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## Tight and Loose Semantics for Transformation Systems.

Orejas, Fernando;
Ehrig, Hartmut;
Pino, Elvira
In:
*LNCS 2267: Recent Trends in Algebraic Development Techniques*, pages 238-pp.
15th International Workshop, WADT 2001, Joint with the CoFI WG Meeting, Genova, Italy, April 1-3, 2001. Selected Papers / M. Cerioli, G. Reggio (Eds.) --- Springer Verlag,
2002.

Abstract:
When defining the requirements of a system, specification units typically
are partial or incomplete descriptions of a system component. In this
context, providing a complete description of a component means integrating
all the existing partial views for that component. However, in many cases
defining the semantics of this integration operation is not an easy task.
In particular, this is the case when the framework used at the
specification level is, in some sense, an ``operational" one (e.g. a
Petri net or a statechart). Moreover, this problem may also apply to the
definition of compositional semantics for modular constructs for this kind
of frameworks. In this paper, we study this problem, at a general level.
First, we define a general notion of framework whose semantics is defined
in terms of transformations over states represented as algebras and
characterize axiomatically the standard tight semantics. Then, inspired in
the double-pullback approach defined for graph transformation, we
axiomatically present a loose semantics for this class of transformation
systems, exploring their compositional properties. In addition, we see how
this approach may be applied to a number of formalisms.

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