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The problem of designing multi-agent systems (MAS) is at the heart of many researches. This is an important issue that refers to a crucial question: how to link a global description of a task and agents whose behavior depends on a view that is necessarily partial and local in the same task.
In the literature, several researches have been made to describe MAS, among others (Brazier, Dunin-Keplicz, Jennings & Treur, 1997) (Caire, Coulier, Garijo, Gomez., Pavón., Leal & Massonet, 2002) (DeLoach,Wood & Sparkman,2001) (Demazeau,1995) (Ferber & Gutknecht, 1998) (Jennings & Wooldridge, 1998) (Fisher, 1994) (Lind, 2001) (Luck,Griffiths & d'Inverno, 1997) (Marik, Müller & Pechoucek, 2003). However, they lack of an efficient methodology enabling designers to build MAS by taking into account its functionalities.
The process of designing multi agent systems involves the use of a design methodology based on a specification model. In fact, in order to design a multi agent systems, many formalisms have been proposed such as Z-language (Regayeg, Kacem & Jmaiel, 2005), Maude (Mokhati, F., Boudiaf, N., Badri, M., & Badri, L. 2007), Logic (Lomuscio & Sergot, 2003), Recursive Petri Nets (RPN for short) (Seghrouchni & Haddad, 1996), Synchronized Petri Nets (SyPN for short) (Kouah, Saïdouni & Ilié, 2013) (Kouah & Saïdouni, 2014). The common feature of these models is that they are based on the interleaving semantics which considers that actions are atomic and with null duration. This semantics interprets the parallel execution of actions by their interleaved ones. Consequently, the interleaving semantics is not appropriate for design approaches based on action refinement.
The consideration of a non-atomicity of actions hypothesis has been deeply studied in the literature through the definition of several semantics supporting the concept of action refinement (Aceto & Hennessy, 1991) (Andrews, Groote & Middelburg, 1993) (Best, Devillers, Kiehn & Pomello, 1991) (Boudol& Castellani, 1988) (Courtiat & Saïdouni, 1994) (Darondeau & Degano, 1993) (Degano & Gorrieri, 1991) (Devillers, 1992) (Hogrefe & Leue, 1994) (Janssen, Poel & Zwiers, 1991) (Saïdouni, 1996) (Van Glabbeek, 1990) (Saidouni, Belala & Bouneb, 2008) (Saïdouni, Belala & Bouneb, 2009). Considering such semantics allows a hierarchical design of the systems by refining actions (actions are seen as abstract processes). Another interest of these semantics is the characterization of parallel executions of non-instantaneous actions.