A Formal Definition of
the Structural Semantics of
Domain-Specific Modeling Languages
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Tao Jiang Xin Wang Yong Yu
School of Mathematics and Computer Science School of Mathematics and Computer Science School of Software
Yunnan University of Nationalities Yunnan University of Nationalities Yunnan University
Kunming, P.R.China Kunming, P.R.China Kunming, P.R.China
jtzwy123@gmail.com wxkmyn@yahoo.com.cn yuy1219@163.com
Abstract—As a Model-Driven Development methodology (MDD)
for the specific domain, Domain-Specific Modeling (DSM) has
been widely and successfully used in system design and
analysis of specific areas. In spite of its general important, due
to informal definition of Domain-Specific Modeling Language
(DSMLs), the structural semantics of DSMLs cannot be strictly
described and the properties based on it also cannot be analyzed
and validated. In response, the paper proposes a formal
definition method of the structural semantics of DSMLs. Firstly,
a formal definition of domain indicating structural semantics of
DSMLs based on a
lgebra is presented to unify DSMLs and its
models in the domain, secondly, a mapping mechanism from
domain to the corresponding first-order logic system is
established to finish analysis and validation of properties of
domain such as consistency based on first-order logical
inference, based on this, the method of formalization and
consistency analysis and validation of structural semantics of
DSMLs based on first-order logic is presented, finally, the
formalization automatic mapping engine for model and
metamodel is introduced to show the application of formalization
of structural semantics in analysis and validation of properties
of models.
Keywords-Domain-Specific Modeling Language (DSMLs);
structural semantics; domain; domain mapping; first-order logic;
consistency
I. INTRODUCTION
As a Model-Driven Development methodology for the
specific domain, compared with the uniformity and
standardization of MDA [1], DSM [2] focuses on simplicity,
practicability and flexibility. As a modeling language for DSM,
DSMLs play an important role in software and system design
of specific areas.
Semantics of DSMLs can be grouped into structural
semantics [3] and behavioral semantics. The former concerns
static semantic constraints of relationship between modeling
elements based on abstract syntax, focusing on the static
structural properties; the latter concerns domain-specific
execution semantics, focusing on the dynamic behavior of the
model. Although structural semantics is very important,
research in structural semantics is not as extensive and deep as
behavioral semantics’s.
There are several problems that have not been solved well
for DSMLs, which include precise mathematical description,
independence of formal specification, and method of analysis
and validation of properties of models based on formalization.
In response, the paper proposes a formal definition method
of the structural semantics of DSMLs, based on this, method of
consistency analysis and validation of structural semantics of
DSMLs based on first-order logic is presented, and then the
corresponding formalization automatic mapping engine is
introduced to show the application of formalization.
II. R
ELATED WORKS
Our view of modeling differs from existing approaches
based on instance semantics [4]. While this top-down
approach is certainly reasonable, it makes it difficult to
disassociate models from the tools used to construct them.
Within the domain-specific language community, graph-
theoretic formalisms have received the most research attention
[5]. The majority of work focuses on model transformations
based on graph, but analysis and validation of properties of
models has not received the same attention. For example, Z [6]
or B [7] formalizations of UML could be a vehicle for
studying rich syntax, but automated analysis is less likely to be
found.
There are much typical work on formalization of modeling
language and validation, such as Andre’s formalization and
validation of UML class diagram based on ADT [8] and
Jackson.E.K’s formalization of DSMLs based on Horn logic
[9] and so on. Without considering automatic translation from
modeling language to the corresponding formal semantic
domain, these approaches have lower level of automated
analysis and validation.
III.
DOMAIN
A. Domain Definition
Intuitively, the domain of a DSML classifies all the
structurally legal (well-formed) models of that language. As
an example, consider the simplified metamodel describing
software architecture domain [10] in Figure 1. It describes
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Research supported by Yunnan Province, Applied Basic Research
Funded Projects (No. 2007F165M and No. 2009cd009)
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