Representing and Reasoning with Modular Ontologies
and
{
}
•
•
•
•
packages
Let O = (S, A) be an ontology,
where S is the set of terms and A is the set of axioms over
terms in S. A package P = (ΔS , ΔA ) of the ontology O
is a fragment ofO, such that ΔS ⊆ S, ΔA ⊆ A. A term
t ∈ ΔS or an axiom t ∈ ΔA is called a
of P , denoted as t ∈ P . P is called the
of t, denoted
as HP(t) = P .
import
A term t that
appears in a package P , but has a different home package
Q is called a
in P . We say that P
t
Q : t and denote thisas Q →
− P . If any term de ned in Q
is imported into P , we say P imports Q, and denote it by
Q → P .
Pi
i
A local interpretation
of a package P is a pair IP =< ΔIP , (.)IP >, where
IP the local domain (set of all objects) and (.)IP is a function that maps each concept name C to C IP ⊆ ΔIP ; each
role name R to RIP ⊆ ΔIP × IP , and each individual
name i to iIP ∈ ΔIP .
projection
A global interpretation of a set of packages {Pi } with local interpretations
Ii = ΔIi , (.)Ii , i = 1, · · · m isIg = ΔIg , (.)Ig , where
Ii
and (.)Id maps each concept name C to
ΔIg = ∪m
i=1 Δ
Ig
Ig
C ⊆ Δ ; each role name R to RIg ⊆ ΔIg × ΔIg , and
each individual name i to iIg ∈ ΔIg .
Each Ii is called a
of Ig . We have: (1)ΔIi ⊆
Ig
Δ ; and (2) for each concept or role name t, tIi ⊆ tIg and
for each individual name t, tIi = tIg . Such a relation is
denoted as (.)Ii ⊆ (.)Ig .
Pi
Pj i = j i
j
O
x
C I1
PAnimal
1 : Dog 1 : Carnivore
1 : Carnivore ∀1 : eats.(1 : Animal)
PPet
2 : P etDog 1 : Dog 2 : P et
2 : P etDog ∃1 : eats.(2 : DogF ood)
1 : Dog 2 : P et
CI
ALC PC
x’
C I2
x ’’
∃1 : eats.(2 : DogF ood)
P
distributed
x
2
ALCP
ΔIi ∩ ΔIj = Ø
C I3
x1
x1
{A 1 ,B 1 }
x2
x3
{A 2 }
x1
{B 1 }
{A 1 }
x3
x2
{B 2 }
{A 2 }
x4
x4
x4
{A 3 ,B 3 }
{A 3 }
{B 3 }
The (conceptual)
global tableau
Local Reasoner
for package A
{B 2 }
Local Reasoner
for package B
The scope limitation modi er of a term
or an axiomtK in package K is a boolean function f (p, tK ),
where p is a URI of an entity, the entity identi ed by p can
access tK iff f (p, t) = true. We denote this by tK ∈f K.
ALCPC
ALC
scope limitation modi ers
x
C
•
•
C ∈ L(x) ALC
membership query message m(x, C)
HP(C)
L(x) = L(x) ∪
reporting message
x
x
Pi =
HP(C)
Li (x ) = Li (x ) ∪ {C}
x
Li (x ) = {C}
{C}
• ∀p, public(p, t) := true
t
• ∀p, private(p, t) := (t ∈ p)
t
scope policy
syntactic
semantic
total
partial
safe
total hiding
partial hiding
scopes
t
Dating Activity
t ∃hasActivity.Dating
t ∃hasActivity.Activity
t
t ∃hasActivity.Dating
concealable
safe
concealable reasoning
k
K
Kv
Kh
t ∈ Kh
f (k, t) = f alse
t ∈ K v
f (k, t ) = true
α
K
γ
α
Kv
Unknown
Yes
Unknown
α
α
CD
A P-DL ontology O
has complete knowledge about concept subsumption α : (i :
C j : D), if for every model {Ii } of O, C Ii ⊆ DIj ;
otherwise, it has incomplete knowledge about α.
1 : Carnivore
P etDog 1 : Animal
2 : P etDog 2 :
safe
scope policy
An
ontology
K = {Kv , Kh } is said to have a safe scope policy if
for any γ, γ ∈ Kh → Kv |= γ.
Kv |= Kh