Process Specification Language (PSL)bbs.w3china.org/dragonstar/PDF-Notes/WS08.pdf · Web Services:...
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Process Specification Language (PSL)
Transcript of Process Specification Language (PSL)bbs.w3china.org/dragonstar/PDF-Notes/WS08.pdf · Web Services:...
Proc
ess
Spec
ifica
tion
Lang
uage
(PS
L)
Web
Ser
vice
s: P
SL
2
PSL:
Pro
cess
Spe
cifi
cati
on L
angu
age
A st
anda
rd d
evel
oped
by
NIS
TRep
rese
ntin
g m
anuf
actu
ring
proc
esse
sPr
oces
s as
dat
aSe
man
tics
Aim
s at
inte
rope
rabi
lity
n2tr
ansl
ator
s 2n
tran
slat
ors
Web
Ser
vice
s: P
SL
3
How
Doe
s PS
LW
ork?
Web
Ser
vice
s: P
SL
4
Proc
ess
Ont
olog
y
An o
ntol
ogy
is a
set
of
logi
c se
nten
ces:
Fund
amen
tal t
heor
ies
Def
initi
ons
over
the
the
orie
s
A pr
oces
s on
tolo
gy n
eeds
:La
ngua
ge –
synt
axM
odel
the
ory
–m
eani
ng o
f th
e sy
ntax
Proo
f th
eory
–ax
iom
s to
tai
lor
to t
he s
peci
fics
of
proc
esse
s
Web
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vice
s: P
SL
5
PSL
Ont
olog
y
PSL
core
: in
tuiti
ve s
eman
tic p
rimiti
ves
that
is a
dequ
ate
for
desc
ribin
g th
e fu
ndam
enta
l con
cept
s of
m
anuf
actu
ring
proc
esse
sTh
ree
fam
ilies
of
exte
nsio
ns:
oute
r co
re, g
ener
ic
activ
ities
, and
sch
edul
esO
uter
cor
e: s
till v
ery
gene
ral
Suba
ctiv
ity, a
ctiv
ity-o
ccur
renc
e, s
tate
Gen
eric
act
iviti
es:
proc
ess
mod
elin
g an
d or
derin
gSc
hedu
les:
mot
ivat
ed f
rom
a p
ilot
impl
emen
tatio
n
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vice
s: P
SL
6
PSL
Sem
anti
c A
rchi
tect
ure
PSL
core
(+fu
ndam
enta
l the
ory)
Exte
nsio
ns
Web
Ser
vice
s: P
SL
7
Mod
els
for
Gene
ric
Act
ivit
ies
and
Ord
erin
g
Ord
erin
gRe
latio
nsN
on-D
eter
.A
ctiv
ities
Com
plex
Se
quen
ce
Junc
tions
Dur
atio
n
Act
iviti
es&
Dur
atio
n
Tem
pora
lO
rder
ing
Reas
onin
g ab
out S
tate
Inte
rval
Acv
ititie
s
PSL
core
(+fu
ndam
enta
l the
ory)
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vice
s: P
SL
8
Elem
ents
of
PSL
A pr
oces
s is
one
or
mor
e ac
tiviti
esth
at o
ccur
ove
r a
a pe
riod
of t
ime
in w
hich
obj
ects
part
icip
ate
Four
(di
sjoi
nt)
clas
ses/
conc
epts
:Ac
tivity
—a
type
of
actio
nAc
tivity
-occ
urre
nce—
an e
vent
or
actio
n th
at t
akes
pl
ace
at a
spe
cific
pla
ce a
nd t
ime
Tim
epoi
nt—
a tim
e in
stan
tO
bjec
t—
anyt
hing
but
not
a t
imep
oint
nor
an a
ctiv
ity
Obj
ect
Activ
ityTi
me
PSL
Web
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vice
s: P
SL
9
Ther
e ar
e fo
ur k
inds
of
entit
ies
requ
ired
for
reas
onin
g ab
out
proc
esse
s –
activ
ities
, act
ivity
occ
urre
nces
, tim
epoi
nts,
and
obj
ects
Activ
ities
may
hav
e m
ultip
le o
ccur
renc
es, o
r th
ere
may
ex
ist
activ
ities
tha
t do
not
occ
ur a
t al
l
Tim
epoi
nts
are
linea
rly o
rder
ed, f
orw
ards
into
the
fu
ture
, and
bac
kwar
ds in
to t
he p
ast
Activ
ity o
ccur
renc
es a
nd o
bjec
ts a
re a
ssoc
iate
d w
ith
uniq
ue t
imep
oint
sth
at m
ark
the
begi
n an
d en
d of
the
oc
curr
ence
or
obje
ct
PSL
Core
Web
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vice
s: P
SL
10
PSL
Form
alis
m
Base
d on
situ
atio
n ca
lcul
usfir
st-o
rder
logi
c pl
us t
ime
Prov
ides
a w
ay t
o re
pres
ent
proc
ess
info
rmat
ion,
i.e.
, pr
oces
ses
as d
ata
Sim
ilar
to “
proc
ess
tabl
es”
and
“con
text
sw
itch”
in O
SEn
able
s an
alys
is a
nd o
ptim
izat
ion
of w
eb s
ervi
ce a
nd/o
r ex
ecut
ions
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vice
s: P
SL
11
Prim
itiv
es in
PSL
Core
: Cla
sses
Four
cla
sses
(se
ts):
Act
ivity
: re
usab
le b
ehav
iors
(e.
g., p
rogr
ams)
Act
ivity
occu
rren
ce:
spec
ific
inst
ance
s of
act
iviti
es,
uniq
uely
ass
ocia
ted
with
act
iviti
esTi
mep
oint
: tim
e in
stan
ts f
or o
bjec
ts a
nd a
ctiv
ity
occu
rren
ces
Obj
ect:
any
thin
g no
t ac
tiviti
es, a
ctiv
ity o
ccur
renc
es,
nor
timep
oint
sTr
eate
d as
una
ry r
elat
ions
Act
ivity
(x) m
eans
the
sta
tem
ent
“xis
an
activ
ity”
Den
oted
as
O,
A, A
o, a
nd T
, res
pect
ivel
y
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vice
s: P
SL
12
Prim
itiv
es in
PSL
Core
: Rel
atio
ns
Thre
e re
latio
ns (
pred
icat
es):
Part
icip
ates
In ⊆
O ×
A ×
TPa
rtic
ipat
esIn
(x, y
, z) :
xpl
ays
som
e ro
le in
an
occu
rren
ce o
f th
e ac
tivity
yat
the
tim
epoi
ntz
Befo
re ⊆
T ×
TBe
fore
(x, y
) : t
he t
imep
oint
xis
ear
lier
than
yin
the
lin
ear
orde
ring
over
tim
epoi
nts
Occ
urre
nceO
f ⊆A
o×
AO
ccur
renc
e Of(
x, y
) :x
is a
par
ticul
ar o
ccur
renc
e of
th
e ac
tivity
y
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vice
s: P
SL
13
Prim
itiv
es in
PSL
Core
: Fun
ctio
ns
Two
unar
y fu
nctio
ns:
Begi
nO
f :O
∪A
o→
TBe
gin
Of(
x) :
retu
rns
the
star
ting
time
of a
n ob
ject
xor
an
activ
ity o
ccur
renc
e x
End
Of :
O ∪
Ao
→T
End
Of(
x) :
retu
rns
the
end
time
of a
n ob
ject
xor
an
activ
ity o
ccur
renc
e x
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vice
s: P
SL
14
Prim
itiv
es in
PSL
Core
: Tim
epoi
ntCo
nsta
nts
Two
cons
tant
s:in
f+:
the
timep
oint
that
is a
fter
all
timep
oint
sin
f−:
the
timep
oint
that
is b
efor
e al
l tim
epoi
nts
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vice
s: P
SL
15
Prim
itiv
es in
PSL
Core
: The
Lan
guag
e
Rel
atio
nsU
nary
: A
(·),
Ao(
·), T
(·),
O(·
)Bi
nary
: B
efore
(·,·
), O
ccur
renc
eOf(
·,·)
, Te
rnar
y :
Part
icip
ates
In(·
,·,·
)Fu
nctio
ns :
Beg
inO
f (·)
, End
Of(
·)Co
nsta
nts
: in
f+, i
nf−
Web
Ser
vice
s: P
SL
16
An
Exam
ple
PSL
can
be u
sed
to r
epre
sent
wha
t ha
ppen
ed a
nd w
hat
is h
appe
ning
dur
ing
serv
ice
exec
utio
n
List
en
Add
2car
t
cart
My
Hea
rt W
ill G
o O
n
Joe
List
en
Back
To
Life
: :
1 2
4 6
7 8
Web
Ser
vice
s: P
SL
17
List
en Add
2car
t
cart
My
Hea
rt W
ill G
o O
n
Joe
List
en
Back
To
Life
: :
1 2
4 6
7 8H
eart
cart
LifeJoe
Obj
ect
Add
2car
tLi
sten
List
en
Add
2car
t1Li
sten
2Li
sten
1O
ccur
renc
eOf
Buy
Add
2car
tLi
sten
Act
ivity
Add
2car
t1Li
sten
2Li
sten
1A
oin
f−
inf+…321T
21
…1inf−Be
fore
……
…8
List
enJo
e7
List
enJo
e6
Add
2car
tJo
e5
Add
2car
tJo
e
2Li
sten
Joe
4A
dd2c
art
Joe
1Li
sten
JoePa
rtic
ipat
esIn
471
Add
2car
t1Li
sten
2Li
sten
1Be
gin
Of
682
Add
2car
t1Li
sten
2Li
sten
1En
dO
f
Web
Ser
vice
s: P
SL
18
Hea
rtca
rtLi
feJoe
Obj
ect
Add
2car
tLi
sten
List
en
Add
2car
t1Li
sten
2Li
sten
1O
ccur
renc
eOf
Buy
Add
2car
tLi
sten
Act
ivity
Add
2car
t1Li
sten
2Li
sten
1A
oin
f−
inf+…321T
21
…1inf−Be
fore
……
…8
List
enJo
e7
List
enJo
e6
Add
2car
tJo
e5
Add
2car
tJo
e
2Li
sten
Joe
4A
dd2c
art
Joe
1Li
sten
JoePa
rtic
ipat
esIn
471
Add
2car
t1Li
sten
2Li
sten
1Be
gin
Of
682
Add
2car
t1Li
sten
2Li
sten
1En
dO
f
SELE
CT
P.1
FRO
MPa
rtic
ipat
es_I
nP
WH
ERE
P.3=
4
SELE
CT
CO
UN
T(∗)
FRO
MPa
rtic
ipat
es_I
nP
WH
ERE
P.2=
“Lis
ten”
Web
Ser
vice
s: P
SL
19
Rela
tion
s an
d Fu
ncti
ons
in P
SL
Wha
t if
Befo
reha
s a
cycl
e?W
hat
if Be
fore
does
not
hav
e (2
,5)?
Wha
t if
the
begi
n tim
e is
late
r th
an t
he e
ndtim
e?W
hat
if so
me
valu
es o
ccur
in b
oth
Act
ivity
and
Act
ivity
Occ
urre
nce
?… So
lutio
n: d
efin
e ax
iom
sth
at a
re c
ondi
tions
to
be a
lway
s sa
tisfie
dby
the
rel
atio
ns a
nd f
unct
ions
The
cond
ition
s ca
n be
def
ined
in t
he L
ogic
41 …
121
41inf−Be
fore 475
Add
2car
t1Li
sten
2Li
sten
1Be
gin
Of
682
Add
2car
t1Li
sten
2Li
sten
1En
dO
f
Web
Ser
vice
s: P
SL
20
Axi
oms
for
PSL
Core
Axio
m 1
:Th
e Be
fore
rela
tion
only
hol
ds b
etw
een
timep
oint
s
Axio
m 2
:Th
e Be
fore
rela
tion
is a
tot
al o
rder
ing
Axio
m 3
:Th
e Be
fore
rela
tion
is ir
refle
xive
Axio
m 4
:Th
e Be
fore
rela
tion
is t
rans
itive
Axio
m 5
:Th
e tim
epoi
ntinf-
is b
efor
e al
l oth
er t
imep
oint
s
Axio
m 6
:Ev
ery
othe
r tim
epoi
ntis
bef
ore inf+
Axio
m 7
: G
iven
any
tim
epoi
ntto
ther
tha
n inf-
, the
re is
a
timep
oint
betw
een inf-
and
tAx
iom
8:
Giv
en a
ny t
imep
oint
toth
er t
han inf+
, the
re is
a
timep
oint
betw
een
tand
inf+
Web
Ser
vice
s: P
SL
21
Axi
oms
for
PSL
Core
Axio
m 9
:Ev
eryt
hing
is e
ither
an
activ
ity, a
ctiv
ity o
ccur
renc
e,
timep
oint
, or
obje
ct
Axio
m 1
0:O
bjec
ts, a
ctiv
ities
, act
ivity
occ
urre
nces
, and
tim
epoi
nts
are
all d
istin
ct k
inds
of
thin
gs
Axio
m 1
1:Th
e oc
curr
ence
rel
atio
n on
ly h
olds
bet
wee
n ac
tiviti
es
and
activ
ity o
ccur
renc
es
Axio
m 1
2:Ev
ery
activ
ity o
ccur
renc
e is
the
occ
urre
nce
of s
ome
activ
ity
Axio
m 1
3:An
act
ivity
occ
urre
nce
is a
ssoc
iate
d w
ith a
uni
que
activ
ity
Web
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vice
s: P
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22
Axi
oms
for
PSL
Core
Axio
m 1
4:Th
e be
gin
and
end
of a
n ac
tivity
occ
urre
nce
or o
bjec
t ar
e tim
epoi
nts
Axio
m 1
5:Th
e be
gin
poin
t of
eve
ry a
ctiv
ity o
ccur
renc
e or
obj
ect
is b
efor
e or
equ
al t
o its
end
poi
nt
Axio
m 1
6:Th
e pa
rtic
ipat
esin
rela
tion
only
hol
ds b
etw
een
obje
cts,
ac
tiviti
es, a
nd t
imep
oint
s, r
espe
ctiv
ely
Axio
m 1
7:An
obj
ect
can
part
icip
ate
in a
n ac
tivity
onl
y at
tho
se
timep
oint
sat
whi
ch b
oth
the
obje
ct e
xist
s an
d th
e ac
tivity
is
occu
rrin
g
Web
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vice
s: P
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23
PSL
Core
: Uni
vers
e
(Axi
om 9
)Ev
eryt
hing
is e
ither
an
activ
ity, a
ctiv
ity
occu
rren
ce, t
imep
oint
, or
obje
ct∀
x(A
(x) ∨
Ao(
x) ∨
T(x
) ∨O
(x))
(Axi
om 1
0)O
bjec
ts, a
ctiv
ities
, act
ivity
occ
urre
nces
, and
tim
epoi
nts
are
all d
istin
ct k
inds
of
thin
gs
∀x
((A
(x) →
¬(A
o(x)
∨T
(x) ∨
O(x
))) ∧
(Ao(
x) →
¬(T
(x) ∨
O(x
))) ∧
(T(x
) →¬
O(x
)))
Web
Ser
vice
s: P
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24
PSL
Core
: Act
ivit
ies
(Axi
om 1
2)Ev
ery
activ
ity o
ccur
renc
e is
the
occ
urre
nce
of s
ome
activ
ity∀
x(A
o(x)
→∃y
A(y
) ∧O
ccur
renc
e Of(
x, y
))
(Axi
om 1
4)Th
e be
gin
and
end
of a
n ac
tivity
occ
urre
nce
or o
bjec
t ar
e tim
epoi
nts
∀x∀
y(O
ccur
renc
e Of(
x, y
) ∨O
(x) →
T(B
egin
Of(
x)) ∧
T(E
ndO
f(x)
) )
(Axi
om 1
3)An
act
ivity
occ
urre
nce
is a
ssoc
iate
d w
ith a
un
ique
act
ivity
∀x∀
y∀z
(Occ
urre
nce O
f(x,
y) ∧
Occ
urre
nceO
f(x,
z)
→y
= z
)
Web
Ser
vice
s: P
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25
PSL
Core
: Tim
e In
stan
ts(A
xiom
5)
The
timep
oint
inf−
is b
efor
e al
l oth
er
timep
oint
s∀
x(T
(x) ∧
¬x
= in
f−→
Befo
re(in
f−, x
))(A
xiom
6)
Ever
y ot
her
timep
oint
is b
efor
e in
f+∀
x(T
(x) ∧
¬x
= in
f+→
Befo
re(x
,inf
+))
(Axi
om 7
)G
iven
any
tim
epoi
ntto
ther
tha
n in
f−, t
here
is
a t
imep
oint
betw
een
inf−
and
t∀
x(T
(x) ∧
¬x
= in
f−→
∃yBe
twee
n(in
f−,
y, x
))
Betw
een
(x, y
, z) ≡
Befo
re(x
, y) ∧
Befo
re(y
, z)
(Axi
om 8
) G
iven
any
tim
epoi
ntto
ther
tha
n in
f+, t
here
is
a t
imep
oint
betw
een
tand
inf+
∀x
(T(x
) ∧¬
x=
inf+
→∃y
Betw
een
(x, y
,inf
+))
Web
Ser
vice
s: P
SL
26
PSL
Core
: Rel
atio
n Be
fore
(Axi
om 1
)Th
e Be
fore
rela
tion
only
hol
ds b
etw
een
timep
oint
s
(Axi
om 2
)Th
e Be
fore
rela
tion
is a
tot
al o
rder
ing
(Axi
om 3
)Th
e Be
fore
rela
tion
is ir
refle
xive
(Axi
om 4
)Th
e Be
fore
rela
tion
is t
rans
itive
Web
Ser
vice
s: P
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27
PSL
Core
: Rel
atio
n O
ccur
renc
eOf
(Axi
om 1
1)Th
e O
ccur
renc
ere
latio
n on
ly h
olds
bet
wee
n ac
tiviti
es a
nd a
ctiv
ity o
ccur
renc
es
(Axi
om 1
2)Ev
ery
activ
ity o
ccur
renc
e is
the
occ
urre
nce
of s
ome
activ
ity
(Axi
om 1
7)An
obj
ect
can
part
icip
ate
in a
n ac
tivity
onl
y at
tho
se t
imep
oint
sat
whi
ch b
oth
the
obje
ct e
xist
s an
d th
e ac
tivity
is o
ccur
ring
Web
Ser
vice
s: P
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28
PSL
Core
: Rel
atio
n Pa
rtic
ipat
esIn
(Axi
om 1
6)Th
e pa
rtic
ipat
esin
rela
tion
only
hol
ds
betw
een
obje
cts,
act
iviti
es, a
nd t
imep
oint
s, r
espe
ctiv
ely
(Axi
om 1
7)An
obj
ect
can
part
icip
ate
in a
n ac
tivity
onl
y at
tho
se t
imep
oint
sat
whi
ch b
oth
the
obje
ct e
xist
s an
d th
e ac
tivity
is o
ccur
ring
Web
Ser
vice
s: P
SL
29
PSL
Core
: Fun
ctio
ns B
egin
Of
and
End
Of
(Axi
om 1
4)Th
e be
gin
and
end
of a
n ac
tivity
occ
urre
nce
or o
bjec
t ar
e tim
epoi
nts
∀x∀
y(O
ccur
renc
eOf(
x, y
) ∨O
(x) →
T(B
egin
Of(
x)) ∧
T(E
ndO
f(x)
) )
(Axi
om 1
5)Th
e be
gin
poin
t of
eve
ry a
ctiv
ity o
ccur
renc
e or
obj
ect
is b
efor
e or
equ
al t
o its
end
poi
nt
Web
Ser
vice
s: P
SL
30
PSL
Core
: Sup
port
ing
Rela
tion
s
Betw
een
(x, y
, z) ≡
Befo
re(x
, y) ∧
Befo
re(y
, z)
Befo
reEq
(x, y
) ≡Be
fore
(x, y
) ∨x
= y
Betw
eenE
q(x,
y, z
) ≡Be
fore
Eq(x
, y) ∧
Befo
reEq
(y, z
)
Exist
sAt(
x, y
) ≡Be
twee
nEq(
Begi
nO
f(x)
, y, E
ndO
f(x)
)
IsO
ccur
ring
At(
x, y
) ≡∃z
Occ
urre
nceO
f (z,
x) ∧
Betw
eenE
q(Be
gin
Of(
z), y
, End
Of(
z))
Web
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vice
s: P
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31
Sum
mar
y of
PSL
Core
The
core
the
ory
is v
ery
limite
dN
o co
mpo
sitio
nN
o co
ncur
renc
y
PSL
oute
r co
re a
ttem
pts
to a
ddre
ss t
his
issu
e w
ith s
ix
exte
nsio
ns:
Suba
ctiv
ity
Occ
urre
nce
tree
s D
iscr
ete
stat
esAt
omic
act
iviti
esCo
mpl
ex a
ctiv
ities
Activ
ity o
ccur
renc
e
Web
Ser
vice
s: P
SL
32
Furt
her
Exte
nsio
ns
PSL
core
(+fu
ndam
enta
l the
ory)
PSL
Out
er C
ore
Web
Ser
vice
?
Web
Ser
vice
s: P
SL
33
PSL
Out
er C
ore
PSL
core
Occ
urre
nce
Tree
Suba
ctiv
ityAto
mic
Act
ivity
Com
plex
Act
ivity
Act
ivity
Occ
urre
nce
Dis
cret
e St
ate
Web
Ser
vice
s: P
SL
34
Suba
ctiv
ity
Exte
nsio
n
Expr
ess
the
logi
calr
elat
ions
hips
of
“com
posi
tion”
But
not
abou
t “h
ow”
The
com
posi
tion
rela
tion
is a
dis
cret
e pa
rtia
l ord
erin
g,
in w
hich
prim
itive
act
iviti
es a
re t
he m
inim
al e
lem
ents
New
rel
atio
n: S
ubac
tivity
(x, y
)x
is a
sub
activ
ity o
f y
New
cla
ss:
Prim
itive
(x)
x is
a p
rimiti
ve a
ctiv
ity
Can
be d
efin
ed u
sing
Suba
ctiv
ity :
Prim
itive
(x) ≡
∀y
(Sub
activ
ity(y
, x)→
y =
x)
Web
Ser
vice
s: P
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35
Axi
oms
Axio
m 1
: Su
bact
ivity
is a
rel
atio
n ov
er a
ctiv
ities
Ax
iom
2:
The
suba
ctiv
ity r
elat
ion
is r
efle
xive
Ax
iom
3:
The
suba
ctiv
ity r
elat
ion
is a
nti-s
ymm
etric
Axio
m 4
: Th
e su
bact
ivity
rel
atio
n is
tra
nsiti
veAx
iom
5:
The
suba
ctiv
ity r
elat
ion
is a
dis
cret
e or
derin
g,
so e
very
act
ivity
has
an
upw
ards
suc
cess
or in
the
or
derin
gAx
iom
6:
The
suba
ctiv
ity r
elat
ion
is a
dis
cret
e or
derin
g,
so e
very
act
ivity
has
a d
ownw
ards
suc
cess
or in
the
or
derin
g
Web
Ser
vice
s: P
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36
PSL
Out
er C
ore
PSL
core
Occ
urre
nce
Tree
Suba
ctiv
ityAto
mic
Act
ivity
Com
plex
Act
ivity
Act
ivity
Occ
urre
nce
Dis
cret
e St
ate
Web
Ser
vice
s: P
SL
37
Occ
urre
nce
Tree
Ext
ensi
on
Capt
ure
the
set
of a
ll di
scre
te s
eque
nces
of
activ
ity
occu
rren
ces
An o
ccur
renc
e tr
eeis
a p
artia
lly o
rder
ed s
et o
f ac
tivity
oc
curr
ence
sfo
r a
give
n se
t of
act
iviti
es, a
ll di
scre
te s
eque
nces
of
thei
r oc
curr
ence
s ar
e br
anch
es o
f th
e tr
ee
a 1
b 1c 1
a 2e 1
d 1b 2
c 2
a 1b 1
a 2. .
.a 1
c 1d 1
. . .
Web
Ser
vice
s: P
SL
38
Occ
urre
nce
Tree
Ther
e ar
e co
nstr
aint
s on
whi
ch a
ctiv
ities
can
pos
sibl
y oc
cur
in s
ome
dom
ain
Ever
y se
quen
ce o
f ac
tivity
occ
urre
nces
has
an
initi
al
occu
rren
ce (
whi
ch is
the
roo
t of
an
occu
rren
ce t
ree)
The
orde
ring
of a
ctiv
ity o
ccur
renc
es in
a b
ranc
h of
an
occu
rren
ce t
ree
resp
ects
the
tem
pora
l ord
erin
g
a 1
b 1c 1
a 2e 1
d 1b 2
c 2
Web
Ser
vice
s: P
SL
39
Conc
epts
Rel
atio
ns:
Earli
er, I
nitia
l, Le
gal
Func
tions
: Su
cces
sor
a 1
b 1c 1
a 2e 1
d 1b 2
c 2
Initi
al(a1)
Earli
er(a1,
c 1)
Earli
er(a1,
c 2)
Succ
esso
r(β,
c 1)
Occ
urre
nceo
f(b 2
,β)
Web
Ser
vice
s: P
SL
40
Sem
anti
cs o
f O
ccur
renc
e Tr
eeEa
rlier
(x, y
):
two
activ
ity o
ccur
renc
es x
and
yar
e on
the
sam
e br
anch
of
the
tree
and
xis
clo
ser
to t
he r
oot
than
yIn
itial
(x)
:th
e ac
tivity
occ
urre
nce
xis
a r
oot
of t
he o
ccur
renc
e tr
eeLe
gal(
x):
the
activ
ity o
ccur
renc
e x
is a
n el
emen
t of
the
lega
l oc
curr
ence
tre
eSu
cces
sor
(x, y
) :re
turn
s th
e oc
curr
ence
of
activ
ity x
that
fol
low
s co
nsec
utiv
ely
afte
r th
e ac
tivity
occ
urre
nce
yin
the
oc
curr
ence
tre
e
Web
Ser
vice
s: P
SL
41
Axi
oms
Axio
m 1
: Th
e Ea
rlier
rela
tion
is r
estr
icte
d to
act
ivity
oc
curr
ence
sAx
iom
2:
Earli
eris
irre
flexi
veAx
iom
3:
Earli
eris
tra
nsiti
veAx
iom
4:
A br
anch
in t
he o
ccur
renc
e tr
ee is
tot
ally
or
dere
dAx
iom
5:
No
occu
rren
ce is
ear
lier
than
an
initi
al
occu
rren
ce
Web
Ser
vice
s: P
SL
42
Axi
oms
Axio
m 6
: Ev
ery
bran
ch o
f th
e oc
curr
ence
tre
e ha
s an
in
itial
occ
urre
nce
Axio
m 7
: Th
ere
is a
uni
que
initi
al o
ccur
renc
e fo
r ea
ch
activ
ity
Axio
m 8
: Th
e su
cces
sor
of a
n ac
tivity
occ
urre
nce
is a
n oc
curr
ence
of
the
activ
ity
Axio
m 9
: Ev
ery
non-
initi
al a
ctiv
ity o
ccur
renc
e is
the
su
cces
sor
of a
noth
er a
ctiv
ity o
ccur
renc
e Ax
iom
10:
An
occu
rren
ce x
is e
arlie
r th
an t
he s
ucce
ssor
oc
curr
ence
of
yif
and
only
if t
he o
ccur
renc
e y
is la
ter
than
x
Web
Ser
vice
s: P
SL
43
Axi
oms
Axio
m 1
1: T
he le
galr
elat
ion
rest
ricts
act
ivity
occ
urre
nces
Ax
iom
12:
If
an a
ctiv
ity o
ccur
renc
e is
lega
l, al
l ear
lier
activ
ity o
ccur
renc
es in
the
occ
urre
nce
tree
are
als
o le
gal
Axio
m 1
3: T
he e
nd o
f an
act
ivity
occ
urre
nce
is b
efor
e to
th
e be
gin
of t
he s
ucce
ssor
of
the
activ
ity o
ccur
renc
e
Web
Ser
vice
s: P
SL
44
Sem
anti
cs o
f O
ccur
renc
e Tr
eepo
ss(x
, y) :
the
activ
ity x
can
poss
ibly
occ
ur a
fter
the
act
ivity
oc
curr
ence
ypr
eced
es(x
, y) :
the
activ
ity o
ccur
renc
e x
is e
arlie
r th
an t
he a
ctiv
ity
occu
rren
ce y
in t
he o
ccur
renc
e tr
ee a
nd s
uch
that
all
activ
ity o
ccur
renc
es b
etw
een
them
cor
resp
ond
to
activ
ities
tha
t ar
e po
ssib
le
Web
Ser
vice
s: P
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45
PSL
Out
er C
ore
PSL
core
Occ
urre
nce
Tree
Suba
ctiv
ityAto
mic
Act
ivity
Com
plex
Act
ivity
Act
ivity
Occ
urre
nce
Dis
cret
e St
ate
Web
Ser
vice
s: P
SL
46
Theo
ry o
f D
iscr
ete
Stat
es
Capt
ure
the
basi
c in
tuiti
ons
abou
t st
ates
and
the
ir re
latio
nshi
p to
act
iviti
esSt
ate
is c
hang
ed b
y th
e oc
curr
ence
of
activ
ities
Stat
e ca
n on
ly b
e ch
ange
d by
the
occ
urre
nce
of
activ
ities
Stat
e do
es n
ot c
hang
e du
ring
the
occu
rren
ce o
f an
ac
tivity
in t
he o
ccur
renc
e tr
ee
Web
Ser
vice
s: P
SL
47
Sem
anti
cs o
f D
iscr
ete
Stat
esst
ate(
x):
xis
a m
embe
r of
the
set
of
stat
es in
the
uni
vers
e of
di
scou
rse
of t
he in
terp
reta
tion
Stat
es a
re a
sub
clas
s of
obj
ect
hold
s(x,
y):
the
stat
e x
is t
rue
afte
r th
e ac
tivity
occ
urre
nce
ypr
ior(
x,y)
:th
e st
ate
xis
tru
e pr
ior
to t
he a
ctiv
ity o
ccur
renc
e y
7 ax
iom
s
Web
Ser
vice
s: P
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48
Axi
oms
for
Dis
cret
e St
ates
Axio
m 1
: St
ates
are
obj
ects
Axio
ms
2, 3
: Th
e ho
lds
and
prio
rre
latio
ns a
re o
nly
betw
een
stat
es a
nd a
ctiv
ity o
ccur
renc
esAx
iom
4:
All i
nitia
l occ
urre
nces
agr
ee o
n th
e st
ates
tha
t ho
ld p
rior
to t
hem
Axio
m 5
: A
stat
e ho
lds
afte
r an
occ
urre
nce
if an
d on
ly if
it
hold
s pr
ior
to t
he s
ucce
ssor
occ
urre
nce
Axio
ms
6, 7
: If
a s
tate
hol
ds (
resp
. doe
s no
t ho
ld)
afte
r so
me
activ
ity o
ccur
renc
e, t
hen
ther
e ex
ists
an
earli
est
activ
ity o
ccur
renc
e al
ong
the
bran
ch w
here
the
sta
te
hold
s (r
esp.
doe
s no
t ho
ld)
Web
Ser
vice
s: P
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49
PSL
Out
er C
ore
PSL
core
Occ
urre
nce
Tree
Suba
ctiv
ityAto
mic
Act
ivity
Com
plex
Act
ivity
Act
ivity
Occ
urre
nce
Dis
cret
e St
ate
Web
Ser
vice
s: P
SL
50
Theo
ry o
f A
tom
ic A
ctiv
itie
s
Conc
urre
nt a
ggre
gatio
n of
prim
itive
act
iviti
es
Conc
urre
ncy
is r
epre
sent
ed b
y th
e oc
curr
ence
of
one
conc
urre
nt a
ctiv
ity r
athe
r th
an m
ultip
le c
oncu
rren
t oc
curr
ence
s Ev
ery
conc
urre
nt a
ctiv
ity is
equ
ival
ent
to t
he
com
posi
tion
of a
set
of
prim
itive
act
iviti
es
Web
Ser
vice
s: P
SL
51
Sem
anti
csat
omic
(x)
:x
is e
ither
prim
itive
or
the
conc
urre
nt s
uper
posi
tion
of a
se
t of
prim
itive
act
iviti
esco
nc(x
,y) :
retu
rns
the
atom
ic a
ctiv
ity t
hat
is t
he c
oncu
rren
t su
perp
ositi
on o
f th
e tw
o at
omic
act
iviti
es x
and
y
9 ax
iom
s
Web
Ser
vice
s: P
SL
52
Axi
oms
for
Ato
mic
Act
ivit
ies
Axio
m 1
: Pr
imiti
ve a
ctiv
ities
are
ato
mic
Axio
m 2
: Th
e fu
nctio
n co
ncis
idem
pote
ntAx
iom
3:
The
func
tion
conc
is c
omm
utat
ive
Axio
m 4
: Th
e fu
nctio
n co
ncis
ass
ocia
tive
Axio
m 5
: Th
e co
ncur
rent
agg
rega
tion
of a
tom
ic a
ctio
n is
an
atom
ic
actio
nAx
iom
6:
An a
tom
ic a
ctiv
ity x
is a
sub
activ
ity o
f an
ato
mic
act
ivity
yif
and
only
if y
is a
n id
empo
tent
for
xAx
iom
7:
An a
tom
ic a
ctio
n ha
s a
suba
ctiv
ity if
and
onl
y if
ther
eex
ists
ano
ther
ato
mic
act
ivity
whi
ch c
an b
e co
ncur
rent
ly
aggr
egat
edAx
iom
8:
The
sem
i-lat
tice
of a
tom
ic a
ctiv
ities
is d
istr
ibut
ive
Axio
m 9
: O
nly
atom
ic a
ctiv
ities
can
be
elem
ents
of
the
lega
l oc
curr
ence
tre
e
Web
Ser
vice
s: P
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53
PSL
Out
er C
ore
PSL
core
Occ
urre
nce
Tree
Suba
ctiv
ityAto
mic
Act
ivity
Com
plex
Act
ivity
Act
ivity
Occ
urre
nce
Dis
cret
e St
ate
Web
Ser
vice
s: P
SL
54
Theo
ry o
f Co
mpl
ex A
ctiv
itie
s
Rep
rese
ntin
g co
mpl
ex a
ctiv
ities
and
the
rel
atio
nshi
p be
twee
n oc
curr
ence
s of
an
activ
ity a
nd o
ccur
renc
es o
f its
sub
activ
ities
An a
ctiv
ity t
ree
cons
ists
of
all p
ossi
ble
sequ
ence
s of
at
omic
sub
activ
ity o
ccur
renc
es b
egin
ning
fro
m a
roo
t su
bact
ivity
occ
urre
nce
a 1
b 1c 1
a 2e 1
d 1b 2
c 2ε
σδ
σγβα
σσσSuba
ctiv
ity
Activ
ity t
ree
for
σ
Web
Ser
vice
s: P
SL
55
Act
ivit
y Tr
ees
Diff
eren
t su
bact
iviti
esm
ay o
ccur
on
diff
eren
t br
anch
es
of t
he a
ctiv
ity t
ree
An a
ctiv
ity w
ill in
gen
eral
hav
e m
ultip
le a
ctiv
ity t
rees
w
ithin
an
occu
rren
ce t
ree,
and
not
all
activ
ity t
rees
for
an
act
ivity
nee
d be
isom
orph
icN
ot e
very
occ
urre
nce
of a
sub
activ
ity is
a s
ubac
tivity
oc
curr
ence
. The
re m
ay b
e ot
her
exte
rnal
act
iviti
es t
hat
occu
r du
ring
an o
ccur
renc
e of
an
activ
ity
a 1
b 1c 1
a 2e 1
d 1b 2
c 2ε
σδ
σγβα
σσσSuba
ctiv
ity
Web
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vice
s: P
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56
Sem
anti
cs o
f Co
mpl
ex A
ctiv
itie
sm
inpr
eced
es(x
, y, z
):
xan
d y
are
suba
ctiv
ity o
ccur
renc
es in
the
act
ivity
tre
e fo
r z,
and
xpr
eced
es y
Any
occu
rren
ce o
f an
act
ivity
zco
rres
pond
s to
an
activ
ity t
ree.
The
act
ivity
occ
urre
nces
with
in t
his
tree
ar
e th
e su
bact
ivity
occ
urre
nces
of
the
occu
rren
ce o
f z
root
(x, y
):th
e ac
tivity
occ
urre
nce
xis
the
roo
t of
an
activ
ity t
ree
for
y
Web
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vice
s: P
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57
Sem
anti
cs o
f Co
mpl
ex A
ctiv
itie
sm
inpr
eced
es(x
, y, z
):
xan
d y
are
suba
ctiv
ity
occu
rren
ces
in t
he a
ctiv
ity t
ree
for
z, a
nd x
prec
edes
yro
ot(x
, y):
the
act
ivity
occ
urre
nce
xis
the
roo
t of
an
activ
ity t
ree
for
y
a 1
b 1c 1
a 2e 1
d 1b 2
c 2ε
σδ
σγβα
σσσSuba
ctiv
ity
min
prec
edes
(a1,
c 1, σ
)
min
prec
edes
(a1,
c 2, σ
)
root
(a1,
σ)
Web
Ser
vice
s: P
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58
Nod
es in
An
Act
ivit
y Tr
ee
Axio
ms
1-2:
Occ
urre
nces
in t
he a
ctiv
ity t
ree
for
an a
ctiv
ity
corr
espo
nd t
o at
omic
sub
activ
ity o
ccur
renc
es o
f th
e ac
tivity
Axio
m 3
: Roo
t oc
curr
ence
s in
the
act
ivity
tre
e co
rres
pond
to
ato
mic
sub
activ
ity o
ccur
renc
es o
f th
e ac
tivity
a 1
b 1c 1
a 2e 1
d 1b 2
c 2min
prec
edes
(c1,
c 2, σ
)
root
(a1,
σ)
Web
Ser
vice
s: P
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59
The
Root
of
An
Act
ivit
y Tr
ee
Axio
m 4
: Al
l act
ivity
tre
es h
ave
a ro
ot s
ubac
tivity
oc
curr
ence
Axio
m 5
: N
o su
bact
ivity
occ
urre
nces
in a
n ac
tivity
tre
e oc
cur
earli
er t
han
the
root
sub
activ
ity o
ccur
renc
e
a 1
b 1c 1
a 2e 1
d 1b 2
c 2min
prec
edes
(c1,
c 2, σ
)
root
(a1,
σ)
Web
Ser
vice
s: P
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60
Act
ivit
y Tr
ee a
nd O
ccur
renc
e Tr
ee
Axio
m 6
: An
act
ivity
tre
e is
a s
ubtr
eeof
the
occ
urre
nce
tree
Axio
m 7
: Roo
t oc
curr
ence
s ar
e el
emen
ts o
f th
e oc
curr
ence
tr
ee
a 1
b 1c 1
a 2e 1
d 1b 2
c 2Ea
rlier
min
prec
edes
(a1,
c 1, σ
)
a 1
Web
Ser
vice
s: P
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61
Prop
erti
es o
f A
n A
ctiv
ity
Tree
Axio
m 8
: Ev
ery
atom
ic a
ctiv
ity o
ccur
renc
e is
an
activ
ity
tree
con
tain
ing
only
one
occ
urre
nce
Axio
m 9
: Ac
tivity
tre
es a
re d
iscr
ete
Axio
m 1
0 &
11:
Sub
activ
ity o
ccur
renc
es o
n th
e sa
me
bran
ch o
f th
e oc
curr
ence
tre
e ar
e on
the
sam
e br
anch
of
the
act
ivity
tre
eAx
iom
12:
The
act
ivity
tre
e fo
r a
com
plex
sub
activ
ity
occu
rren
ce is
a s
ubtr
eeof
the
act
ivity
tre
e fo
r th
e ac
tivity
occ
urre
nce
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Ser
vice
s: P
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62
Sem
anti
cs o
f Co
mpl
ex A
ctiv
itie
ssu
btre
e(x,
y)
:ev
ery
atom
ic s
ubac
tivity
occ
urre
nce
in t
he a
ctiv
ity t
ree
for
xis
an
elem
ent
of t
he a
ctiv
ity t
ree
for
ydo
(x, y
, z):
yis
the
roo
t of
an
activ
ity t
ree
for
x, z
is a
leaf
of
the
sam
e ac
tivity
tre
e, b
oth
activ
ity o
ccur
renc
es a
re
elem
ents
of
the
sam
e br
anch
of
the
activ
ity t
ree
leaf (
x, y
):th
e ac
tivity
occ
urre
nce
xis
the
leaf
of
an a
ctiv
ity t
ree
for
yne
xtsu
bocc
(x, y
, z):
xpr
eced
es y
in t
he t
ree
for
zan
d th
ere
does
not
exi
st a
su
bact
ivity
occ
urre
nce
betw
een
them
in t
he t
ree
Web
Ser
vice
s: P
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63
PSL
Out
er C
ore
PSL
core
Occ
urre
nce
Tree
Suba
ctiv
ityAto
mic
Act
ivity
Com
plex
Act
ivity
Act
ivity
Occ
urre
nce
Dis
cret
e St
ate
Web
Ser
vice
s: P
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64
Com
plex
Act
ivit
y O
ccur
renc
es
Com
plex
act
ivity
occ
urre
nces
cor
resp
ond
to a
ctiv
ity
tree
sN
ot e
lem
ents
of
the
lega
l occ
urre
nce
tree
This
the
ory
ensu
re t
hat
com
plex
act
ivity
occ
urre
nces
co
rres
pond
to
bran
ches
of
activ
ity t
rees
Each
com
plex
act
ivity
occ
urre
nce
has
a un
ique
at
omic
roo
t oc
curr
ence
Ea
ch f
inite
com
plex
act
ivity
occ
urre
nce
has
a un
ique
at
omic
leaf
occ
urre
nce
A su
bact
ivity
occ
urre
nce
corr
espo
nds
to a
sub
-bra
nch
of t
he b
ranc
h co
rres
pond
ing
to t
he c
ompl
ex a
ctiv
ity
occu
rren
ce
Web
Ser
vice
s: P
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65
Sem
anti
cs f
or A
ctiv
ity
Occ
urre
nces
suba
ctiv
ityoc
curr
ence
(x, y
):th
e br
anch
cor
resp
ondi
ng t
o th
e ac
tivity
occ
urre
nce
xis
a
subs
et o
f th
e br
anch
cor
resp
ondi
ng t
o ac
tivity
oc
curr
ence
y a 1
b 1c 1
a 2e 1
d 1b 2
c 2min
prec
edes
(c1,
c 2, σ
)
Suba
ctiv
ityoc
curr
ence
(c1,
s 1)
Occ
urre
nceo
f (s 1
, σ)
Web
Ser
vice
s: P
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66
Axi
oms
for
Com
plex
Act
ivit
y O
ccur
renc
esAx
iom
1:
Ther
e ex
ists
an
occu
rren
ce o
f an
act
ivity
xfo
r ev
ery
bran
ch o
f an
act
ivity
tre
e fo
r x.
All
atom
ic
suba
ctiv
ity o
ccur
renc
es o
n th
e br
anch
are
sub
activ
ity
occu
rren
ces
of t
he o
ccur
renc
e of
xAx
iom
2:
Ther
e ex
ists
an
occu
rren
ce o
f an
act
ivity
xfo
r ev
ery
bran
ch o
f an
act
ivity
tre
e fo
r x.
All
root
su
bact
ivity
occ
urre
nces
on
the
bran
ch a
re s
ubac
tivity
oc
curr
ence
s of
the
occ
urre
nce
of x
Web
Ser
vice
s: P
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67
Axi
oms
for
Com
plex
Act
ivit
y O
ccur
renc
es
Axio
m 3
: Al
l ato
mic
sub
activ
ityoc
curr
ence
s of
a c
ompl
ex
activ
ity o
ccur
renc
e ar
e el
emen
ts o
f th
e sa
me
bran
ch o
f th
e ac
tivity
tre
eAx
iom
4:
All e
lem
ents
of
the
sam
e br
anch
of
an a
ctiv
ity
tree
are
ato
mic
sub
activ
ityoc
curr
ence
s of
the
sam
e ac
tivity
occ
urre
nces
a 1
b 1c 1
a 2e 1
d 1b 2
c 2
Suba
ctiv
ityoc
curr
ence
(c1,
s 1)
Occ
urre
nceo
f (s 1
, σ)
Web
Ser
vice
s: P
SL
68
Axi
oms
for
Com
plex
Act
ivit
y O
ccur
renc
esAx
iom
5:
The
suba
ctiv
ityoc
curr
ence
rela
tion
pres
erve
s th
e su
bact
ivity
rel
atio
nAx
iom
6:
The
suba
ctiv
ityoc
curr
ence
rela
tion
is t
rans
itive
Suba
ctiv
ityoc
curr
ence
(c1,
s 1)
Occ
urre
nceo
f (s 1
, σ)
Occ
urre
nceo
f (c 1
, γ)
Suba
ctiv
ity(γ
, σ)
Web
Ser
vice
s: P
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69
Axi
oms
for
Com
plex
Act
ivit
y O
ccur
renc
es
Axio
m 7
: O
ccur
renc
es o
f su
bact
iviti
esar
e su
bact
ivity
oc
curr
ence
s if
the
occu
rren
ces
satis
fy b
ranc
h co
ntai
nmen
tAx
iom
8:
The
begi
n of
tim
epoi
ntfo
r a
com
plex
act
ivity
oc
curr
ence
is e
qual
to
the
begi
n of
tim
epoi
ntof
its
root
oc
curr
ence
Axio
m 9
: Th
e en
d of
tim
epoi
ntfo
r a
com
plex
act
ivity
oc
curr
ence
is e
qual
to
the
end
of t
imep
oint
of it
s le
af
occu
rren
ce
Web
Ser
vice
s: P
SL
70
Sem
anti
cs f
or A
ctiv
ity
Occ
urre
nces
mon
o (x
, y, z
):th
ere
is a
one
-to-
one
map
ping
bet
wee
n br
anch
es o
f an
ac
tivity
tre
e fo
r z
that
map
s th
e at
omic
sub
activ
ity
occu
rren
ce x
to t
he a
tom
ic s
ubac
tivity
occ
urre
nce
y
Web
Ser
vice
s: P
SL
71
Axi
oms
for
Com
plex
Act
ivit
y O
ccur
renc
es
Axio
m 1
0: T
he m
ono
rela
tion
is a
bra
nch
hom
omor
phis
mAx
iom
11:
If
an a
tom
ic s
ubac
tivity
occ
urre
nce
is m
appe
d in
a b
ranc
h ho
mom
orph
ism
, the
n th
ere
exis
ts a
noth
er
atom
ic s
ubac
tivity
occ
urre
nce
that
is m
ono
with
itAx
iom
12:
The
mon
o re
latio
n is
res
tric
ted
to o
ne-t
o-on
e ho
mom
orph
ism
sbe
twee
n di
ffer
ent
bran
ches
of
the
activ
ity t
ree
Web
Ser
vice
s: P
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72
PSL:
Sum
mar
y
PSL
core
+ o
uter
cor
e pr
ovid
es a
goo
d st
artin
g po
int
for
desc
ribin
g ac
tiviti
es a
nd e
xecu
tions
Capa
ble
of e
xpre
ssin
g FS
A ba
sed
form
alis
mFo
rmal
ism
with
wel
l def
ined
sem
antic
s ba
sed
on
situ
atio
n ca
lcul
us (
first
ord
er lo
gic
plus
tim
e)Li
near
tim
e lo
gic?
Mes
sage
s: n
eeds
add
ition
al t
heor
y (t
heor
ies)
