation) of an order relation between the source representations and the target representations. For instance, one can identify:

• Syntactic properties: based on the organisation of syntactic elements, like the completion ((o)o , in which denotes structural subsumption between representations);

• Semantic properties: based on the concepts of model and consequence, like consequence preservation ( );

• Semiotic properties: based on the interpretation of the manipulated objects as signs, like interpretation preservation (let be the interpretation rules and L, i be the interpretation of individual i , ).

Our goal is to study transformations based on transformation properties rather than on representations or transformation structures. This does not deal only with semantics but considers various properties, e.g., content or structure preservation, traceability, and confidentiality. However, we more specifically address semantic properties. We also consider properties of transformation systems (given a transformation system, is information preservation decidable and at what cost?). We try to characterise, given a particular type of property, which transformations leave them invariant and what is the action of composition operators.

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