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a formal notation and provide mechanisms for reasoning about the architecture. They focus on defining
architectural elements that can be combined to form a configuration. Few research efforts aim at truly
defining an ADL for MAS architectures. Nor do they address the design from logic specifications.
There are some formal languages proposed to address design issues of MASs. For example, Skw-
yRL-ADL (Faulkner & Kolp, 2002) is proposed as a BDI-MAS language to capture a “core” set of
structural and behavioral abstractions, including relationships and constraints that are fundamental to
the description of any BDI-MAS architecture. Kokar, Baclawski, and Eracar (1999) developed a control-
theory-based architecture for self-controlling software. However, none of them is a complete formal
system based on a finished computation model and serve as a language that encourages program design
by derivation or transformation.
Back to the classical program derivation area, the deductive-tableau method (Manna & Waldinger,
1992) synthesizes programs in a proof of the specification in the first-order logic. This method requires
the use of an intelligent strategy. Instead, the method presented in this paper constructs a program from
the process of semantic proving of the specification. RAPTS system is based on the SETL language
and derivation techniques have been developed based on ''generate-and-test'' algorithms (Kaldewaij, &
Schoenmakers, 1990; Smith & Lowry, 1990; Smith, 1990). In these techniques, parallelism, however, is
not addressed. In these methods, the most difficult task is the deductions in the logic level. We believe
that the difficulty can be relieved by using a high-level programming language such as γ-Calculus. By
bridging the logic specifications and operational specifications, we provide a design method in a multi-
phase transformational fashion, and we find that this method is effective in the design of the architectures
of multi-agent systems.
We would like to point out that using γ-Calculus to facilitate a system design method in the transfor-
mational style is congruent to the current research themes in γ-Calculus. As the inventors of γ-Calculus
stated: “Another direction is to propose a realistic higher-order chemical programming language based
on γ-Calculus. It would consist in defining the already mentioned syntactic sugar, a type system, as well
as expressive pattern and module languages.” (Banâtre, Fradet, & Radenac, 2004). In the author's point
of view, a realistic chemical programming language must be based on, directly or indirectly, a realistic
computational model. If the module language is to express construct details of higher-order chemical
programming languages, it should be implementable by a realistic computational model in order to
make the chemical programming language realistic. In addition, because the chemical programming
languages, including γ-Calculus, are primarily used as specification languages, it would be sensible
to address the practicability issue by providing a system that transforms Gamma specifications into
specifications in the module language.
Despite the promises this method has made, there are limitations that come from the traditional area
of automatic software design, specifically, from the use of logic specifications in MASs. Firstly, program
derivation from logic specification requires mastering logic proofing. Secondly, MASs are complex
systems with a lot of non-functional facets that cannot be directly captured by a functional program-
ming language such as γ-Calculus. On the theoretical study side, we are planning to apply γ-Calculus
to aspect-oriented programming to develop a framework for designing complex systems and use this
framework in MAS design. On the practical side, we are continuing to develop the module language
and implement it in common network programming environments.
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