SEKE 2012 Proceedings - Knowledge Systems Institute

will never be bound again. An undecided feature means that it is
currently not in the bound state, but still has the chance to be bound or
removed in later binding-times. In addition, we use “tailoring” to
denote the action of changing a feature’s binding state from undecided
to removed,use“binding” to denote the action of changing a feature’s
binding state from undecided to bound [11].
III.
SEMANTIC FEATURE MODELING
A. Description Logics
Description logics play an important role in Semantic Web since
they are the basis of the OWL 1 (Web ontology language). DLs offer
considerable expressive power, while reasoning is still decidable [12].
Concepts and roles are basic elements in DLs. The syntax and
semantics of a description logic are summarized in table 1, where C
and R are concepts and roles respectively.
TABLE I.
SYNTAX AND SEMANTICS FORDLS CONSTRUCTORS
Constructor Syntax Semantics
top concept
Δ I
bottom concept
concept negation ¬C Δ I \ C I
intersection CD C I D I
union CD C I D I
existential restriction R.C {aΔ I |b.(a,b) R I bC I }
value restriction R.C {aΔ I |b.(a,b) R I b C I }
set { a 1,…,a n }
A knowledge base K of DLs is constituted by the Tbox T and the
Abox A, denoted as K=(T, A), where the TBox introduces the
terminology (that is, concepts), as well as axioms like general concept
inclusion (GCI) and general role inclusion (GRI); while the ABox
contains assertions about named individuals in terms of this vocabulary
[12]. In TBox, there are concepts definition and axioms. Inclusion
axioms are of the form “C D”. GCI and GRI axioms express the
inclusion relation between concepts and roles respectively. For
example, axiom “Woman Person” indicates that Woman is a subconcept
of Person.
In ABox, each assertion states a fact. Assertions are divided into
two types: concept assertions (written as “C(x)”) and role assertions
(written as “r(x,y)”). For example, the assertion ”Woman(mary)” states
that mary is an individual (instance) that belongs to the concept Woman,
while “hasMother(peter, mary)” states that peter has mother mary.
B. Semantic feature modeling based on DLs
Our DLs-based feature model is composed of two levels: the
feature meta-model and models. The feature meta-model is domainindependent,
and defined in TBox. Feature models are domaindependent
and built in ABox. The domain engineers instantiate models
according to the meta-model.
1) Feature class
In DLs, the feature in meta-model is expressed as a concept, and its
definition is as follows. The concept Feature has role hasBindTime,
1 http://www.w3.org/TR/owl-guide/
whose range is the concept BindTime, and has role hasState, whose
range is the concept BindState.
Feature::= hasBindTime.BindTime hasState.BindState
The binding time consists of reuse-time, compile-time and run-time.
So the concept BindTime is defined by using the set constructor as:
BindTime ::= {reuse-time, compile-time, run-time}
The binding state consists of bound, removed, undecided and
conflict. A new state conflict is appended, which is used for consistency
verification (see conflict-rule in detail). So the concept BindState is
defined by using the set constructor as:
BindState ::= {bound, removed, undecided,conflict}
A dimension feature has variable behavior. The dimension feature
concept DimFeature is the sub-class of concept Feature, anditis
associated with some value features DimValue.
DimFeature::=Feature hasValue.DimValue
The concept DimValue is the sub-class of concept Feature too. The
sub-class relation is defined in GCI axiom as:
DimValue Feature.
Figure 2 depicts the concepts of feature meta-model.
BindState
hasState
DimFeature
Figure 2.
Feature
hasPart
hasValue
DimValue
concept role
sub-concept/role
BindTime
hasBindingTime
Semantic feature meta-model (concepts)
2) Relations between features
The features are organized in hierarchy. For example, the feature
graph-manipulate is composed of graph-add, graph-select and graphmove.
The whole-part relation is described as role hasPart, whose
domain and range are both Feature.
hasPart
require
mutex
hasValue
Feature
hasOptionalPart
hasMandatoryPart
hasPart
hasAlternativeValue
concept role
sub-concept/role
Figure3.
Semantic feature meta-model (roles and constraints).
There are two kinds of whole-part relations: optional and
mandatory. These two relations are defined as role hasOptionalPart
and hasMandatoryPart. Both of them are sub-role of hasPart, written
as following GRI axioms:
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