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UVL: Fea u e modelling wi h he Uni e sal Va iabili y Language✩
Da id Bena idesa,∗, Chico Sunde mannb, Ke in Feich inge c, José A. Galindoa, Rick Rabise d,
Thomas Thüme
aDepa men o Compu e Languages and Sys ems, I3US, Uni e sidad de Se illa, A . Reina Me cedes, Se ille, 41012, Spain
bIns i u e o So wa e Enginee ing and P og amming Languages, Uni e si y o Ulm, Albe -Eins ein-Allee 11, Ulm, 89069, Ge many
cCRC 1608, KASTEL – Dependabili y o So wa e-in ensi e Sys ems, Ka ls uhe Ins i u e o Technology, Am Fasanenga en 5, Ka ls uhe, 76131, Ge many
dCh is ian Dopple Labo a o y VaSiCS, LIT CPS Lab, Johannes Keple Uni e si y Linz, Al enbe ge S aße 69, Linz, 4040, Aus ia
eIns i u e o So wa e Enginee ing and Au omo i e In o ma ics, TU B aunschweig, Mühlenp o d s . 23, B aunschweig, 38106, Ge many
ARTICLE INFO
Da ase link:h ps://gi hub.com/Uni e sal-Va
iabili y-Language
Keywo ds:
Fea u e model
So wa e p oduc lines
Va iabili y
ABSTRACT
Fea u e modelling is a co ne s one o so wa e p oduc line enginee ing, p o iding a means o ep esen
so wa e a iabili y h ough ea u es and hei ela ionships. Since i s incep ion in 1990, ea u e modelling has
e ol ed h ough a ious ex ensions, and a e h ee decades o de elopmen , he e is a g owing consensus on
he need o a s anda dised ea u e modelling language. Despi e mul iple endea ou s o s anda dise a iabili y
modelling and he c ea ion o a ious ex ual languages, esea che s and p ac i ione s con inue o use hei
own app oaches, impeding e ec i e model sha ing. In 2018, a collabo a i e ini ia i e was launched by a g oup
o esea che s o de elop a no el ex ual language o ep esen ing ea u e models. This pape in oduces he
ou come o his e o : he Uni e sal Va iabili y Language (UVL), which is designed o be human- eadable
and se es as a pi o language o di e se so wa e enginee ing ools. The de elopmen o UVL d ew upon
communi y eedback and le e aged es ablished li e a u e in he ield o a iabili y modelling. The language is
s uc u ed in o h ee le els – Boolean, A i hme ic, and Type – and allows o language ex ensions o in oduce
addi ional cons uc s enhancing i s exp essi eness. UVL is in eg a ed in o a ious exis ing so wa e ools,
such as Fea u eIDE and lamapy, and is main ained by a conso ium o ins i u ions. All ools ha suppo
he language a e eleased in an open-sou ce o ma , complemen ed by dedica ed pa se implemen a ions o
Py hon and Ja a. Beyond academia, UVL has ound adop ion wi hin a ange o ins i u ions and companies. I
is en isaged ha UVL will become he language o choice in he u u e o a mul i ude o pu poses, including
knowledge sha ing, educa ional ins uc ion, and ool in eg a ion and in e ope abili y. We en ision UVL as a
pi o al solu ion, add essing he limi a ions o p io a emp s and os e ing collabo a ion and inno a ion in he
domain o so wa e p oduc line enginee ing.
1. In oduc ion
Fea u e modelling (Kang e al.,1990), a c ucial componen o
so wa e p oduc line enginee ing, is one o he mos used app oaches
o ep esen ing so wa e a iabili y h ough he abs ac ion o ea u es
and hei ela ionships (Apel e al.,2013). A ea u e is de ined as an
inc emen in p oduc unc ionali y (Ba o y,2005). A so wa e p oduc
line is modelled using aFea u e Model (FM) whe e ea u es a e a anged
in a ee-like s uc u e wi h addi ional c oss- ee cons ain s. FMswi h
housands o ea u es a e epo ed in he li e a u e (Be ge e al.,2013;
Küble e al.,2010;Oh e al.,2023;Sunde mann e al.,2023a). FMsa e
ep esen ed using ea u e diag ams bu can also be ep esen ed using
✩Edi o : Lau ence Duchien.
∗Co esponding au ho .
E-mail add esses: [email p o ec ed] (D. Bena ides), [email p o ec ed] (C. Sunde mann), [email p o ec ed] (K. Feich inge ),
[email p o ec ed] (J.A. Galindo), [email p o ec ed] (R. Rabise ), [email p o ec ed] (T. Thüm).
1h ps://mode a .gi hub.io/
di e en ex ual no a ions. Tex ual no a ions o FMs ange om XML–
based o ool-speci ic ones (Beek e al.,2019). O e he pas hi y
yea s, he e olu ion o ea u e modelling has gi en ise o di e se ex en-
sions and ep esen a ions (Eichelbe ge and Schmid,2015). Howe e ,
he absence o a s anda dised language has impeded e ec i e model
sha ing among esea che s and p ac i ione s, hinde ing p og ess in he
ield.
The yea 2018 ma ked a u ning poin as a collabo a i e ini ia i e
eme ged in ending o add ess he s anda disa ion challenge. This ini ia-
i e b ough oge he a g oup o esea che s om di e en uni e si ies
and esea ch cen es unde he umb ella o he MODEVAR1wo kshop
h ps://doi.o g/10.1016/j.jss.2024.112326
Recei ed 15 Ma ch 2024; Recei ed in e ised o m 1 Oc obe 2024; Accep ed 18 Decembe 2024
The Jou nal o Sys ems and So wa e 225 (2025) 112326
A ailable online 31 Janua y 2025
0164-1212/© 2025 The Au ho s. Published by Else ie Inc. This is an open access a icle unde he CC BY license ( h p://c ea i ecommons.o g/licenses/by/4.0/ ).
D. Bena ides e al.
se ies. This e o was dedica ed o c a ing a new ex ual and simple
language o FMs(Sunde mann e al.,2021a). The ou come o his
collec i e e o is he Uni e sal Va iabili y Language (UVL), a solu ion
designed o be bo h human- eadable and a pi o language o a a ie y
o so wa e enginee ing ools.
UVL’s de elopmen was no only in o med by communi y eed-
back bu also based on es ablished li e a u e in he ield o a i-
abili y modelling. The language is me iculously s uc u ed in o h ee
le els –Boolean,A i hme ic, and Type– allowing o a ep esen a ion
o di e en ea u es and a ying ypes o ela ionships. Fu he mo e,
UVL emb aces ex ensibili y, pe mi ing he in oduc ion o addi ional
cons uc s o enhance i s exp essi eness and accommoda e di e se
modelling needs.
UVL is in eg a ed in o exis ing a iabili y modelling ools, such as
Fea u eIDE (Käs ne e al.,2009) and lamapy (Galindo e al.,2023).
All he ools ha suppo he language a e a ailable in an open-sou ce
o ma , complemen ed by dedica ed pa se implemen a ions o Py hon
and Ja a using ANTLR (Pa ,2013),2which allows designing pa se s
o o he languages. This openness pai ed wi h a s uc u ed p ocess
o in ol e he communi y encou ages anspa ency, collabo a ion, and
wide adop ion.
We en ision an impac o UVL beyond academia, wi h ins i u ions
and companies ecognising i s po en ial. As an example, an impo e o
UVL models was al eady in eg a ed in a comme cial a ian manage-
men ool (Romano e al.,2022). UVL could be used as he language
o choice o a my iad o applica ions, including knowledge sha ing,
educa ional ins uc ion, and seamless ool in eg a ion. The b oad ision
o UVL is o o e come he limi a ions o p e ious s anda disa ion a -
emp s, such as he Common Va iabili y Language (CVL) (Haugen e al.,
2012) o ISO-26558 (ISO/IEC 26558:2017(en),2017). CVL (Haugen
e al.,2012) e en ually and un o una ely ailed o become a s an-
da d due o legal easons (Rabise ,2019) and ISO-26558 (ISO/IEC
26558:2017(en),2017) did no each he communi y and indus y.
Howe e , as UVL is communi y d i en, we en ision UVL o os e
collabo a ion and inno a ion wi hin he ealm o so wa e p oduc line
enginee ing.
In his pape , we del e in o he de elopmen , ea u es, and applica-
ions o UVL, o e ing a comp ehensi e explo a ion o i s signi icance
in he e ol ing landscape o a iabili y modelling. The con ibu ions o
he pape a e as ollows:
•A u o ial p esen a ion o UVL wi h a s able e sion o he lan-
guage (Sec ion 4) alida ed by di e en ounds o pa icipa ion
by he communi y.
•An ex ensible language design ha p o ides exp essi e language
ea u es while p ese ing simplici y wi h a co e language di ided
in o h ee majo le els and an op ion o decompose la ge ea u e
models.
•A o mal ex ual syn ax and seman ics o UVL (Sec ion 5).
•An open sou ce implemen a ion3o he language wi h pa se s o
Py hon and Ja a using ANTLR ha allows suppo ing new gene al
languages such as Ja aSc ip o C# in he u u e (Sec ion 6).
•A epo o ou expe iences ega ding he easibili y o he lan-
guage based on an in e ac i e and pa icipa ed p ocess wi h he
communi y (Sec ion 3) as well as he in eg a ion o UVL wi h
di e en ools (Sec ion 6).
Rega ding no el y since p e ious publica ions (Feich inge e al.,
2021;Munoz e al.,2023;Romano e al.,2022;Sunde mann e al.,
2021a,2023b), di e en changes ha e been in oduced and no s able
e sion o UVL was p esen ed so a . The o mal syn ax o his s able
e sion o UVL as well as he pa se implemen a ion suppo ing Ja a
2h ps://www.an l .o g/
3h ps://gi hub.com/Uni e sal-Va iabili y-Language
and Py hon a e new. Fu he mo e, his wo k includes he i s o mal
speci ica ion and discussion on he seman ics o UVL.
The emainde o he pape is s uc u ed as ollows. Sec ion 2
in oduced he necessa y backg ound on FMs. We ou line he de elop-
men p ocess and he design goals o UVL in Sec ion 3. A e ha , we
in oduce he UVL in a u o ial-like manne and discuss i s syn ax and
seman ics in Sec ions 4and 5, espec i ely. We p o ide an o e iew o
he cu en UVL implemen a ion and exis ing ools in eg a ing UVL in
Sec ion 6. We hen discuss challenges and nex s eps ega ding u he
adop ion o UVL in gene al and in indus y in pa icula in Sec ion 7.
Sec ion 8concludes he pape .
2. Fea u e models
The e m Fea u e Model (FM) was coined by Kang e al. in he well-
known FODA epo in 1990 (Kang e al.,1990). Since hen, ea u e
modelling has been one o he main opics o esea ch in so wa e
p oduc lines (Galindo e al.,2019;Fel e nig e al.,2024). The e a e
di e en FM dialec s (Schobbens e al.,2007), each wi h di e en ypes
o ea u es o ela ionships, bu also wi h di e en ex ual and g aphical
no a ions. In he ollowing, we e iew he mos used no a ions o hose
languages o pa e he way o he p esen a ion o UVL. In gene al, he e
is no FM language ha can be used in all scena ios and adap a ions a e
o en done o conc e e domains (Al é ez e al.,2019).
An FM is a ep esen a ion o all possible con igu a ions o a so wa e
p oduc line (Fel e nig e al.,2024). Gi en 𝑛 ea u es, wi h no es ic-
ions in he combina ions o hem, 2𝑛is he numbe o all po en ial
con igu a ions. Wi h a small 𝑛in e ms o hund eds, he numbe o
con igu a ions is al eady e y big. An FM es ic s his numbe using
ea u e ela ionships ha ep esen he cons ain s o he applica ion
domain. FMsa e also used in o he domains han so wa e p oduc
lines such as ideo encoding (Al é ez e al.,2019), biological in o -
ma ion (Cashman e al.,2019) o exam op ions (Le e al.,2021) jus
o men ion a ew examples. One o he mos used examples in he
communi y is he Linux ke nel FM, which has housands o modules
and con igu a ion op ions (Thüm,2020). Fu he mo e, la ge FMs om
o he domains, such as au omo i e, wi h housands o e en ens o
housands o ea u es we e epo ed in he li e a u e (Küble e al.,
2010;Knüppel e al.,2017;Sunde mann e al.,2023a;Be ge e al.,
2013). S ill, he e migh be e en la ge FMsused in p ac ice as FMs
om indus y a e ypically no made a ailable.
Fig. 1shows ou unning example o he FM o a ic i ious eShop
p oduc line. An FM is composed o a hie a chically a anged se o
ea u es (a.k.a. ea u e diag am o ea u e ee) and a se o c oss- ee
cons ain s. FMs ha do no ha e c oss- ee cons ain s can exis , bu
hey a e no e y common. Rela ionships among ea u es can be o
wo di e en ypes (Bena ides e al.,2010): 𝑖) ela ionships be ween a
pa en ea u e and i s child ea u es; 𝑖𝑖)c oss– ee cons ain s ha a e
ypically inclusion o exclusion s a emen s o mo e complex cons ain s
in he o m o a bi a y (p oposi ional) o mulae.
The e a e se e al FM dialec s (Schobbens e al.,2007). In his
sec ion, we will e isi he mos used ela ionships in he li e a u e
and also men ion some o he ex ensions p oposed. In basic FMs, he
ollowing ela ionships among ea u es a e de ined (Bena ides e al.,
2010):
•Manda o y. A child ea u e has amanda o y ela ionship wi h i s
pa en i he child is pa o all con igu a ions in which i s pa en
ea u e is included, e.g., any con igu a ion o an eShop has o
ha e aCa alogue.
•Op ional. A child ea u e has an op ional ela ionship wi h i s
pa en i he child can op ionally be pa o all con igu a ions in
which i s pa en ea u e is included, e.g., a con igu a ion o an
eShop can op ionally ha e SEO suppo .
The Jou nal o Sys ems & So wa e 225 (2025) 112326
2
D. Bena ides e al.
Fig. 1. Running example o he online shop case s udy (Rodas-Sil a e al.,2019).
•Al e na i e. Child ea u es ha e an al e na i e ela ionship wi h
hei pa en i exac ly one o hem can be pa o a con igu a ion i
he pa en ea u e is included. In he example, he Paymen o he
eShop mus be ei he Bank ans e o C edi ca d (bu
no bo h in he same con igu a ion).
•O . Child ea u es ha e an o ela ionship wi h hei pa en i one
o mo e o hem can be pa o he con igu a ion i he pa en
ea u e is included. In Fig. 1, whene e Pla o m is selec ed,
Mobileapp,B owse o any combina ion he eo including a
leas one o hese wo ea u es can be selec ed.
No e ha always a child ea u e can only be pa o a con igu a ion
i i s pa en ea u e is pa o he con igu a ion. Addi ionally, he oo
ea u e is included in all he con igu a ions o he p oduc line. An FM
can also con ain c oss- ee cons ain s be ween ea u es — basic ones
a e he ollowing:
•Requi es. I a ea u e 𝐴 equi es a ea u e 𝐵, he inclusion o 𝐴in
a con igu a ion implies he inclusion o B in such a con igu a ion.
In he example, an eShop including C edi ca d mus include
High secu i y suppo .
•Excludes. I a ea u e 𝐴excludes a ea u e 𝐵, bo h canno be
included in he same con igu a ion, i.e., he e is a ea u e exclu-
sion. The Bank ans e ea u e canno be combined wi h a
Mobileapp, i.e., hese wo ea u es a e incompa ible.
Mo e complex c oss- ee ela ionships a e o en used allowing con-
s ain s in he o m o gene ic p oposi ional o mulas, e.g., ‘‘Aand
no Bimplies C’’ (Ba o y,2005). In some cases, he e is a dis inc ion
be ween conc e e and abs ac ea u es (Thüm e al.,2011). Conc e e
ea u es ha e a mapping wi h domain implemen a ion a e ac s in he
solu ion space (Apel e al.,2013), while abs ac ea u es a e used
o o ganisa ion pu poses and do no ha e any di ec mapping o any
a e ac in he solu ion space. O en, only lea es o he ee a e conc e e
ea u es and all he o he in e media e ea u es a e abs ac (Ba o y,
2020a).
2.1. Fea u e model ex ensions
The e a e di e en ways o ex end FMswi h di e en cons uc s.
The mos well-known amilies o ex ensions a e ca dinali y–based and
a ibu e–based FMs. These ex ensions include a discussion ha has been
going on in he communi y o e he yea s: wha a e he seman ics
o ea u e ca dinali ies, cloning, o a ibu es? (Classen e al.,2011;
Cza necki e al.,2005b;El-Sha kawy e al.,2015;Riebisch e al.,2002;
Ro hbe g e al.,2016) In his sec ion, we do no epea such discussions
in de ail. In ollowing sec ions when UVL is p esen ed, mo e de ails on
how hose discussions a e aken in o accoun will be epo ed.
Ca dinali y–based FMsin oduce wo ela ionships ha esemble
hose o he Uni ied Modelling Language (UML) wi h mul iplici ies in
class diag ams — see Cza necki e al. (2005), Riebisch e al. (2002).
The ela ionships in oduced in ca dinali y–based ea u e modelling a e
he ollowing (Bena ides e al.,2010):
•Fea u e ca dinali y. A ea u e ca dinali y is a sequence o in-
e als [𝑛..𝑚]wi h 𝑛as lowe bound and 𝑚as uppe bound (𝑛≤
𝑚). Fea u e ca dinali ies a e also known as ea u e clones. The
in e als desc ibe he numbe o ins ances o he ea u e ha
can be pa o a con igu a ion. This ela ionship may be used as
a gene alisa ion o he o iginal manda o y ([1,1]) and op ional
([0,1]) ela ionships de ined in classical FMsdesc ibed p e iously.
Cloning a ea u e means ha ing di e en ins ances o he same
ea u e se e al imes in a con igu a ion.
•G oup ca dinali y. A g oup ca dinali y is an in e al ⟨𝑛..𝑚⟩, wi h
𝑛being he lowe and 𝑚 he uppe bound (𝑛≤𝑚) limi ing he
numbe o child ea u es ha can be included in a con igu a ion
when he pa en ea u e is selec ed ( emembe ha i he pa en
is no included in a con igu a ion, none o i s child en a e in-
cluded). An al e na i e ela ionship is equi alen o a⟨1..1⟩g oup
ca dinali y. An o - ela ionship is equi alen o ⟨1..𝑁⟩, being 𝑁 he
numbe o ea u es in he ela ionship.
A ibu e–based FMs. In ce ain si ua ions, FMsinclude addi ional
in o ma ion abou he ea u es. Fo example, he cos o memo y
consump ion o a pa icula ea u e in an eShop con igu a ion. Such
in o ma ion can be included using ea u e a ibu es, which a e designed
o his speci ic pu pose. When FMsa e expanded by including ad-
di ional in o ma ion in he o m o a ibu es, hey a e e e ed o as
ex ended, ad anced, o a ibu e-based FMs(Al é ez e al.,2019). Mos
p oposals o a ibu e-based FMsag ee ha an a ibu e should consis
a leas o aname, a ype, adomain and a alue.
3. De elopmen p ocess and design goals o UVL
We i s desc ibe how UVL was de eloped in a pa icipa o y e o
in he SPL communi y and hen summa ise i s design goals.
3.1. Pa icipa o y de elopmen p ocess
UVL is he esul o a communi y e o ha s a ed in 2018 as
depic ed in Fig. 2. The idea began wi h an in o mal mee ing a SPLC
2018 wi h a ound wen y key esea che s om he SPL communi y.
A e a b ains o ming session, we ag eed on se e al ac ion poin s.
Among hose, i was decided o un a wo kshop (MODEVAR4) o be
‘‘an in e ac i e e en whe e all pa icipan s shall sha e knowledge
abou how o build up a simple ea u e model language ha all he
communi y can ag ee on’’.
In he 2019 edi ion (Bena ides e al.,2019), he main ou pu s
we e a e isi ed li e a u e e iew on ex ual a iabili y modelling
languages (Beek e al.,2019), he p oposal o ha ing di e en language
le els (Thüm e al.,2019) and a se o ou een usage scena ios o
he language (Be ge and Colle ,2019) desc ibed by examples. Those
scena ios we e he esul o a sys ema ic p ocess, whe e membe s o
he communi y ga e o iginal desc ip ions, which ecei ed eedback ia
4h ps://mode a .gi hub.io/
The Jou nal o Sys ems & So wa e 225 (2025) 112326
3
D. Bena ides e al.
Fig. 2. UVL de elopmen p ocess since 2018.
a su ey and expe eedback. The su ey, he language le els, and he
usage scena ios we e used o he nex s eps in he p ocess.
Du ing he 2020 VaMoS e en , a su ey ( esul s la e published
a SPLC 2021 (Sunde mann e al.,2021a)) aimed a in o ming he
language’s design decisions was pe o med. This su ey comp ised a
ques ionnai e adminis e ed o 20 wo kshop a endees. In he ini ial
pa o he ques ionnai e, pa icipan s sha ed hei p e e ences conce n-
ing he ga he ed s uc u al a ibu es o he language. Subsequen ly,
in he la e pa , a endees delibe a ed on which language ea u es
should be inco po a ed based on hei conside a ions. Th oughou he
ques ionnai e, pa icipan s collabo a ed in pai s o delibe a e on hei
iewpoin s and o e mo e me iculously conside ed esponses.
The wo kshop was un again in 2020 a SPLC (Ache e al.,2020)
(online due o he pandemic). T ans o ming di e en a iabili y mod-
els is a challenge, in Feich inge and Rabise (2020a) usage scena -
ios, equi ed capabili ies and challenges o an app oach o semi-
au oma ically ans o ming a iabili y models we e p esen ed. One o
he conclusions was ha a pi o al common language can help o
ans o m a iabili y a e ac s and unde lines he necessi y o UVL in
his sense as a pi o al language o ans o ma ions. In addi ion, a
new ool based on Py hon o analyse FMswas p esen ed (Galindo and
Bena ides,2020) wi h he po en ial o including UVL as a iabili y
language (see Sec ion 6.2.3).
In 2021 (Thüm e al.,2021), wo conc e e in eg a ions o UVL
in di e en ools we e p esen ed. Fi s , an in eg a ion o one o he
p e ious e sions o UVL in Fea u eIDE showed he easibili y o he
language (Sunde mann e al.,2021b). Second, a p o o ype o a epos-
i o y o sha e UVL models was p esen ed (Rome o e al.,2021). This
way, some o he objec i es o he language s a ed o ma e ialise: ools
in eg a ion and knowledge sha ing (see Sec ion 6).
In 2022 (Ho cas e al.,2022b), ano he in eg a ion, in his case wi h
a comme cial a ian managemen ool was p esen ed (Romano e al.,
2022). Conc e ely, UVL was in eg a ed wi h pu e:: a ian s
(pu e::sys ems,2017), one o he mos well-known comme cial ools in
he so wa e p oduc line enginee ing a ea. In addi ion, a i s u o ial
on a p e ious e sion o UVL was gi en.
Du ing hese yea s, some ools in eg a ed di e en e sions o UVL
p oducing hei own pa se s (Galindo e al.,2023;Lo h e al.,2023;
Heß e al.,2022a). In 2023, he e was an implemen a ion e o o
p oduce a common s able pa se o UVL wi h suppo o Py hon and
Ja a. This pa se was b ie ly in oduced du ing he MODEVAR 2024
edi ion a VaMoS 2024 and i is one o he con ibu ions o his pape
(c . sec ions 4and 6). Addi ionally, u he de elopmen s a ound UVL
and i s exp essi eness we e p esen ed (Aga wal e al.,2024;Heß e al.,
2024;Rome o-O gan idez e al.,2024a).
In 2024 a second MODEVAR edi ion ook place (Feich inge and
Galasso-Ca bonnel,2024). This ime he ocus o he communi y u ned
owa ds he adop ion o UVL in indus y. Fo ha , po en ial chal-
lenges (Rabise ,2024) and necessa y ex ensions (Fadhlillah and Ra-
bise ,2024) o UVL we e discussed wi h a ep esen a i e o pu e:: a -
ian s (pu e::sys ems,2017). Addi ionally, a gene a o o UVL mod-
els in a bi a y size and complexi y was in oduced, which acili ies
scalabili y analysis (Sunde mann e al.,2024).
Al hough MODEVAR has been he mee ing poin o esea che s and
p ac i ione s wi h in e es in he de elopmen o a simple, common
ex ual ea u e modelling language, he ou pu s and discussions o
he wo kshop se ed o p oduce o he a e ac s ou side o he wo k-
shop (K ie e e al.,2023;Sunde mann e al.,2022). Conc e ely, he e
we e wo u o ials a SPLC 2022 and 2023 p esen ing he ad ances
o UVL as well as analysis and ans o ma ion capabili ies. Also, he e
we e wo majo pape s a SPLC 2021 and 2023 p esen ing a i s e sion
o he language (Sunde mann e al.,2021a) and some ans o ma ion
and analysis capabili ies (Sunde mann e al.,2023b).
In summa y, one unique selling poin o UVL is he communi y-
d i en design o he language (Sunde mann e al.,2021a). Wi h a -
ious su eys and discussions wi h expe s o he communi y, di e en
au ho s de i ed equi emen s o he design o a widely adop ed a i-
abili y language (Beek e al.,2019;Bena ides e al.,2019;Be ge
and Colle ,2019;Sunde mann e al.,2021a;Thüm e al.,2019). In
he ollowing, we p esen de i ed equi emen s ha in luenced he
language design and how we add ess hese in UVL.
3.2. Design goals
Designing a language is di icul (Wąsowski and Be ge ,2023).
Wi h he pa icipa o y p ocess desc ibed in he p e ious sec ion, we
mi iga ed he possibili y o ha ing a language ha was no accep ed by
he communi y. Wi h he inpu s o he wo kshops and wo king sessions,
we de ined se e al design goals ha a e summa ised as ollows:
The Jou nal o Sys ems & So wa e 225 (2025) 112326
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Fig. 3. Language le el hie a chy in UVL.
Simplici y.In gene al, UVL should be simple o use. Fo simplici y,
we conside wo dimensions: (1) UVL should be easy o use, unde -
s and (wi h simple cons uc s), lea n and comp ehend ( acili a ing he
comp ehension o he a iabili y in hand) o humans (Be ge and
Colle ,2019) and (2) i should no equi e oo much e o o in eg a e
UVL in a iabili y modelling ools. Fo human unde s andabili y and
comp ehension, UVL should use concep s amilia o use s. As po en ial
use s, we conside people wo king in he compu e science ield and/o
using a iabili y modelling. Hence, we aim o use concep s om p o-
g amming languages, modelling in compu e science (e.g., g amma s
o me a-models), and exis ing a iabili y languages. Fo easie in eg a-
ion, we conside he ollowing equi emen s o UVL. Fi s , he co e
language should be simple so ha de elope s do no ha e o in eg a e
a ious complex cons uc s. Second, he language should euse exis ing
concep s om o he a iabili y languages, e.g., common keywo ds like
al e na i e. Thi d, he co e language should be simple o analyse wi h
con en ional analysis ools used in he domain, such as SAT (Cza necki
and Wąsowski,2007;Mendonça e al.,2009b;Zhang e al.,2004),
BDD (He adio e al.,2022) o #SAT sol e s (Küble e al.,2010;Liang
e al.,2015;Sunde mann e al.,2023a).
In o ma ion hiding.In p ac ice, i o en makes sense o only wo k on
small subpa s o a a iabili y model. Fi s , la ge a iabili y models
a e ypically ha d o o e see Ache e al. (2009). Second, di e en
s akeholde s commonly do no wo k on he en i e a iabili y model
bu speci ic pa s (Ache e al.,2009). Hence, UVL should ha e a
mechanism o suppo ocusing on a subse o in e es .
Exp essi eness.To be widely applicable, one o UVL’s goals is o co e
many p ac ical use cases. Fi s , use s o UVL should be able o speci y
cons ain s as needed o desc ibe he se o alid con igu a ions, which
may include p oposi ional logic, cons ain s o e nume ic alues, o
e en easoning abou con en o s ings (Beek e al.,2019). Second,
UVL should be able o desc ibe cons uc s used in a ailable ea u e
modelling ools (Ache e al.,2013;Galindo e al.,2023;Meinicke e al.,
2017;Mendonça e al.,2009a).
Ex ensibili y.A highe exp essi eness con lic s wi h he goal o sim-
plici y (Thüm e al.,2019), as mo e and po en ially mo e complex
language cons uc s need o be suppo ed. As a comp omise in UVL,
we aim o ha e an ex ensible language design wi h a simple co e
language ha can be easily adop ed and ex ensions ha in oduce mo e
exp essi eness. He e, we use he concep o language le els (Thüm
e al.,2019) ha encapsula e di e en language cons uc s and ex end
he UVL co e language.
Exchange.Models o a common a iabili y language should be ex-
changeable be ween di e en ools (Be ge and Colle ,2019). Fo
simpli ying exchange, we conside wo aspec s. Fi s , a ailable ool
suppo (e.g., o pa sing) should be eusable o di e en use s o UVL.
Second, he e should be a mechanism o exchange UVL models be ween
ools ha suppo di e en le els o exp essi eness.
4. The Uni e sal Va iabili y Language (UVL)
In his sec ion, we illus a e how o speci y a iabili y models wi h
UVL5using ou unning example. The design o UVL consis s o a
simple base language wi h se e al language ex ensions, which we call
language le els (c . Sec ion 5). He e, we s a wi h a simple e sion and
ex end i i e a i ely o showcase mo e exp essi e UVL language le els.
Fo a o mal desc ip ion on he language, we e e o Sec ion 5.
4.1. Language le els
In UVL, we use language le els o ackle exp essi eness and ex ensi-
bili y while p ese ing a simple co e language. The idea is ha use s o
UVL can limi hei models o speci ic language cons uc s. I a ool
only suppo s e y simple cons uc s, highe language le els can be
o bidden. I mo e exp essi eness is needed, addi ional language le els
can be enabled.
Fig. 3shows he language le els cu en ly a ailable in UVL. Each
language le el encapsula es ce ain language cons uc s. We dis inguish
be ween majo and mino language le els. The majo le els ha e a
hie a chical o de . The Boolean-le el is he co e language o UVL. The
A i hme ic-le el ully includes he majo Boolean le el and ex ends i
wi h nume ic cons ain s o e ea u e a ibu es. The Type-le el ex ends
bo h wi h yped ea u es, such as s ing o nume ic ea u es. The goal o
hese le els is o sepa a e he language acco ding o easoning engines
ha could be used o eason abou hem. Fo ins ance, he Boolean-
le el can be simply encoded as a SAT p oblem. Mino language le els
a e op ional ex ensions o he majo le els. The idea is o sepa a e
cons uc s ha can be analysed wi h he same easoning engine bu
may equi e u he handling o a e no always suppo ed by a ailable
ools. They a e no au oma ically included in highe language le els.
5We discussed di e en name al e na i es o he p oposed language and
we decide o use UVL because he in en ion is o make i an Uni e sal language
used by many s akeholde s in he a iabili y modelling communi y.
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Lis ing 1: UVL Running Example: Co e
1 ea u es
eShop
3manda o y // selec all
Secu i y
5al e na i e // selec exac ly one
High {P ice 100}
7S anda d {P ice 50}
Ca alogue
9op ional
SEO
11 Paymen
al e na i e
13 "Bank T ans e " {P ice 10, SEPA ue}
"C edi Ca d" {P ice 20}
15 Pla o m
o // selec a leas one
17 "Mobile App"
B owse {URL ’www.u leshop.o g’}
19
cons ain s
21 !("Bank T ans e " &"Mobile App")
"C edi Ca d" => High
G oup Ca dinali y ex ends he boolean le el wi h ca dinali y g oup
ela ionships which enable selec ing [n..m] ea u es om he g oup.
Fea u e Ca dinali y and Agg ega e Func ions a e op ional ex ensions o
he a i hme ic le el. They enable (1) selec ing a ea u e mul iple imes
and (2) agg ega es, such as sums, o e nume ical a ibu es, espec-
i ely. S ing Cons ain s add cons ain s o compa e s ings and leng hs
o s ings. In he ollowing, we showcase he di e en language le els
by ex ending ou base example shown in Lis ing 1.
4.2. Boolean le el
Lis ing 1shows ou unning example om Fig. 1in UVL syn ax. The
UVL model consis s o wo main pa s: he ea u e ee and he c oss-
ee cons ain s. The ee hie a chy is ep esen ed using inden a ion.
Keywo ds a e used o speci y he pa en –child ela ionship. As in
Fig. 1,eShop has wo manda o y and h ee op ional child ea u es.
Fu he mo e, exac ly one Secu i y op ion and exac ly one Paymen
op ion can be selec ed as deno ed by he al e na i e-keywo d. Fo he
ea u e Pla o m, he o -g oup deno es ha a leas one pla o m
can be selec ed. The c oss- ee cons ain s a e used o impose u he
limi a ions on he ea u es. Fo ins ance, Bank T ans e and Mo-
bile App canno be included in he same con igu a ion, i.e., hey a e
incompa ible ea u es. Also, aC edi Ca d equi es aHigh secu i y
le el. Fo he co e language, he cons ain s a e limi ed o p oposi ional
logic.
In addi ion o ea u e dependencies, he UVL model con ains some
a ibu es ha p o ide in o ma ion on he espec i e ea u es. In ou
model, we ha e a numbe a ibu e (p ice), a Boolean a ibu e (SEPA),
and a s ing a ibu e (URL). In he co e language o UVL, a ibu es
can only be used o s o ing in o ma ion abou ea u es ha do no
in luence he alidi y o con igu a ions. Cons ain s o e a ibu es a e
excluded in he co e language, since he easoning is conside ably
mo e complex and no s aigh o wa d o encode o many au oma ed
easoning engines, such as SAT sol e s. S ill, a ibu es a e ele an o
(1) s o e ool-speci ic in o ma ion, (2) a ach gene al in o ma ion o
ea u es, and (3) can be used o compu e me ics o con igu a ions
based on use selec ions, such as a p ice.
Fo u he in o ma ion, commen s can be added ei he single line
wi h // o mul iple lines wi h /* <commen > */. All commen s a e
disca ded du ing he pa sing p ocess.
Lis ing 2shows an adap a ion o he p e ious eShop bu using
now he ca dinali y capaci y o a ea u e g oup. Ano he change is he
include a he e y op o he lis ing. The include mechanism allows
use s o speci y explici ly which language cons uc s a e suppo ed.
This can be used o (1) p o iding in o ma ion on he con en s o he
language le el and (2) ensu e ha use s do no in oduce cons uc s
ha a e no suppo ed by he ool using UVL. In he la e case, he
UVL pa se should p o ide in o ma ion on he misma ch o decla ed
and used le els. By de aul , i.e., when no language le els a e speci ied
in includes, all language le els a e included. Each cons uc in he
ini ial eShop Lis ing 1is pa o he co e language. G oup ca dinali y
is amino le el o he Boolean (i.e., co e) language le el. Including
he mino le el g oup-ca dinali y au oma ically includes i s majo le el
Boolean. In Sec ion 4.3 and Sec ion 4.4, we illus a e he o he wo
majo language le els in UVL, namely A i hme ic and Type, using ou
unning example.
Lis ing 2: UVL Running Example: G oup Ca dinali y
1include
Boolean.g oup-ca dinali y
3
ea u es
5...
Pla o m
7[2..3]
"Desk op App"
9"Mobile App"
B owse {URL ’www.u leshop.o g’}
11 ...
G oup ca dinali y. In addi ion o he speci ica ion o included language
le els, he e a e changes in he ea u e ee. Now, in Lis ing 2 he
cus ome has h ee Pla o m op ions o choose om. In addi ion,
he g oup- ype changed o ag oup ca dinali y. The g oup deno es ha
he cus ome needs o selec be ween wo and h ee ([2..3]) pla o m
ea u es ins ead o a leas one.
4.3. A i hme ic le el
In his sec ion, we ex end ou FM wi h cons uc s om he A i h-
me ic-le el and i s mino le els. Lis ing 3 u he en iches ou eShop
wi h an a i hme ic cons ain o e he p ice a ibu e. The cons ain
deno es ha he o e all sum in p ice o all selec ed ea u es should
be smalle han 200. Wi h he A i hme ic-le el, he ollowing ope a o s
a e suppo ed: +, -, *, /, ==, <,>,<=, and >=. The mino le el
agg ega e- unc ion also in oduces sum() and a g().
Lis ing 3: UVL Running Example: A i hme ic
1include
Boolean.g oup-ca dinali y
3A i hme ic.agg ega e- unc ion
5 ea u es
...
7
cons ain s
9!("Bank T ans e " &"Mobile App")
"C edi Ca d" => High
11 sum(P ice) <200
Fea u e ca dinali y. In Lis ing 4, we in oduce ea u e ca dinali y, which
is a mino le el o he A i hme ic-le el. In ou example, he use can
decide o ha e be ween one and i e Ca alogue ea u es as deno ed
by ca dinali y [1..5]. A cus ome may selec a ying ca alogues o
di e en ma ke s, e.g., Eu ope and No h Ame ica. No e ha each
selec ed Ca alogue would inc ease he o e all p ice by 30.
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D. Bena ides e al.
Lis ing 4: UVL Running Example: Fea u e Ca dinali y
1include
Boolean.g oup-ca dinali y
3A i hme ic.agg ega e- unc ion
A i hme ic. ea u e-ca dinali y
5
ea u es
7eShop
manda o y
9Secu i y
al e na i e
11 High {P ice 100}
S anda d {P ice 50}
13 Ca alogue ca dinali y [1..5] {P ice 30}
...
4.4. Type le el
Lis ing 5shows he las e sion o ou eShop wi h all language
le els included. He e, we newly added he Type-le el, which in oduces
ea u es wi h he ollowing ypes: in ege , loa , and s ing. No e ha
any ea u e can s ill be deselec ed e en i i is no Boolean. Fo ,
ins ance he cus ome can now con igu e an in ege ea u e I ems
in Baske , which can be used o limi he maximum numbe o
i ems a cus ome can pu in his baske a he same ime. A c oss- ee
cons ain ensu es ha he maximum numbe o i ems is highe han
ze o. Fu he , B owse is now a s ing ea u e whe e he URL can
be di ec ly con igu ed. Ano he c oss- ee cons ain deno es ha he
URL may no be longe han 30 cha ac e s. The used len- unc ion is
pa o he s ing-cons ain s mino le el which also in oduces equali y
checks be ween s ings. No e ha we also eplaced he wo lines o
speci ying bo h mino le els o he A i hme ic le el wi h a wildca d
A i hme ic.*.
4.5. Impo mechanism
Wi h housands o ea u es and cons ain s in p ac ice (Lo u o e al.,
2010;Küble e al.,2010;Sunde mann e al.,2023a), FMsa e o en
ha d o o e iew. Fu he , s akeholde s o en only need o conside a
subse o he FM. To simpli y managing la ge FMsand ocusing on pa s
o in e es , UVL p o ides a mechanism o decomposing models in o
subpa s ha can hen be impo ed in an o e all model i needed.
Lis ing 6showcases he impo mechanism o UVL whe e we ha e
he Pla o m sub ee (Lis ing 7) and he Secu i y sub ee (Lis ing
8as sepa a e iles. Those sub ees a e impo ed using he impo s-
keywo d. Impo s a e speci ied using a ela i e ile pa h o he impo ed
UVL model. Fo ins ance, pla o m e e s o a ile in he same di ec-
o y named pla o m.u l. Non- i ial pa hs can be speci ied wi h a
Py hon-like do no a ion (e.g., submodels.pla o m). Impo s can also be
gi en an alias wi h he as keywo d. The submodel can hen be a ached
o an a bi a y loca ion in he ea u e ee by e e encing i s oo
ea u e (e.g., pl.Pla o m). In he c oss- ee cons ain s all ea u es
o submodels can be e e enced using he submodels’ namespace. The
shown model (Lis ing 6) is equi alen o Lis ing 5. Seman ically, he
ea u e e e ence in he composed model is expanded o include he
en i e sub ee. Fo ins ance, pl.Pla o m e e ences he en i e FM in
Lis ing 7. Also, all c oss- ee cons ain s in he impo ed submodels a e
applied o he composed model. C oss- ee cons ain s in he composed
can e e ence ea u es om impo ed submodels using he ilename
o alias and he ea u e name. Fo example, in line 21 pl."Mobile
App" is e e enced. The impo mechanism may ha e he ollowing
wo ad an ages o ou unning example. Fi s , Lis ing 6is sho e and
easie o o e iew han he en i e model shown in Lis ing 5. Second,
a de elope only esponsible o pla o m o secu i y de elopmen can
sepa a ely wo k on he submodels Lis ing 7and Lis ing 8, espec i ely.
Lis ing 5: UVL Running Example: Typed Fea u es
include
2Boolean.g oup-ca dinali y
A i hme ic.*
4Type.s ing-cons ain s
6 ea u es
eShop
8manda o y
Secu i y
10 al e na i e
High {P ice 100}
12 S anda d {P ice 50}
Ca alogue ca dinali y [1..5] {P ice 30}
14 In ege "I ems in Baske "
op ional
16 SEO {P ice 40}
Paymen
18 al e na i e
"Bank T ans e " {P ice 10, SEPA ue}
20 "C edi Ca d" {P ice 20}
Pla o m
22 [2..3]
"Desk op App" {P ice 70}
24 Boolean "Mobile App" {P ice 80}
S ing B owse {P ice 20}
26
cons ain s
28 !("Bank T ans e " &"Mobile App")
"C edi Ca d" => High
30 sum(P ice) <200
0<"I ems in Baske "
32 len(B owse ) <30
Lis ing 6: UVL Running Example: Impo Mechanism
impo s
2pla o m as pl
secu i y
4
ea u es
6eShop
manda o y
8secu i y.Secu i y
Ca alogue ca dinali y [1..5] {P ice 30}
10 In ege "I ems in Baske "
op ional
12 SEO {P ice 40}
Paymen
14 al e na i e
"Bank T ans e " {P ice 10, SEPA ue}
16 "C edi Ca d" {P ice 20}
pl.Pla o m
18
20 cons ain s
!("Bank T ans e " &pl."Mobile App")
22 "C edi Ca d" => secu i y.High
sum(P ice) <200
24 "I ems in Baske " > 0
Summa y. UVL p o ides a simple co e language and an impo mech-
anism ha enables decomposing models in o manageable small sub-
models o ackle i s design goal simplici y. Addi ional language le els
p o ide mo e exp essi eness wi h cons uc s o speci y ca dinali ies, di -
e en cons ain s o e nume ic alues, yped ea u es, and cons ain s
o e s ings. The design o he language le els is ex ensible o allow
The Jou nal o Sys ems & So wa e 225 (2025) 112326
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D. Bena ides e al.
Lis ing 7: UVL Running Example: Pla o m Submodel
ea u es
2Pla o m
[2..3]
4"Desk op App" {P ice 70}
Boolean "Mobile App" {P ice 80}
6S ing B owse {P ice 20}
8cons ain s
len(B owse ) <30
Lis ing 8: UVL Running Example: Secu i y Submodel
1 ea u es
Secu i y
3al e na i e
High {P ice 100}
5S anda d {P ice 50}
di e en use s o ailo hei UVL models o hei use case and ool
limi a ions. We used his sec ion o in oduce UVL wi h an example,
in Sec ion 5we de ine UVL models mo e o mally and discuss he
seman ics o di e en cons ain s.
5. Syn ax & seman ics: Language speci ica ion
In his sec ion, we discuss he syn ax and seman ics o UVL mo e
o mally. The goal is o cla i y possible ambigui ies and p o ide clea
guidelines on how o in e p e UVL and wo k wi h he language. No e
ha we use some concep s he e equi ing compu e science backg ound
o unde s and.
5.1. UVL syn ax
Fig. 4shows a simpli ied iew on he abs ac syn ax o aUVL model
in o m o a me a-model (mo e de ails on conc e e pa s o he me a-
model will be elabo a ed la e ). AUVL model consis s o ou majo
pa s: impo s,language le els, ea u e ee, and c oss- ee cons ain s. In
he ollowing, we explain he ou majo pa s in mo e de ail and he
language cons uc s ha can be used wi hin.
Impo s. As discussed in Sec ion 3, decomposing a ea u e model in o
smalle sub-pa s is bene icial. S ill, knowledge abou c oss-dependen-
cies be ween hose sub-pa s needs o be main ained as hey may
impac he con igu a ion space. Wi h UVL, we suppo composi ion
o a ious smalle sub-models wi h an impo mechanism. He eby,
ano he UVL model can be impo ed ia impo submodel. Then,
he submodel can be e e enced a an a bi a y loca ion in he ea u e
ee wi h submodel.Roo . No e ha Roo is he name o he oo
ea u e he e. While he composed model only con ains one line o
adding he oo ea u e, his is seman ically equi alen o copying he
en i e sub-model a his loca ion. C oss- ee cons ain s o he sub-
model also apply o he composed model. Cons ain s be ween ea u es
o di e en sub-models can be speci ied using he same syn ax as in
he ea u e ee (e.g., submodel1.A & submodel2.B). Fo each
impo , an alias can be speci ied wi h he as-keywo d (e.g., impo
submodel1 as s1). Fea u es can hen be e e enced wi h s1.A.
Submodels in o he , possibly nes ed, di ec o ies can be e e enced wi h
<di 1>.<di 2>.<u l ile>.
Language le els. Language le els can be explici ly speci ied wi h he in-
clude keywo d. The included language le els a e lis ed in sepa a e lines
using he syn ax <majo >.(<mino >|*)?. So, one line can ei he
speci y a majo le el (<majo >), a mino le el (<majo >.<mino >,
o all mino le els (<majo >.*). I a de elope iola es he language
le els by adding an unsuppo ed cons uc , he pa se would p o ide a
wa ning o e o o him. No e ha using a mino le el always includes
he espec i e majo le el. By de aul , all language le els a e included.
Hence, no speci ying any le el includes enables he ull exp essi eness
o UVL.
Fig. 3shows he language le els cu en ly suppo ed in UVL and
he language cons uc s hey include. The h ee majo le els Boolean,
A i hme ic,Type encapsula e language cons uc s ha can be easoned
abou wi h a speci ic easoning engine. Fo ins ance, UVL models
o he Boolean le el should be s aigh o wa d o encode as a SAT
ins ance (e.g., CNF) (Ba o y,2005;Kui e e al.,2022). In con as , he
A i hme ic le el can be di ec ly ep esen ed as SMT (De Mou a and
Bjø ne ,2011) o CP (Jussien e al.,2008) p oblem, bu equi es u he
p ocessing o be encoded as SAT ins ance.
Fea u e ee. The UVL ea u e ee consis s o wo main elemen s:
ea u es and g oups. The ee equi es exac ly one oo ea u e. Each
ea u e may ha e an a bi a y numbe o g oups which in u n may
ha e an a bi a y numbe o ea u es each. The ela ionship be ween
ea u es and g oups a e deno ed wi h inden a ion. Fo a ea u e, i s
co esponding g oups a e inden ed by one line and ice e sa o
g oups. A ea u e always equi es a unique name as iden i ie . He e,
he iden i ie needs o be enclosed by quo a ion ma ks i he used
symbols may in oduce an ambigui y in he UVL model.6Each ea u e
can ha e a ea u e ca dinali y [n..m], which deno es ha he ea u e can
be selec ed be ween n and m imes. Also, a lis o a ibu es {a 1, a 2,
...} can be a ached. The e a e i e ea u e g oup ypes suppo ed in
UVL as seen in Fig. 5.Op ional,manda o y,o , and al e na i e a e pa
o he co e (Boolean) le el, while g oup ca dinali y is a Boolean mino
le el.
Fea u e a ibu es. Fo each ea u e, an a bi a y numbe o a ibu es
can be a ached. Gene ally, a ibu es a e key– alue pai s wi h he key
being an iden i ie and he alue being o one o he ypes shown
in Fig. 6. One excep ion is ha i is allowed o only speci y a key,
which is hen conside ed as Boolean a ibu e wi h ue as alue.
The a ibu es o a ea u e a e decla ed in cu ly b acke s as ollows:
{<key1> < al1>, <key2> < al2>}. Nes ed a ibu e lis s can be
speci ied wi h {<key> {<key1> < al1> ...}}. Types o a ibu es
a e no explici ly s a ed bu a he in e ed om he alue. S ing
cons an s (i.e., alues o s ing a ibu es) a e speci ied wi h single
quo a ion ma ks o p e en ambigui ies wi h ea u e names.
Cons ain s. The cons ain s pa o aUVL model consis s o a lis o
cons ain s ha can e alua e o ei he ue o alse (see Fig. 7). A
alid con igu a ion needs o sa is y e e y a ached cons ain . In UVL,
cons ain s a e mos ly based on common p oposi ional logic ope a o s,
namely !(no ), &(and), |(o ), => (implies), <=> (equals), and b ack-
e s. These ope a o s combine Boolean a iables, Boolean cons an s (i.e.,
ue o alse), o p edica es(c . Fig. 8), which each need o e alua e o
a Boolean. The Boolean a iables can e e o ei he a ea u e name o
a Boolean-a ibu e key.
P edica es. P edica es a e used in UVL o speci y dependencies based
on s ing and nume ical alues. As shown in Fig. 8, each p edica e
has exac ly one ope a o o equals (== in UVL), g ea e (>), lesse
(<), unequal (!=), g ea e equal (>=), and lesse equal (<=). No e ha
each o hese ope a o s e alua es o a Boolean alue. Those ope a o s
connec wo e ms, which a e illus a ed in Fig. 9.
6Iden i ie s no ma ching [a-zA-Z0-9_]*[a-zA-Z_][a-zA-Z0-
9_]* mus be p o ec ed.
The Jou nal o Sys ems & So wa e 225 (2025) 112326
8
D. Bena ides e al.
Fig. 4. UVL me a model.
Fig. 5. UVL ea u e-g oup ypes.
Fig. 6. UVL ea u e a ibu es.
Te ms can only be used wi hin p edica es in UVL. A e m can be
(1) a e e ence o a a iable, (2) a cons an , (3) a unc ion, o (4) a
bina y exp ession. The e e enced a iables can be ei he ea u es o
a ibu es. Cons an s can be ei he s ings o nume ic alues. S ing
cons an s a e always enclosed wi h single quo a ion ma ks o p e en
ambigui ies wi h e e ences. O he wise, i would be impossible o dis-
inguish be ween a s ing cons an ma ching a ea u e name and said
ea u e. Fo unc ions, sum,a e age a e cu en ly suppo ed o nume ic
alues and leng h o s ings. The bina y exp ession can connec wo
nume ic alues wi h simple a i hme ic ope a o s, namely add (+in
UVL), sub ac (-), mul iply (*), and di ision (/).
5.2. Cons ain seman ics
In his sec ion, we discuss he seman ics o cons ain s in UVL
conside ing on how hey a ec he se o alid con igu a ions. Ou goal
he e is o cla i y po en ial ambigui ies in he seman ics o speci ic con-
s ain s. Table 1shows a o mal de ini ion o he es ic ions di e en
cons ain s impose on he con igu a ion space 𝑉 𝐶(i.e., he se o alid,
comple e con igu a ions modelled by aUVL model). Fo 𝐶= (𝐼 , 𝐸),𝐼
is he se o included ea u es and 𝐸o excluded ea u es. Fu he , 𝑓
is a ea u e, 𝑝(𝑓) he pa en ea u e o 𝑓,𝑠(𝑓 , 𝐶) he selec ion s a us
o 𝑓in 𝐶, ca d(𝑓 , 𝐶) he ca dinali y o 𝑓in 𝐶. The selec ion s a us
is a unc ion 𝑠∶ ( ea u e, con igu a ion)→{0,1} ha maps a ea u e
selec ed (1) o deselec ed (0). The ca dinali y o a ea u e ca d(𝑓 , 𝐶)
The Jou nal o Sys ems & So wa e 225 (2025) 112326
9
D. Bena ides e al.
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