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Dec 18, 2023 482 likes •1.37k views

tt t s rrs s strt t

SLIDE 1

▼♦t✐✈❛t✐♦♥ ❖♥t♦■❖♣ ❉❖▲ ❋♦❝✉s❡❞ ❖▼❙ ❖▼❙ ▲✐❜r❛r✐❡s ❈♦♥❝❧✉s✐♦♥

❚❤❡ ❉✐str✐❜✉t❡❞ ❖♥t♦❧♦❣②✱ ▼♦❞❡❧✐♥❣ ❛♥❞ ❙♣❡❝✐✜❝❛t✐♦♥ ▲❛♥❣✉❛❣❡ ✭❉❖▲✮ ▲❛♥❣✉❛❣❡ ♦✈❡r✈✐❡✇

❚✐❧❧ ▼♦ss❛❦♦✇s❦✐✶ ❖❧✐✈❡r ❑✉t③✶ ❋❛❜✐❛♥ ◆❡✉❤❛✉s✶ ❈❤r✐st♦♣❤ ▲❛♥❣❡✷ ▼✐❤❛✐ ❈♦❞❡s❝✉✶

✶❯♥✐✈❡rs✐t② ♦❢ ▼❛❣❞❡❜✉r❣ ✷❯♥✐✈❡rs✐t② ♦❢ ❇♦♥♥

❖❜❡rs❡♠✐♥❛r✱ ✷✵✶✹✲✶✶✲✶✷

▼♦ss❛❦♦✇s❦✐ ❉✐str✐❜✉t❡❞ ❖♥t♦❧♦❣②✱ ▼♦❞❡❧✐♥❣ ❛♥❞ ❙♣❡❝✐✜❝❛t✐♦♥ ▲❛♥❣✉❛❣❡ ✭❉❖▲✮ ✷✵✶✹✲✶✶✲✶✷ ✶

SLIDE 2

▼♦t✐✈❛t✐♦♥ ❖♥t♦■❖♣ ❉❖▲ ❋♦❝✉s❡❞ ❖▼❙ ❖▼❙ ▲✐❜r❛r✐❡s ❈♦♥❝❧✉s✐♦♥

▼♦t✐✈❛t✐♦♥

▼♦ss❛❦♦✇s❦✐ ❉✐str✐❜✉t❡❞ ❖♥t♦❧♦❣②✱ ▼♦❞❡❧✐♥❣ ❛♥❞ ❙♣❡❝✐✜❝❛t✐♦♥ ▲❛♥❣✉❛❣❡ ✭❉❖▲✮ ✷✵✶✹✲✶✶✲✶✷ ✷

SLIDE 3

▼♦t✐✈❛t✐♦♥ ❖♥t♦■❖♣ ❉❖▲ ❋♦❝✉s❡❞ ❖▼❙ ❖▼❙ ▲✐❜r❛r✐❡s ❈♦♥❝❧✉s✐♦♥

❚❤❡ ❇✐❣ P✐❝t✉r❡ ♦❢ ■♥t❡r♦♣❡r❛❜✐❧✐t②

▼♦❞❡❧✐♥❣ ❙♣❡❝✐✜❝❛t✐♦♥ ❑♥♦✇❧❡❞❣❡ ❡♥❣✐♥❡❡r✐♥❣ ❖❜❥❡❝ts✴❞❛t❛ ❙♦❢t✇❛r❡ ❈♦♥❝❡♣ts✴❞❛t❛ ▼♦❞❡❧s ❙♣❡❝✐✜❝❛t✐♦♥s ❖♥t♦❧♦❣✐❡s ▼❡t❛♠♦❞❡❧s ❙♣❡❝✐✜❝❛t✐♦♥ ❧❛♥❣✉❛❣❡s ❖♥t♦❧♦❣② ❧❛♥❣✉❛❣❡s ❉✐✈❡rs✐t② ❛♥❞ t❤❡ ♥❡❡❞ ❢♦r ✐♥t❡r♦♣❡r❛❜✐❧✐t② ♦❝❝✉r ❛t ❛❧❧ t❤❡s❡ ❧❡✈❡❧s✦

▼♦ss❛❦♦✇s❦✐ ❉✐str✐❜✉t❡❞ ❖♥t♦❧♦❣②✱ ▼♦❞❡❧✐♥❣ ❛♥❞ ❙♣❡❝✐✜❝❛t✐♦♥ ▲❛♥❣✉❛❣❡ ✭❉❖▲✮ ✷✵✶✹✲✶✶✲✶✷ ✸

SLIDE 4

▼♦t✐✈❛t✐♦♥ ❖♥t♦■❖♣ ❉❖▲ ❋♦❝✉s❡❞ ❖▼❙ ❖▼❙ ▲✐❜r❛r✐❡s ❈♦♥❝❧✉s✐♦♥

❖♥t♦❧♦❣✐❡s

Class: Person Class: Female Class: Woman EquivalentTo: Person and Female Class: Man EquivalentTo: Person and not Woman ObjectProperty: hasParent ObjectProperty: hasChild InverseOf: hasParent ObjectProperty: hasHusband Class: Mother EquivalentTo: Woman and hasChild some Person Class: Father EquivalentTo: Man and hasChild some Person Class: Parent EquivalentTo: Father or Mother

▼♦ss❛❦♦✇s❦✐ ❉✐str✐❜✉t❡❞ ❖♥t♦❧♦❣②✱ ▼♦❞❡❧✐♥❣ ❛♥❞ ❙♣❡❝✐✜❝❛t✐♦♥ ▲❛♥❣✉❛❣❡ ✭❉❖▲✮ ✷✵✶✹✲✶✶✲✶✷ ✹

SLIDE 5

▼♦t✐✈❛t✐♦♥ ❖♥t♦■❖♣ ❉❖▲ ❋♦❝✉s❡❞ ❖▼❙ ❖▼❙ ▲✐❜r❛r✐❡s ❈♦♥❝❧✉s✐♦♥

▼♦❞❡❧s

Pr♦t♦❝♦❧ st❛t❡ ♠❛❝❤✐♥❡ ❙t❛t❡ ♠❛❝❤✐♥❡

▼♦ss❛❦♦✇s❦✐ ❉✐str✐❜✉t❡❞ ❖♥t♦❧♦❣②✱ ▼♦❞❡❧✐♥❣ ❛♥❞ ❙♣❡❝✐✜❝❛t✐♦♥ ▲❛♥❣✉❛❣❡ ✭❉❖▲✮ ✷✵✶✹✲✶✶✲✶✷ ✺

SLIDE 6

▼♦t✐✈❛t✐♦♥ ❖♥t♦■❖♣ ❉❖▲ ❋♦❝✉s❡❞ ❖▼❙ ❖▼❙ ▲✐❜r❛r✐❡s ❈♦♥❝❧✉s✐♦♥

❙♣❡❝✐✜❝❛t✐♦♥s

sort Elem free type List[Elem] ::= [] | __::__(Elem; List[Elem]) pred __elem__ : Elem * List[Elem} preds is_ordered : List[Elem]; permutation : List[Elem] * List[Elem]

p sorter : List[Elem]->List[Elem]

forall x,y:Elem; L,L1,L2:List[Elem] . not x elem [] . x elem (y :: L) <=> x=y \/ x elem L . is_ordered([]) . is_ordered(x::[]) . is_ordered(x::y::L) <=> x<=y /\ is_ordered(y::L) . permutation(L1,L2) <=> (forall x:Elem . x elem L1 <=> x elem L2) . is_ordered(sorter(L)) . permutation(L,sorter(L))

▼♦ss❛❦♦✇s❦✐ ❉✐str✐❜✉t❡❞ ❖♥t♦❧♦❣②✱ ▼♦❞❡❧✐♥❣ ❛♥❞ ❙♣❡❝✐✜❝❛t✐♦♥ ▲❛♥❣✉❛❣❡ ✭❉❖▲✮ ✷✵✶✹✲✶✶✲✶✷ ✻

SLIDE 7

▼♦t✐✈❛t✐♦♥ ❖♥t♦■❖♣ ❉❖▲ ❋♦❝✉s❡❞ ❖▼❙ ❖▼❙ ▲✐❜r❛r✐❡s ❈♦♥❝❧✉s✐♦♥

❲❤❛t ❤❛✈❡ ♦♥t♦❧♦❣✐❡s✱ ♠♦❞❡❧s ❛♥❞ s♣❡❝✐✜❝❛t✐♦♥s ✐♥ ❝♦♠♠♦♥❄

❢♦r♠❛❧✐s❡❞ ✐♥ s♦♠❡ ❧♦❣✐❝❛❧ s②st❡♠ s✐❣♥❛t✉r❡ ✇✐t❤ ♥♦♥✲❧♦❣✐❝❛❧ s②♠❜♦❧s ✭❞♦♠❛✐♥ ✈♦❝❛❜✉❧❛r②✮ ❛①✐♦♠s ❡①♣r❡ss✐♥❣ t❤❡ ❞♦♠❛✐♥✲s♣❡❝✐✜❝ ❢❛❝ts s❡♠❛♥t✐❝s✿ ❝❧❛ss ♦❢ str✉❝t✉r❡s ✭♠♦❞❡❧s✮ ✐♥t❡r♣r❡t✐♥❣ s✐❣♥❛t✉r❡ s②♠❜♦❧s ✐♥ s♦♠❡ s❡♠❛♥t✐❝ ❞♦♠❛✐♥ ✇❡ ❛r❡ ✐♥t❡r❡st❡❞ ✐♥ t❤♦s❡ str✉❝t✉r❡s ✭♠♦❞❡❧s✮ s❛t✐s❢②✐♥❣ t❤❡ ❛①✐♦♠s ❲❡ ❤❡♥❝❡❢♦rt❤ ❝❛❧❧ t❤❡♠ ✏❖▼❙✑✦

▼♦ss❛❦♦✇s❦✐ ❉✐str✐❜✉t❡❞ ❖♥t♦❧♦❣②✱ ▼♦❞❡❧✐♥❣ ❛♥❞ ❙♣❡❝✐✜❝❛t✐♦♥ ▲❛♥❣✉❛❣❡ ✭❉❖▲✮ ✷✵✶✹✲✶✶✲✶✷ ✼

SLIDE 8

▼♦t✐✈❛t✐♦♥ ❖♥t♦■❖♣ ❉❖▲ ❋♦❝✉s❡❞ ❖▼❙ ❖▼❙ ▲✐❜r❛r✐❡s ❈♦♥❝❧✉s✐♦♥

▼♦t✐✈❛t✐♦♥✿ ❉✐✈❡rs✐t② ♦❢ ❖♣❡r❛t✐♦♥s ♦♥ ❛♥❞ ❘❡❧❛t✐♦♥s ❛♠♦♥❣ ❖▼❙

❱❛r✐♦✉s ♦♣❡r❛t✐♦♥s ❛♥❞ r❡❧❛t✐♦♥s ♦♥ ❖▼❙ ❛r❡ ✐♥ ✉s❡✿ str✉❝t✉r✐♥❣✿ ✉♥✐♦♥✱ tr❛♥s❧❛t✐♦♥✱ ❤✐❞✐♥❣✱ ✳ ✳ ✳ r❡✜♥❡♠❡♥t ♠❛t❝❤✐♥❣ ❛♥❞ ❛❧✐❣♥♠❡♥t

♦❢ ♠❛♥② ❖▼❙ ❝♦✈❡r✐♥❣ ♦♥❡ ❞♦♠❛✐♥

♠♦❞✉❧❡ ❡①tr❛❝t✐♦♥

❣❡t r❡❧❡✈❛♥t ✐♥❢♦r♠❛t✐♦♥ ♦✉t ♦❢ ❧❛r❣❡ ❖▼❙

❛♣♣r♦①✐♠❛t✐♦♥

♠♦❞❡❧ ✐♥ ❛♥ ❡①♣r❡ss✐✈❡ ❧❛♥❣✉❛❣❡✱ r❡❛s♦♥ ❢❛st ✐♥ ❛ ❧✐❣❤t✇❡✐❣❤t ♦♥❡

♦♥t♦❧♦❣②✲❜❛s❡❞ ❞❛t❛❜❛s❡ ❛❝❝❡ss✴❞❛t❛ ♠❛♥❛❣❡♠❡♥t ❞✐str✐❜✉t❡❞ ❖▼❙

❜r✐❞❣❡s ❜❡t✇❡❡♥ ❞✐✛❡r❡♥t ♠♦❞❡❧❧✐♥❣s

▼♦ss❛❦♦✇s❦✐ ❉✐str✐❜✉t❡❞ ❖♥t♦❧♦❣②✱ ▼♦❞❡❧✐♥❣ ❛♥❞ ❙♣❡❝✐✜❝❛t✐♦♥ ▲❛♥❣✉❛❣❡ ✭❉❖▲✮ ✷✵✶✹✲✶✶✲✶✷ ✽

SLIDE 9

▼♦t✐✈❛t✐♦♥ ❖♥t♦■❖♣ ❉❖▲ ❋♦❝✉s❡❞ ❖▼❙ ❖▼❙ ▲✐❜r❛r✐❡s ❈♦♥❝❧✉s✐♦♥

❖♥t♦■❖♣

▼♦ss❛❦♦✇s❦✐ ❉✐str✐❜✉t❡❞ ❖♥t♦❧♦❣②✱ ▼♦❞❡❧✐♥❣ ❛♥❞ ❙♣❡❝✐✜❝❛t✐♦♥ ▲❛♥❣✉❛❣❡ ✭❉❖▲✮ ✷✵✶✹✲✶✶✲✶✷ ✾

SLIDE 10

▼♦t✐✈❛t✐♦♥ ❖♥t♦■❖♣ ❉❖▲ ❋♦❝✉s❡❞ ❖▼❙ ❖▼❙ ▲✐❜r❛r✐❡s ❈♦♥❝❧✉s✐♦♥

◆❡❡❞ ❢♦r ❛ ❯♥✐❢②✐♥❣ ▼❡t❛ ▲❛♥❣✉❛❣❡

◆♦t ②❡t ❛♥♦t❤❡r ❖▼❙ ❧❛♥❣✉❛❣❡✱ ❜✉t ❛ ♠❡t❛ ❧❛♥❣✉❛❣❡ ❝♦✈❡r✐♥❣ ❞✐✈❡rs✐t② ♦❢ ❖▼❙ ❧❛♥❣✉❛❣❡s tr❛♥s❧❛t✐♦♥s ❜❡t✇❡❡♥ t❤❡s❡ ❞✐✈❡rs✐t② ♦❢ ♦♣❡r❛t✐♦♥s ♦♥ ❛♥❞ r❡❧❛t✐♦♥s ❛♠♦♥❣ ❖▼❙ ❈✉rr❡♥t st❛♥❞❛r❞s ❧✐❦❡ t❤❡ ❖❲▲ ❆P■ ♦r t❤❡ ❛❧✐❣♠❡♥t ❆P■ ♦♥❧② ❝♦✈❡r ♣❛rts ♦❢ t❤✐s ❚❤❡ ❖♥t♦❧♦❣②✱ ▼♦❞❡❧✐♥❣ ❛♥❞ ❙♣❡❝✐✜❝❛t✐♦♥ ■♥t❡❣r❛t✐♦♥ ❛♥❞ ■♥t❡r♦♣❡r❛❜✐❧✐t② ✭❖♥t♦■❖♣✮ ✐♥✐t✐❛t✐✈❡ ❛❞❞r❡ss❡s t❤✐s

▼♦ss❛❦♦✇s❦✐ ❉✐str✐❜✉t❡❞ ❖♥t♦❧♦❣②✱ ▼♦❞❡❧✐♥❣ ❛♥❞ ❙♣❡❝✐✜❝❛t✐♦♥ ▲❛♥❣✉❛❣❡ ✭❉❖▲✮ ✷✵✶✹✲✶✶✲✶✷ ✶✵

SLIDE 11

▼♦t✐✈❛t✐♦♥ ❖♥t♦■❖♣ ❉❖▲ ❋♦❝✉s❡❞ ❖▼❙ ❖▼❙ ▲✐❜r❛r✐❡s ❈♦♥❝❧✉s✐♦♥

❚❤❡ ❖♥t♦■❖♣ ✐♥✐t✐❛t✐✈❡ ✭♦♥t♦✐♦♣✳♦r❣✮

st❛rt❡❞ ✐♥ ✷✵✶✶ ❛s ■❙❖ ✶✼✸✹✼ ✇✐t❤✐♥ ■❙❖✴❚❈ ✸✼✴❙❈ ✸ ♥♦✇ ❝♦♥t✐♥✉❡❞ ❛s ❖▼● st❛♥❞❛r❞

❖▼● ❤❛s ♠♦r❡ ❡①♣❡r✐❡♥❝❡ ✇✐t❤ ❢♦r♠❛❧ s❡♠❛♥t✐❝s ❖▼● ❞♦❝✉♠❡♥ts ✇✐❧❧ ❜❡ ❢r❡❡❧② ❛✈❛✐❧❛❜❧❡ ❢♦❝✉s ❡①t❡♥❞❡❞ ❢r♦♠ ♦♥t♦❧♦❣✐❡s ♦♥❧② t♦ ❢♦r♠❛❧ ♠♦❞❡❧s ❛♥❞ s♣❡❝✐✜❝❛t✐♦♥s ✭✐✳❡✳ ❧♦❣✐❝❛❧ t❤❡♦r✐❡s✮ r❡q✉❡st ❢♦r ♣r♦♣♦s❛❧s ✭❘❋P✮ ❤❛s ❜❡❡♥ ✐ss✉❡❞ ✐♥ ❉❡❝❡♠❜❡r ✷✵✶✸ ♣r♦♣♦s❛❧s ❛♥s✇❡r✐♥❣ ❘❋P ❞✉❡ ✐♥ ❉❡❝❡♠❜❡r ✷✵✶✹

✺✵ ❡①♣❡rts ♣❛rt✐❝✐♣❛t❡✱ ∼ ✶✺ ❤❛✈❡ ❝♦♥tr✐❜✉t❡❞ ❖♥t♦■❖♣ ✐s ♦♣❡♥ ❢♦r ②♦✉r ✐❞❡❛s✱ s♦ ❥♦✐♥ ✉s✦ ❉✐str✐❜✉t❡❞ ❖♥t♦❧♦❣②✱ ▼♦❞❡❧✐♥❣ ❛♥❞ ❙♣❡❝✐✜❝❛t✐♦♥ ▲❛♥❣✉❛❣❡

❉❖▲ ❂ ♦♥❡ s♣❡❝✐✜❝ ❛♥s✇❡r t♦ t❤❡ ❘❋P r❡q✉✐r❡♠❡♥ts t❤❡r❡ ♠❛② ❜❡ ♦t❤❡r ❛♥s✇❡rs t♦ t❤❡ ❘❋P ❉❖▲ ✐s ❜❛s❡❞ ♦♥ s♦♠❡ ❣r❛♣❤ ♦❢ ✐♥st✐t✉t✐♦♥s ❛♥❞ ✭❝♦✮♠♦r♣❤✐s♠s ❉❖▲ ❤❛s ❛ ♠♦❞❡❧✲❧❡✈❡❧ ❛♥❞ ❛ t❤❡♦r②✲❧❡✈❡❧ s❡♠❛♥t✐❝s

▼♦ss❛❦♦✇s❦✐ ❉✐str✐❜✉t❡❞ ❖♥t♦❧♦❣②✱ ▼♦❞❡❧✐♥❣ ❛♥❞ ❙♣❡❝✐✜❝❛t✐♦♥ ▲❛♥❣✉❛❣❡ ✭❉❖▲✮ ✷✵✶✹✲✶✶✲✶✷ ✶✶

SLIDE 12

▼♦t✐✈❛t✐♦♥ ❖♥t♦■❖♣ ❉❖▲ ❋♦❝✉s❡❞ ❖▼❙ ❖▼❙ ▲✐❜r❛r✐❡s ❈♦♥❝❧✉s✐♦♥

❉❖▲

▼♦ss❛❦♦✇s❦✐ ❉✐str✐❜✉t❡❞ ❖♥t♦❧♦❣②✱ ▼♦❞❡❧✐♥❣ ❛♥❞ ❙♣❡❝✐✜❝❛t✐♦♥ ▲❛♥❣✉❛❣❡ ✭❉❖▲✮ ✷✵✶✹✲✶✶✲✶✷ ✶✷

SLIDE 13

▼♦t✐✈❛t✐♦♥ ❖♥t♦■❖♣ ❉❖▲ ❋♦❝✉s❡❞ ❖▼❙ ❖▼❙ ▲✐❜r❛r✐❡s ❈♦♥❝❧✉s✐♦♥

❖✈❡r✈✐❡✇ ♦❢ ❉❖▲

✶ ❖▼❙

❜❛s✐❝ ❖▼❙ ✭✢❛tt❡♥❛❜❧❡✮ r❡❢❡r❡♥❝❡s t♦ ♥❛♠❡❞ ❖▼❙ ❡①t❡♥s✐♦♥s✱ ✉♥✐♦♥s✱ tr❛♥s❧❛t✐♦♥s ✭✢❛tt❡♥❛❜❧❡✮ r❡❞✉❝t✐♦♥s✱ ♠✐♥✐♠✐③❛t✐♦♥✱ ♠❛①✐♠✐③❛t✐♦♥ ✭❡❧✉s✐✈❡✮ ❛♣♣r♦①✐♠❛t✐♦♥s✱ ♠♦❞✉❧❡ ❡①tr❛❝t✐♦♥s ✭✢❛tt❡♥❛❜❧❡✮ ❝♦♠❜✐♥❛t✐♦♥✱ ❖▼❙ ❜r✐❞❣❡s ✭✢❛tt❡♥❛❜❧❡✮

♦♥❧② ❖▼❙ ✇✐t❤ ✢❛tt❡♥❛❜❧❡ ❝♦♠♣♦♥❡♥ts ❛r❡ ✢❛tt❡♥❛❜❧❡

✷ ❖▼❙ ♠❛♣♣✐♥❣s ✸ ❖▼❙ ♥❡t✇♦r❦s ✭❜❛s❡❞ ♦♥ ❢♦❝✉s❡❞ ❖▼❙✮

❝♦♥s✐st ♦❢ ❛ ♥✉♠❜❡r ♦❢ ❖▼❙ ❛♥❞ ♠❛♣♣✐♥❣s ✭✐♥t❡r♣r❡t❛t✐♦♥s✱ ❛❧✐❣♥♠❡♥ts ✳ ✳ ✳ ✮

✹ ❖▼❙ ❧✐❜r❛r✐❡s ✭❜❛s❡❞ ♦♥ ❖▼❙✱ ♠❛♣♣✐♥❣s✱ ♥❡t✇♦r❦s✮

❖▼❙ ❞❡✜♥✐t✐♦♥s ✭❣✐✈✐♥❣ ❛ ♥❛♠❡ t♦ ❛♥ ❖▼❙✮ ❞❡✜♥✐t✐♦♥s ♦❢ ✐♥t❡r♣r❡t❛t✐♦♥s ✭♦❢ t❤❡♦r✐❡s✮✱ ❡q✉✐✈❛❧❡♥❝❡s ❞❡✜♥✐t✐♦♥s ♠♦❞✉❧❡ r❡❧❛t✐♦♥s✱ ❛❧✐❣♥♠❡♥ts

▼♦ss❛❦♦✇s❦✐ ❉✐str✐❜✉t❡❞ ❖♥t♦❧♦❣②✱ ▼♦❞❡❧✐♥❣ ❛♥❞ ❙♣❡❝✐✜❝❛t✐♦♥ ▲❛♥❣✉❛❣❡ ✭❉❖▲✮ ✷✵✶✹✲✶✶✲✶✷ ✶✸

SLIDE 14

▼♦t✐✈❛t✐♦♥ ❖♥t♦■❖♣ ❉❖▲ ❋♦❝✉s❡❞ ❖▼❙ ❖▼❙ ▲✐❜r❛r✐❡s ❈♦♥❝❧✉s✐♦♥

❋♦❝✉s❡❞ ❖▼❙

▼♦ss❛❦♦✇s❦✐ ❉✐str✐❜✉t❡❞ ❖♥t♦❧♦❣②✱ ▼♦❞❡❧✐♥❣ ❛♥❞ ❙♣❡❝✐✜❝❛t✐♦♥ ▲❛♥❣✉❛❣❡ ✭❉❖▲✮ ✷✵✶✹✲✶✶✲✶✷ ✶✹

SLIDE 15

▼♦t✐✈❛t✐♦♥ ❖♥t♦■❖♣ ❉❖▲ ❋♦❝✉s❡❞ ❖▼❙ ❖▼❙ ▲✐❜r❛r✐❡s ❈♦♥❝❧✉s✐♦♥

BasicOMS ::= OMSInConformingLanguage MinimizableOMS ::= BasicOMS | OMSRef [ImportName] ExtendingOMS ::= MinimizableOMS | MinimizeKeyword ’{’ MinimizableOMS ’}’ | OMS Extraction OMS ::= ExtendingOMS | OMS Minimization | OMS Translation | OMS Reduction | OMS Approximation | OMS Filtering | OMS ’and’ [ConsStrength] OMS | OMS ’then’ ExtensionOMS | Qualification* ’:’ GroupOMS | OMS ’bridge’ Translation* OMS | ’combine’ NetworkElements [ExcludeExtensions] | ’apply’ SubstName Sentence | GroupOMS GroupOMS ::= ’{’ OMS ’}’ | OMSRef ImportName ::= ’%(’ IRI ’)%’ OMSRef ::= IRI

▼♦ss❛❦♦✇s❦✐ ❉✐str✐❜✉t❡❞ ❖♥t♦❧♦❣②✱ ▼♦❞❡❧✐♥❣ ❛♥❞ ❙♣❡❝✐✜❝❛t✐♦♥ ▲❛♥❣✉❛❣❡ ✭❉❖▲✮ ✷✵✶✹✲✶✶✲✶✷ ✶✺

SLIDE 16

▼♦t✐✈❛t✐♦♥ ❖♥t♦■❖♣ ❉❖▲ ❋♦❝✉s❡❞ ❖▼❙ ❖▼❙ ▲✐❜r❛r✐❡s ❈♦♥❝❧✉s✐♦♥

❇❛s✐❝ ❖▼❙

✇r✐tt❡♥ ✐♥ s♦♠❡ ❖▼❙ ❧❛♥❣✉❛❣❡ ❢r♦♠ t❤❡ ❧♦❣✐❝ ❣r❛♣❤ s❡♠❛♥t✐❝s ✐s ✐♥❤❡r✐t❡❞ ❢r♦♠ t❤❡ ❖▼❙ ❧❛♥❣✉❛❣❡ ❡✳❣✳ ✐♥ ❖❲▲✿

Class: Woman EquivalentTo: Person and Female ObjectProperty: hasParent

❡✳❣✳ ✐♥ ❈♦♠♠♦♥ ▲♦❣✐❝✿

(cl-text PreOrder (forall (x) (le x x)) (forall (x y z) (if (and (le x y) (le y z)) (le x z))))

▼♦ss❛❦♦✇s❦✐ ❉✐str✐❜✉t❡❞ ❖♥t♦❧♦❣②✱ ▼♦❞❡❧✐♥❣ ❛♥❞ ❙♣❡❝✐✜❝❛t✐♦♥ ▲❛♥❣✉❛❣❡ ✭❉❖▲✮ ✷✵✶✹✲✶✶✲✶✷ ✶✻

SLIDE 17

▼♦t✐✈❛t✐♦♥ ❖♥t♦■❖♣ ❉❖▲ ❋♦❝✉s❡❞ ❖▼❙ ❖▼❙ ▲✐❜r❛r✐❡s ❈♦♥❝❧✉s✐♦♥

ExtensionOMS ::= [ExtConsStrength] [ExtensionName] ExtendingOMS ExtensionName ::= ’%(’ IRI ’)%’

▼♦ss❛❦♦✇s❦✐ ❉✐str✐❜✉t❡❞ ❖♥t♦❧♦❣②✱ ▼♦❞❡❧✐♥❣ ❛♥❞ ❙♣❡❝✐✜❝❛t✐♦♥ ▲❛♥❣✉❛❣❡ ✭❉❖▲✮ ✷✵✶✹✲✶✶✲✶✷ ✶✼

SLIDE 18

▼♦t✐✈❛t✐♦♥ ❖♥t♦■❖♣ ❉❖▲ ❋♦❝✉s❡❞ ❖▼❙ ❖▼❙ ▲✐❜r❛r✐❡s ❈♦♥❝❧✉s✐♦♥

❊①t❡♥s✐♦♥s

❖✶ t❤❡♥ ❖✷✿ ❡①t❡♥s✐♦♥ ♦❢ ❖✶ ❜② ♥❡✇ s②♠❜♦❧s ❛♥❞ ❛①✐♦♠s ❖✷ ❡①❛♠♣❧❡ ✐♥ ❖❲▲✿

Class Person Class Female then Class: Woman EquivalentTo: Person and Female

▼♦ss❛❦♦✇s❦✐ ❉✐str✐❜✉t❡❞ ❖♥t♦❧♦❣②✱ ▼♦❞❡❧✐♥❣ ❛♥❞ ❙♣❡❝✐✜❝❛t✐♦♥ ▲❛♥❣✉❛❣❡ ✭❉❖▲✮ ✷✵✶✹✲✶✶✲✶✷ ✶✽

SLIDE 19

▼♦t✐✈❛t✐♦♥ ❖♥t♦■❖♣ ❉❖▲ ❋♦❝✉s❡❞ ❖▼❙ ❖▼❙ ▲✐❜r❛r✐❡s ❈♦♥❝❧✉s✐♦♥

▼♦ss❛❦♦✇s❦✐ ❉✐str✐❜✉t❡❞ ❖♥t♦❧♦❣②✱ ▼♦❞❡❧✐♥❣ ❛♥❞ ❙♣❡❝✐✜❝❛t✐♦♥ ▲❛♥❣✉❛❣❡ ✭❉❖▲✮ ✷✵✶✹✲✶✶✲✶✷ ✶✾

SLIDE 20

▼♦t✐✈❛t✐♦♥ ❖♥t♦■❖♣ ❉❖▲ ❋♦❝✉s❡❞ ❖▼❙ ❖▼❙ ▲✐❜r❛r✐❡s ❈♦♥❝❧✉s✐♦♥

❊①t❡♥s✐♦♥s ✇✐t❤ ❛♥♥♦t❛t✐♦♥s

❖✶ t❤❡♥ ✪♠❝♦♥s ❖✷✿ ♠♦❞❡❧✲❝♦♥s❡r✈❛t✐✈❡ ❡①t❡♥s✐♦♥

❡❛❝❤ ❖✶✲♠♦❞❡❧ ❤❛s ❛♥ ❡①♣❛♥s✐♦♥ t♦ ❖✶ t❤❡♥ ❖✷

❖✶ t❤❡♥ ✪❝❝♦♥s ❖✷✿ ❝♦♥s❡q✉❡♥❝❡✲❝♦♥s❡r✈❛t✐✈❡ ❡①t❡♥s✐♦♥

❖✶ t❤❡♥ ❖✷ | = ϕ ✐♠♣❧✐❡s ❖✶ | = ϕ✱ ❢♦r ϕ ✐♥ t❤❡ ❧❛♥❣✉❛❣❡ ♦❢ ❖✶

❖✶ t❤❡♥ ✪❞❡❢ ❖✷✿ ❞❡✜♥✐t✐♦♥❛❧ ❡①t❡♥s✐♦♥

❡❛❝❤ ❖✶✲♠♦❞❡❧ ❤❛s ❛ ✉♥✐q✉❡ ❡①♣❛♥s✐♦♥ t♦ ❖✶ t❤❡♥ ❖✷

❖✶ t❤❡♥ ✪✐♠♣❧✐❡s ❖✷✿ ❧✐❦❡ ✪♠❝♦♥s✱ ❜✉t ❖✷ ♠✉st ♥♦t ❡①t❡♥❞ t❤❡ s✐❣♥❛t✉r❡ ❡①❛♠♣❧❡ ✐♥ ❖❲▲✿

Class Person Class Female then %def Class: Woman EquivalentTo: Person and Female

▼♦ss❛❦♦✇s❦✐ ❉✐str✐❜✉t❡❞ ❖♥t♦❧♦❣②✱ ▼♦❞❡❧✐♥❣ ❛♥❞ ❙♣❡❝✐✜❝❛t✐♦♥ ▲❛♥❣✉❛❣❡ ✭❉❖▲✮ ✷✵✶✹✲✶✶✲✶✷ ✷✵

SLIDE 21

▼♦t✐✈❛t✐♦♥ ❖♥t♦■❖♣ ❉❖▲ ❋♦❝✉s❡❞ ❖▼❙ ❖▼❙ ▲✐❜r❛r✐❡s ❈♦♥❝❧✉s✐♦♥

❘❡❢❡r❡♥❝❡s t♦ ◆❛♠❡❞ ❖▼❙

❘❡❢❡r❡♥❝❡ t♦ ❛♥ ❖▼❙ ❡①✐st✐♥❣ ♦♥ t❤❡ ❲❡❜ ✇r✐tt❡♥ ❞✐r❡❝t❧② ❛s ❛ ❯❘▲ ✭♦r ■❘■✮ Pr❡✜①✐♥❣ ♠❛② ❜❡ ✉s❡❞ ❢♦r ❛❜❜r❡✈✐❛t✐♦♥

http://owl.cs.manchester.ac.uk/co-ode-files/

ntologies/pizza.owl

co-ode:pizza.owl

❙❡♠❛♥t✐❝s ❘❡❢❡r❡♥❝❡ t♦ ◆❛♠❡❞ ❖▼❙✿ [ [✐r✐] ]Γ = Γ(✐r✐)

▼♦ss❛❦♦✇s❦✐ ❉✐str✐❜✉t❡❞ ❖♥t♦❧♦❣②✱ ▼♦❞❡❧✐♥❣ ❛♥❞ ❙♣❡❝✐✜❝❛t✐♦♥ ▲❛♥❣✉❛❣❡ ✭❉❖▲✮ ✷✵✶✹✲✶✶✲✶✷ ✷✶

SLIDE 22

▼♦t✐✈❛t✐♦♥ ❖♥t♦■❖♣ ❉❖▲ ❋♦❝✉s❡❞ ❖▼❙ ❖▼❙ ▲✐❜r❛r✐❡s ❈♦♥❝❧✉s✐♦♥

❯♥✐♦♥s

❖✶ ❛♥❞ ❖✷✿ ✉♥✐♦♥ ♦❢ t✇♦ st❛♥❞✲❛❧♦♥❡ ❖▼❙ ✭❢♦r ❡①t❡♥s✐♦♥s ❖✷ ♥❡❡❞s t♦ ❜❡ ❜❛s✐❝✮ ❙✐❣♥❛t✉r❡s ✭❛♥❞ ❛①✐♦♠s✮ ❛r❡ ✉♥✐t❡❞ ♠♦❞❡❧ ❝❧❛ss❡s ❛r❡ ✐♥t❡rs❡❝t❡❞

algebra:Monoid and algebra:Commutative

▼♦ss❛❦♦✇s❦✐ ❉✐str✐❜✉t❡❞ ❖♥t♦❧♦❣②✱ ▼♦❞❡❧✐♥❣ ❛♥❞ ❙♣❡❝✐✜❝❛t✐♦♥ ▲❛♥❣✉❛❣❡ ✭❉❖▲✮ ✷✵✶✹✲✶✶✲✶✷ ✷✷

SLIDE 23

▼♦t✐✈❛t✐♦♥ ❖♥t♦■❖♣ ❉❖▲ ❋♦❝✉s❡❞ ❖▼❙ ❖▼❙ ▲✐❜r❛r✐❡s ❈♦♥❝❧✉s✐♦♥

Translation ::= ’with’ LogicTranslation* [SymbolMapItems] SymbolMapItems ::= SymbolOrMap ( ’,’ SymbolOrMap )* LogicTranslation ::= ’translation’ OMSLangTrans SymbolMap ::= Symbol ’$\mapsto$’ Symbol SymbolOrMap ::= Symbol | SymbolMap LoLaRef ::= LanguageRef | LogicRef OMSLangTrans ::= OMSLangTransRef | ’<$\to$>’ LoLaRef OMSLangTransRef ::= IRI

▼♦ss❛❦♦✇s❦✐ ❉✐str✐❜✉t❡❞ ❖♥t♦❧♦❣②✱ ▼♦❞❡❧✐♥❣ ❛♥❞ ❙♣❡❝✐✜❝❛t✐♦♥ ▲❛♥❣✉❛❣❡ ✭❉❖▲✮ ✷✵✶✹✲✶✶✲✶✷ ✷✸

SLIDE 24

▼♦t✐✈❛t✐♦♥ ❖♥t♦■❖♣ ❉❖▲ ❋♦❝✉s❡❞ ❖▼❙ ❖▼❙ ▲✐❜r❛r✐❡s ❈♦♥❝❧✉s✐♦♥

❚r❛♥s❧❛t✐♦♥s

❖ ✇✐t❤ σ✱ ✇❤❡r❡ σ ✐s ❛ s✐❣♥❛t✉r❡ ♠♦r♣❤✐s♠ ❖ ✇✐t❤ tr❛♥s❧❛t✐♦♥ ρ✱ ✇❤❡r❡ ρ ✐s ❛♥ ✐♥st✐t✉t✐♦♥ ❝♦♠♦r♣❤✐s♠

ObjectProperty: isProperPartOf Characteristics: Asymmetric SubPropertyOf: isPartOf with translation trans:SROIQtoCL then (if (and (isProperPartOf x y) (isProperPartOf y z)) (isProperPartOf x z)) %% transitivity; can’t be expressed in OWL together %% with asymmetry

▼♦ss❛❦♦✇s❦✐ ❉✐str✐❜✉t❡❞ ❖♥t♦❧♦❣②✱ ▼♦❞❡❧✐♥❣ ❛♥❞ ❙♣❡❝✐✜❝❛t✐♦♥ ▲❛♥❣✉❛❣❡ ✭❉❖▲✮ ✷✵✶✹✲✶✶✲✶✷ ✷✹

SLIDE 25

▼♦t✐✈❛t✐♦♥ ❖♥t♦■❖♣ ❉❖▲ ❋♦❝✉s❡❞ ❖▼❙ ❖▼❙ ▲✐❜r❛r✐❡s ❈♦♥❝❧✉s✐♦♥

❍✐❞❡ ✕ ❊①tr❛❝t ✕ ❋♦r❣❡t ✕ ❙❡❧❡❝t

❤✐❞❡✴r❡✈❡❛❧ r❡♠♦✈❡ ✴ ❡①tr❛❝t ❢♦r❣❡t✴❦❡❡♣ s❡❧❡❝t✴r❡❥❡❝t s❡♠❛♥t✐❝ ❜❛❝❦❣r♦✉♥❞ ♠♦❞❡❧ r❡❞✉❝t ❝♦♥s❡r✈❛t✐✈❡ ❡①t❡♥s✐♦♥ ✉♥✐❢♦r♠ ✐♥t❡r♣♦❧❛t✐♦♥ t❤❡♦r② ✜❧t❡r✐♥❣ r❡❧❛t✐♦♥ t♦ ♦r✐❣✐♥❛❧ ✐♥t❡r♣r❡t❛❜❧❡ s✉❜t❤❡♦r② ✐♥t❡r♣r❡t❛❜❧❡ s✉❜t❤❡♦r② ❛♣♣r♦❛❝❤ ♠♦❞❡❧ ❧❡✈❡❧ t❤❡♦r② ❧❡✈❡❧ t❤❡♦r② ❧❡✈❡❧ t❤❡♦r② ❧❡✈❡❧ t②♣❡ ♦❢ ❖▼❙ ❡❧✉s✐✈❡ ✢❛tt❡♥❛❜❧❡ ✢❛tt❡♥❛❜❧❡ ✢❛tt❡♥❛❜❧❡ s✐❣♥❛t✉r❡ ♦❢ r❡s✉❧t = Σ ≥ Σ = Σ ≥ Σ ❝❤❛♥❣❡ ♦❢ ❧♦❣✐❝ ♣♦ss✐❜❧❡ ♥♦t ♣♦ss✐❜❧❡ ♣♦ss✐❜❧❡ ♥♦t ♣♦ss✐❜❧❡ ❛♣♣❧✐❝❛t✐♦♥ s♣❡❝✐✜❝❛t✐♦♥ ♦♥t♦❧♦❣✐❡s ♦♥t♦❧♦❣✐❡s ❜❧❡♥❞✐♥❣

▼♦ss❛❦♦✇s❦✐ ❉✐str✐❜✉t❡❞ ❖♥t♦❧♦❣②✱ ▼♦❞❡❧✐♥❣ ❛♥❞ ❙♣❡❝✐✜❝❛t✐♦♥ ▲❛♥❣✉❛❣❡ ✭❉❖▲✮ ✷✵✶✹✲✶✶✲✶✷ ✷✺

SLIDE 26

▼♦t✐✈❛t✐♦♥ ❖♥t♦■❖♣ ❉❖▲ ❋♦❝✉s❡❞ ❖▼❙ ❖▼❙ ▲✐❜r❛r✐❡s ❈♦♥❝❧✉s✐♦♥

Reduction ::= ’hide’ LogicReduction* [SymbolItems] | ’reveal’ [SymbolMapItems] SymbolItems ::= Symbol ( ’,’ Symbol )* LogicReduction ::= ’along’ OMSLangTrans

▼♦ss❛❦♦✇s❦✐ ❉✐str✐❜✉t❡❞ ❖♥t♦❧♦❣②✱ ▼♦❞❡❧✐♥❣ ❛♥❞ ❙♣❡❝✐✜❝❛t✐♦♥ ▲❛♥❣✉❛❣❡ ✭❉❖▲✮ ✷✵✶✹✲✶✶✲✶✷ ✷✻

SLIDE 27

▼♦t✐✈❛t✐♦♥ ❖♥t♦■❖♣ ❉❖▲ ❋♦❝✉s❡❞ ❖▼❙ ❖▼❙ ▲✐❜r❛r✐❡s ❈♦♥❝❧✉s✐♦♥

❘❡❞✉❝t✐♦♥✿ ❍✐❞❡✴r❡✈❡❛❧

✐♥t✉✐t✐♦♥✿ s♦♠❡ ❧♦❣✐❝❛❧ ♦r ♥♦♥✲❧♦❣✐❝❛❧ s②♠❜♦❧s ❛r❡ ❤✐❞❞❡♥✱ ❜✉t t❤❡ s❡♠❛♥t✐❝ ❡✛❡❝t ♦❢ s❡♥t❡♥❝❡s ✭❛❧s♦ t❤♦s❡ ✐♥✈♦❧✈✐♥❣ t❤❡s❡ s②♠❜♦❧s✮ ✐s ❦❡♣t ❖ r❡✈❡❛❧ Σ✱ ✇❤❡r❡ Σ ✐s ❛ s✉❜s✐❣♥❛t✉r❡ ♦❢ t❤❛t ♦❢ ❖ ❖ ❤✐❞❡ Σ✱ ✇❤❡r❡ Σ ✐s ❛ s✉❜s✐❣♥❛t✉r❡ ♦❢ t❤❛t ♦❢ ❖ ❖ ❤✐❞❡ ❛❧♦♥❣ µ✱ ✇❤❡r❡ µ ✐s ❛♥ ✐♥st✐t✉t✐♦♥ ♠♦r♣❤✐s♠

▼♦ss❛❦♦✇s❦✐ ❉✐str✐❜✉t❡❞ ❖♥t♦❧♦❣②✱ ▼♦❞❡❧✐♥❣ ❛♥❞ ❙♣❡❝✐✜❝❛t✐♦♥ ▲❛♥❣✉❛❣❡ ✭❉❖▲✮ ✷✵✶✹✲✶✶✲✶✷ ✷✼

SLIDE 28

▼♦t✐✈❛t✐♦♥ ❖♥t♦■❖♣ ❉❖▲ ❋♦❝✉s❡❞ ❖▼❙ ❖▼❙ ▲✐❜r❛r✐❡s ❈♦♥❝❧✉s✐♦♥

❘❡❞✉❝t✐♦♥✿ ❡①❛♠♣❧❡

sort Elem

ps 0:Elem; __+__:Elem*Elem->Elem; inv:Elem->Elem

forall x,y,z:elem . x+0=x . x+(y+z) = (x+y)+z . x+inv(x)=0 hide inv

❙❡♠❛♥t✐❝s✿ ❝❧❛ss ♦❢ ❛❧❧ ♠♦♥♦✐❞s t❤❛t ❝❛♥ ❜❡ ❡①t❡♥❞❡❞ ✇✐t❤ ❛♥ ✐♥✈❡rs❡✱ ✐✳❡✳ ❝❧❛ss ♦❢ ❛❧❧ ❣r♦✉♣s✳ ❚❤❡ ❡✛❡❝t ✐s s❡❝♦♥❞✲♦r❞❡r q✉❛♥t✐✜❝❛t✐♦♥✿

sort Elem

ps 0:Elem; __+__:Elem*Elem->Elem;

exists inv:Elem->Elem . forall x,y,z:elem . x+0=x /\ x+(y+z) = (x+y)+z /\ x+inv(x)=0 hide inv

▼♦ss❛❦♦✇s❦✐ ❉✐str✐❜✉t❡❞ ❖♥t♦❧♦❣②✱ ▼♦❞❡❧✐♥❣ ❛♥❞ ❙♣❡❝✐✜❝❛t✐♦♥ ▲❛♥❣✉❛❣❡ ✭❉❖▲✮ ✷✵✶✹✲✶✶✲✶✷ ✷✽

SLIDE 29

▼♦t✐✈❛t✐♦♥ ❖♥t♦■❖♣ ❉❖▲ ❋♦❝✉s❡❞ ❖▼❙ ❖▼❙ ▲✐❜r❛r✐❡s ❈♦♥❝❧✉s✐♦♥

Extraction ::= ’extract’ ModuleProperties InterfaceSignature | ’remove’ ModuleProperties InterfaceSignature ModuleProperties ::= Conservative | ’%min’ | ’%depliting’ | ’%safe’ InterfaceSignature ::= SymbolItems SymbolItems ::= Symbol ( ’,’ Symbol )*

▼♦ss❛❦♦✇s❦✐ ❉✐str✐❜✉t❡❞ ❖♥t♦❧♦❣②✱ ▼♦❞❡❧✐♥❣ ❛♥❞ ❙♣❡❝✐✜❝❛t✐♦♥ ▲❛♥❣✉❛❣❡ ✭❉❖▲✮ ✷✵✶✹✲✶✶✲✶✷ ✷✾

SLIDE 30

▼♦t✐✈❛t✐♦♥ ❖♥t♦■❖♣ ❉❖▲ ❋♦❝✉s❡❞ ❖▼❙ ❖▼❙ ▲✐❜r❛r✐❡s ❈♦♥❝❧✉s✐♦♥

▼♦❞✉❧❡ ❊①tr❛❝t✐♦♥✿ r❡♠♦✈❡✴❡①tr❛❝t

❖ ❡①tr❛❝t Σ Σ✿ r❡str✐❝t✐♦♥ s✐❣♥❛t✉r❡ ✭s✉❜s✐❣♥❛t✉r❡ ♦❢ t❤❛t ♦❢ ❖✮ ❖ ♠✉st ❜❡ ❛ ❝♦♥s❡r✈❛t✐✈❡ ❡①t❡♥s✐♦♥ ♦❢ t❤❡ r❡s✉❧t✐♥❣ ❡①tr❛❝t❡❞ ♠♦❞✉❧❡✳ ✭■❢ ♥♦t✱ t❤❡ ♠♦❞✉❧❡ ✐s s✉✐t❛❜❧② ❡♥❧❛r❣❡❞✳✮ ❉✉❛❧❧②✿ ❖ r❡♠♦✈❡ Σ ◆♦t❡✿ ❚❤❡ ❡①tr❛❝t✐♦♥ ♠❡t❤♦❞s ❢r♦♠ t❤❡ ❧✐t❡r❛t✉r❡ ❛❧❧ ❣✉❛r❛♥t❡❡ ♠♦❞❡❧✲t❤❡♦r❡t✐❝ ❝♦♥s❡r✈❛t✐✈✐t②✳

▼♦ss❛❦♦✇s❦✐ ❉✐str✐❜✉t❡❞ ❖♥t♦❧♦❣②✱ ▼♦❞❡❧✐♥❣ ❛♥❞ ❙♣❡❝✐✜❝❛t✐♦♥ ▲❛♥❣✉❛❣❡ ✭❉❖▲✮ ✷✵✶✹✲✶✶✲✶✷ ✸✵

SLIDE 31

▼♦t✐✈❛t✐♦♥ ❖♥t♦■❖♣ ❉❖▲ ❋♦❝✉s❡❞ ❖▼❙ ❖▼❙ ▲✐❜r❛r✐❡s ❈♦♥❝❧✉s✐♦♥

▼♦❞✉❧❡ ❊①tr❛❝t✐♦♥✿ ❡①❛♠♣❧❡

sort Elem

ps 0:Elem; __+__:Elem*Elem->Elem; inv:Elem->Elem

forall x,y,z:elem . x+0=x . x+(y+z) = (x+y)+z . x+inv(x) = 0 remove inv

❚❤❡ s❡♠❛♥t✐❝s ✐s t❤❡ ❢♦❧❧♦✇✐♥❣ t❤❡♦r②✿

sort Elem

ps 0:Elem; __+__:Elem*Elem->Elem; inv:Elem->Elem

forall x,y,z:elem . x+0=x . x+(y+z) = (x+y)+z . x+inv(x) = 0

❚❤❡ ♠♦❞✉❧❡ ♥❡❡❞s t♦ ❜❡ ❡♥❧❛r❣❡❞ t♦ t❤❡ ✇❤♦❧❡ ❖▼❙✳

▼♦ss❛❦♦✇s❦✐ ❉✐str✐❜✉t❡❞ ❖♥t♦❧♦❣②✱ ▼♦❞❡❧✐♥❣ ❛♥❞ ❙♣❡❝✐✜❝❛t✐♦♥ ▲❛♥❣✉❛❣❡ ✭❉❖▲✮ ✷✵✶✹✲✶✶✲✶✷ ✸✶

SLIDE 32

▼♦t✐✈❛t✐♦♥ ❖♥t♦■❖♣ ❉❖▲ ❋♦❝✉s❡❞ ❖▼❙ ❖▼❙ ▲✐❜r❛r✐❡s ❈♦♥❝❧✉s✐♦♥

▼♦❞✉❧❡ ❊①tr❛❝t✐♦♥✿ ✷♥❞ ❡①❛♠♣❧❡

sort Elem

ps 0:Elem; __+__:Elem*Elem->Elem; inv:Elem->Elem

forall x,y,z:elem . x+0=x . x+(y+z) = (x+y)+z . x+inv(x) = 0 . exists y:Elem . x+y=0 remove inv

❚❤❡ s❡♠❛♥t✐❝s ✐s t❤❡ ❢♦❧❧♦✇✐♥❣ t❤❡♦r②✿

sort Elem

ps 0:Elem; __+__:Elem*Elem->Elem

forall x,y,z:elem . x+0=x . x+(y+z) = (x+y)+z . exists y:Elem . x+y=0

❍❡r❡✱ ❛❞❞✐♥❣ inv ✐s ❝♦♥s❡r✈❛t✐✈❡✳

▼♦ss❛❦♦✇s❦✐ ❉✐str✐❜✉t❡❞ ❖♥t♦❧♦❣②✱ ▼♦❞❡❧✐♥❣ ❛♥❞ ❙♣❡❝✐✜❝❛t✐♦♥ ▲❛♥❣✉❛❣❡ ✭❉❖▲✮ ✷✵✶✹✲✶✶✲✶✷ ✸✷

SLIDE 33

▼♦t✐✈❛t✐♦♥ ❖♥t♦■❖♣ ❉❖▲ ❋♦❝✉s❡❞ ❖▼❙ ❖▼❙ ▲✐❜r❛r✐❡s ❈♦♥❝❧✉s✐♦♥

Approximation ::= ’forget’ InterfaceSignature [’with’ LogicRef] | ’keep’ InterfaceSignature [’with’ LogicRef] InterfaceSignature ::= SymbolItems SymbolItems ::= Symbol ( ’,’ Symbol )*

▼♦ss❛❦♦✇s❦✐ ❉✐str✐❜✉t❡❞ ❖♥t♦❧♦❣②✱ ▼♦❞❡❧✐♥❣ ❛♥❞ ❙♣❡❝✐✜❝❛t✐♦♥ ▲❛♥❣✉❛❣❡ ✭❉❖▲✮ ✷✵✶✹✲✶✶✲✶✷ ✸✸

SLIDE 34

▼♦t✐✈❛t✐♦♥ ❖♥t♦■❖♣ ❉❖▲ ❋♦❝✉s❡❞ ❖▼❙ ❖▼❙ ▲✐❜r❛r✐❡s ❈♦♥❝❧✉s✐♦♥

■♥t❡r♣♦❧❛t✐♦♥✿ ❢♦r❣❡t✴❦❡❡♣

❖ ❦❡❡♣ ✐♥ Σ✱ ✇❤❡r❡ Σ ✐s ❛ s✉❜s✐❣♥❛t✉r❡ ♦❢ t❤❛t ♦❢ ❖ ❖ ❦❡❡♣ ✐♥ Σ ✇✐t❤ ■✱ ✇❤❡r❡ Σ ✐s ❛ s✉❜s✐❣♥❛t✉r❡ ♦❢ t❤❛t ♦❢ ❖✱ ❛♥❞ ■ ✐s ❛ s✉❜✐♥st✐t✉t✐♦♥ ♦❢ t❤❛t ♦❢ ❖ ❖ ❦❡❡♣ ✐♥ ■✱ ✇❤❡r❡ ■ ✐s ❛ s✉❜✐♥st✐t✉t✐♦♥ ♦❢ t❤❛t ♦❢ ❖

✐♥t✉✐t✐♦♥✿ t❤❡♦r② ♦❢ ❖ ✐s ✐♥t❡r♣♦❧❛t❡❞ ✐♥ s♠❛❧❧❡r s✐❣♥❛t✉r❡✴❧♦❣✐❝

❞✉❛❧❧②

❖ ❢♦r❣❡t Σ ❖ ❢♦r❣❡t Σ ✇✐t❤ ■

▼♦ss❛❦♦✇s❦✐ ❉✐str✐❜✉t❡❞ ❖♥t♦❧♦❣②✱ ▼♦❞❡❧✐♥❣ ❛♥❞ ❙♣❡❝✐✜❝❛t✐♦♥ ▲❛♥❣✉❛❣❡ ✭❉❖▲✮ ✷✵✶✹✲✶✶✲✶✷ ✸✹

SLIDE 35

▼♦t✐✈❛t✐♦♥ ❖♥t♦■❖♣ ❉❖▲ ❋♦❝✉s❡❞ ❖▼❙ ❖▼❙ ▲✐❜r❛r✐❡s ❈♦♥❝❧✉s✐♦♥

■♥t❡r♣♦❧❛t✐♦♥✿ ❡①❛♠♣❧❡

sort Elem

ps 0:Elem; __+__:Elem*Elem->Elem; inv:Elem->Elem

forall x,y,z:elem . x+0=x . x+(y+z) = (x+y)+z . x+inv(x) = 0 forget inv

❚❤❡ s❡♠❛♥t✐❝s ✐s t❤❡ ❢♦❧❧♦✇✐♥❣ t❤❡♦r②✿

sort Elem

ps 0:Elem; __+__:Elem*Elem->Elem

forall x,y,z:elem . x+0=x . x+(y+z) = (x+y)+z . exists y:Elem . x+y=0

❈♦♠♣✉t✐♥❣ ✐♥t❡r♣♦❧❛♥ts ❝❛♥ ❜❡ ❤❛r❞✱ ❡✈❡♥ ✉♥❞❡❝✐❞❛❜❧❡✳

▼♦ss❛❦♦✇s❦✐ ❉✐str✐❜✉t❡❞ ❖♥t♦❧♦❣②✱ ▼♦❞❡❧✐♥❣ ❛♥❞ ❙♣❡❝✐✜❝❛t✐♦♥ ▲❛♥❣✉❛❣❡ ✭❉❖▲✮ ✷✵✶✹✲✶✶✲✶✷ ✸✺

SLIDE 36

▼♦t✐✈❛t✐♦♥ ❖♥t♦■❖♣ ❉❖▲ ❋♦❝✉s❡❞ ❖▼❙ ❖▼❙ ▲✐❜r❛r✐❡s ❈♦♥❝❧✉s✐♦♥

Filtering ::= ’select’ BasicOMS | ’reject’ BasicOMS

▼♦ss❛❦♦✇s❦✐ ❉✐str✐❜✉t❡❞ ❖♥t♦❧♦❣②✱ ▼♦❞❡❧✐♥❣ ❛♥❞ ❙♣❡❝✐✜❝❛t✐♦♥ ▲❛♥❣✉❛❣❡ ✭❉❖▲✮ ✷✵✶✹✲✶✶✲✶✷ ✸✻

SLIDE 37

▼♦t✐✈❛t✐♦♥ ❖♥t♦■❖♣ ❉❖▲ ❋♦❝✉s❡❞ ❖▼❙ ❖▼❙ ▲✐❜r❛r✐❡s ❈♦♥❝❧✉s✐♦♥

❋✐❧t❡r✐♥❣

❖ s❡❧❡❝t ❚✱ ✇❤❡r❡ ❚ ✐s ❛ s✉❜t❤❡♦r② ✭❢r❛❣♠❡♥t✮ ♦❢ t❤❛t ♦❢ ❖

✐♥t✉✐t✐♦♥✿ ❛①✐♦♠s ✐♥✈♦❧✈✐♥❣ ♦♥❧② s②♠❜♦❧s ✐♥ ❙✐❣(❚) ❛r❡ ❦❡♣t ♠♦r❡♦✈❡r✱ ❛❧❧ ❛①✐♦♠s ❝♦♥t❛✐♥❡❞ ✐♥ ❚ ❛r❡ ❦❡♣t ❛s ✇❡❧❧

❖ r❡❥❡❝t ❚✱ ✇❤❡r❡ ❚ ✐s ❛ s✉❜t❤❡♦r② ✭❢r❛❣♠❡♥t✮ ♦❢ t❤❛t ♦❢ ❖

✐♥t✉✐t✐♦♥✿ ❛❧❧ ❛①✐♦♠s ✐♥✈♦❧✈✐♥❣ s②♠❜♦❧s ✐♥ ❙✐❣(❚) ❛r❡ ❞❡❧❡t❡❞ ♠♦r❡♦✈❡r✱ ❛❧❧ ❛①✐♦♠s ❝♦♥t❛✐♥❡❞ ✐♥ ❚ ❛r❡ ❞❡❧❡t❡❞ ❛s ✇❡❧❧

▼♦ss❛❦♦✇s❦✐ ❉✐str✐❜✉t❡❞ ❖♥t♦❧♦❣②✱ ▼♦❞❡❧✐♥❣ ❛♥❞ ❙♣❡❝✐✜❝❛t✐♦♥ ▲❛♥❣✉❛❣❡ ✭❉❖▲✮ ✷✵✶✹✲✶✶✲✶✷ ✸✼

SLIDE 38

▼♦t✐✈❛t✐♦♥ ❖♥t♦■❖♣ ❉❖▲ ❋♦❝✉s❡❞ ❖▼❙ ❖▼❙ ▲✐❜r❛r✐❡s ❈♦♥❝❧✉s✐♦♥

❋✐❧t❡r✐♥❣✿ ❡①❛♠♣❧❡

sort Elem

ps 0:Elem; __+__:Elem*Elem->Elem; inv:Elem->Elem

forall x,y,z:elem . x+0=x . x+(y+z) = (x+y)+z . x+inv(x) = 0 reject inv

❚❤❡ s❡♠❛♥t✐❝s ✐s t❤❡ ❢♦❧❧♦✇✐♥❣ t❤❡♦r②✿

sort Elem

ps 0:Elem; __+__:Elem*Elem->Elem

forall x,y,z:elem . x+0=x . x+(y+z) = (x+y)+z

▼♦ss❛❦♦✇s❦✐ ❉✐str✐❜✉t❡❞ ❖♥t♦❧♦❣②✱ ▼♦❞❡❧✐♥❣ ❛♥❞ ❙♣❡❝✐✜❝❛t✐♦♥ ▲❛♥❣✉❛❣❡ ✭❉❖▲✮ ✷✵✶✹✲✶✶✲✶✷ ✸✽

SLIDE 39

▼♦t✐✈❛t✐♦♥ ❖♥t♦■❖♣ ❉❖▲ ❋♦❝✉s❡❞ ❖▼❙ ❖▼❙ ▲✐❜r❛r✐❡s ❈♦♥❝❧✉s✐♦♥

❍✐❞❡ ✕ ❊①tr❛❝t ✕ ❋♦r❣❡t ✕ ❙❡❧❡❝t

▼♦ss❛❦♦✇s❦✐ ❉✐str✐❜✉t❡❞ ❖♥t♦❧♦❣②✱ ▼♦❞❡❧✐♥❣ ❛♥❞ ❙♣❡❝✐✜❝❛t✐♦♥ ▲❛♥❣✉❛❣❡ ✭❉❖▲✮ ✷✵✶✹✲✶✶✲✶✷ ✸✾

SLIDE 40

▼♦t✐✈❛t✐♦♥ ❖♥t♦■❖♣ ❉❖▲ ❋♦❝✉s❡❞ ❖▼❙ ❖▼❙ ▲✐❜r❛r✐❡s ❈♦♥❝❧✉s✐♦♥

❘❡❞✉❝t✐♦♥✿ s♣❡❝✐✜❝❛t✐♦♥ ❡①❛♠♣❧❡

spec List = sort Elem free type List[Elem] ::= [] | __::__(Elem; List[Elem]) pred __elem__ : Elem * List[Elem} forall x,y:Elem; L,L1,L2:List[Elem] . not x elem [] . x elem (y :: L) <=> x=y \/ x elem L spec Sorting = List then preds is_ordered : List[Elem]; permutation : List[Elem] * List[Elem]

p sorter : List[Elem]->List[Elem]

forall x,y:Elem; L,L1,L2:List[Elem] . is_ordered([]) . is_ordered(x::[]) . is_ordered(x::y::L) <=> x<=y /\ is_ordered(y::L) . permutation(L1,L2) <=> (forall x:Elem . x elem L1 <=> x elem L2) . is_ordered(sorter(L)) . permutation(L,sorter(L)) hide permutation, is_ordered

▼♦ss❛❦♦✇s❦✐ ❉✐str✐❜✉t❡❞ ❖♥t♦❧♦❣②✱ ▼♦❞❡❧✐♥❣ ❛♥❞ ❙♣❡❝✐✜❝❛t✐♦♥ ▲❛♥❣✉❛❣❡ ✭❉❖▲✮ ✷✵✶✹✲✶✶✲✶✷ ✹✵

SLIDE 41

▼♦t✐✈❛t✐♦♥ ❖♥t♦■❖♣ ❉❖▲ ❋♦❝✉s❡❞ ❖▼❙ ❖▼❙ ▲✐❜r❛r✐❡s ❈♦♥❝❧✉s✐♦♥

❘❡❧❛t✐♦♥s ❛♠♦♥❣ t❤❡ ❞✐✛❡r❡♥t ♥♦t✐♦♥s

▼♦❞(❖ ❤✐❞❡ Σ) = ▼♦❞(❖ r❡♠♦✈❡ Σ)|❙✐❣(❖)\Σ ⊆ ▼♦❞(❖ ❢♦r❣❡t Σ) ⊆ ▼♦❞(❖ r❡❥❡❝t Σ)

▼♦ss❛❦♦✇s❦✐ ❉✐str✐❜✉t❡❞ ❖♥t♦❧♦❣②✱ ▼♦❞❡❧✐♥❣ ❛♥❞ ❙♣❡❝✐✜❝❛t✐♦♥ ▲❛♥❣✉❛❣❡ ✭❉❖▲✮ ✷✵✶✹✲✶✶✲✶✷ ✹✶

SLIDE 42

▼♦t✐✈❛t✐♦♥ ❖♥t♦■❖♣ ❉❖▲ ❋♦❝✉s❡❞ ❖▼❙ ❖▼❙ ▲✐❜r❛r✐❡s ❈♦♥❝❧✉s✐♦♥

Pr♦s ❛♥❞ ❈♦♥s

❤✐❞❡✴r❡✈❡❛❧ r❡♠♦✈❡ ✴ ❡①tr❛❝t ❢♦r❣❡t✴❦❡❡♣ s❡❧❡❝t✴r❡❥❡❝t ✐♥❢♦r♠❛t✐♦♥ ❧♦ss ♥♦♥❡ ♥♦♥❡ ♠✐♥✐♠❛❧ ❧❛r❣❡ ❝♦♠♣✉t❛❜✐❧✐t② ❜❛❞ ❣♦♦❞✴❞❡♣❡♥❞s ❞❡♣❡♥❞s ❡❛s② s✐❣♥❛t✉r❡ ♦❢ r❡s✉❧t = Σ ≥ Σ = Σ = Σ ❝❤❛♥❣❡ ♦❢ ❧♦❣✐❝ ♣♦ss✐❜❧❡ ♥♦t ♣♦ss✐❜❧❡ ♣♦ss✐❜❧❡ ♥♦t ♣♦ss✐❜❧❡ ❝♦♥❝❡♣t✉❛❧ s✐♠♣❧✐❝✐t② s✐♠♣❧❡ ✭❜✉t ✉♥✐♥t✉✐t✐✈❡✮ ❝♦♠♣❧❡① ❢❛r✐❧② s✐♠♣❧❡ s✐♠♣❧❡

▼♦ss❛❦♦✇s❦✐ ❉✐str✐❜✉t❡❞ ❖♥t♦❧♦❣②✱ ▼♦❞❡❧✐♥❣ ❛♥❞ ❙♣❡❝✐✜❝❛t✐♦♥ ▲❛♥❣✉❛❣❡ ✭❉❖▲✮ ✷✵✶✹✲✶✶✲✶✷ ✹✷

SLIDE 43

▼♦t✐✈❛t✐♦♥ ❖♥t♦■❖♣ ❉❖▲ ❋♦❝✉s❡❞ ❖▼❙ ❖▼❙ ▲✐❜r❛r✐❡s ❈♦♥❝❧✉s✐♦♥

Minimization ::= MinimizeKeyword CircMin [CircVars] MinimizeKeyword ::= ’minimize’ | ’closed-world’ | ’maximize’ | ’free’ | ’cofree’ CircMin ::= Symbol Symbol* CircVars ::= ’vars’ (Symbol Symbol*)

▼♦ss❛❦♦✇s❦✐ ❉✐str✐❜✉t❡❞ ❖♥t♦❧♦❣②✱ ▼♦❞❡❧✐♥❣ ❛♥❞ ❙♣❡❝✐✜❝❛t✐♦♥ ▲❛♥❣✉❛❣❡ ✭❉❖▲✮ ✷✵✶✹✲✶✶✲✶✷ ✹✸

SLIDE 44

▼♦t✐✈❛t✐♦♥ ❖♥t♦■❖♣ ❉❖▲ ❋♦❝✉s❡❞ ❖▼❙ ❖▼❙ ▲✐❜r❛r✐❡s ❈♦♥❝❧✉s✐♦♥

▼✐♥✐♠✐③❛t✐♦♥s ✭❝✐r❝✉♠s❝r✐♣t✐♦♥✮

❖✶ t❤❡♥ ♠✐♥✐♠✐③❡ ④ ❖✷ ⑥ ❢♦r❝❡s ♠✐♥✐♠❛❧ ✐♥t❡r♣r❡t❛t✐♦♥ ♦❢ ♥♦♥✲❧♦❣✐❝❛❧ s②♠❜♦❧s ✐♥ ❖✷

Class: Block Individual: B1 Types: Block Individual: B2 Types: Block DifferentFrom: B1 then minimize { Class: Abnormal Individual: B1 Types: Abnormal } then Class: Ontable Class: BlockNotAbnormal EquivalentTo: Block and not Abnormal SubClassOf: Ontable then %implied Individual: B2 Types: Ontable

▼♦ss❛❦♦✇s❦✐ ❉✐str✐❜✉t❡❞ ❖♥t♦❧♦❣②✱ ▼♦❞❡❧✐♥❣ ❛♥❞ ❙♣❡❝✐✜❝❛t✐♦♥ ▲❛♥❣✉❛❣❡ ✭❉❖▲✮ ✷✵✶✹✲✶✶✲✶✷ ✹✹

SLIDE 45

▼♦t✐✈❛t✐♦♥ ❖♥t♦■❖♣ ❉❖▲ ❋♦❝✉s❡❞ ❖▼❙ ❖▼❙ ▲✐❜r❛r✐❡s ❈♦♥❝❧✉s✐♦♥

❋r❡❡♥❡ss

❖✶ t❤❡♥ ❢r❡❡ ④ ❖✷ ⑥ ❢♦r❝❡s ✐♥✐t✐❛❧ ✐♥t❡r♣r❡t❛t✐♦♥ ♦❢ ♥♦♥✲❧♦❣✐❝❛❧ s②♠❜♦❧s ✐♥ ❖✷

sort Elem then free { sort Bag

ps mt:Bag;

__union__:Bag*Bag->Bag, assoc, comm, unit mt }

▼♦ss❛❦♦✇s❦✐ ❉✐str✐❜✉t❡❞ ❖♥t♦❧♦❣②✱ ▼♦❞❡❧✐♥❣ ❛♥❞ ❙♣❡❝✐✜❝❛t✐♦♥ ▲❛♥❣✉❛❣❡ ✭❉❖▲✮ ✷✵✶✹✲✶✶✲✶✷ ✹✺

SLIDE 46

▼♦t✐✈❛t✐♦♥ ❖♥t♦■❖♣ ❉❖▲ ❋♦❝✉s❡❞ ❖▼❙ ❖▼❙ ▲✐❜r❛r✐❡s ❈♦♥❝❧✉s✐♦♥

❈♦❢r❡❡♥❡ss

❖✶ t❤❡♥ ❝♦❢r❡❡ ④ ❖✷ ⑥ ❢♦r❝❡s ✜♥❛❧ ✐♥t❡r♣r❡t❛t✐♦♥ ♦❢ ♥♦♥✲❧♦❣✐❝❛❧ s②♠❜♦❧s ✐♥ ❖✷

sort Elem then cofree { sort Stream

ps head:Stream->Elem;

tail:Stream->Stream }

▼♦ss❛❦♦✇s❦✐ ❉✐str✐❜✉t❡❞ ❖♥t♦❧♦❣②✱ ▼♦❞❡❧✐♥❣ ❛♥❞ ❙♣❡❝✐✜❝❛t✐♦♥ ▲❛♥❣✉❛❣❡ ✭❉❖▲✮ ✷✵✶✹✲✶✶✲✶✷ ✹✻

SLIDE 47

▼♦t✐✈❛t✐♦♥ ❖♥t♦■❖♣ ❉❖▲ ❋♦❝✉s❡❞ ❖▼❙ ❖▼❙ ▲✐❜r❛r✐❡s ❈♦♥❝❧✉s✐♦♥

❖▼❙ ▲✐❜r❛r✐❡s

▼♦ss❛❦♦✇s❦✐ ❉✐str✐❜✉t❡❞ ❖♥t♦❧♦❣②✱ ▼♦❞❡❧✐♥❣ ❛♥❞ ❙♣❡❝✐✜❝❛t✐♦♥ ▲❛♥❣✉❛❣❡ ✭❉❖▲✮ ✷✵✶✹✲✶✶✲✶✷ ✹✼

SLIDE 48

▼♦t✐✈❛t✐♦♥ ❖♥t♦■❖♣ ❉❖▲ ❋♦❝✉s❡❞ ❖▼❙ ❖▼❙ ▲✐❜r❛r✐❡s ❈♦♥❝❧✉s✐♦♥

Library ::= [PrefixMap] LibraryDefn | OMSInConformingLanguage LibraryDefn ::= ’library’ LibraryName LibraryItem* OMSInConformingLanguage ::= ($<$) language and serialization specific ($>$) LibraryItem ::= OMSDefn | NetworkDefn | MappingDefn | QueryRelatedDefn | Qualification LanguageQual ::= ’language’ LanguageRef LogicQual ::= ’logic’ LogicRef SyntaxQual ::= ’serialization’ SyntaxRef LibraryName ::= IRI PrefixMap ::= ’%prefix(’ PrefixBinding* ’)%’ PrefixBinding ::= BoundPrefix IRIBoundToPrefix BoundPrefix ::= ’:’ | Prefix OMSkeyword ::= ’ontology’ | ’onto’ | ’specification’ | ’spec’ | ’model’ OMSDefn ::= OMSkeyword OMSName ’=’ [ConsStrength] OMS [’end’]

▼♦ss❛❦♦✇s❦✐ ❉✐str✐❜✉t❡❞ ❖♥t♦❧♦❣②✱ ▼♦❞❡❧✐♥❣ ❛♥❞ ❙♣❡❝✐✜❝❛t✐♦♥ ▲❛♥❣✉❛❣❡ ✭❉❖▲✮ ✷✵✶✹✲✶✶✲✶✷ ✹✽

SLIDE 49

▼♦t✐✈❛t✐♦♥ ❖♥t♦■❖♣ ❉❖▲ ❋♦❝✉s❡❞ ❖▼❙ ❖▼❙ ▲✐❜r❛r✐❡s ❈♦♥❝❧✉s✐♦♥

❖▼❙ ❞❡✜♥✐t✐♦♥s

❖▼❙ ■❘■ ❂ ❖ ❡♥❞ ❛ss✐❣♥s ♥❛♠❡ ■❘■ t♦ ❖▼❙ ❖✱ ❢♦r ❧❛t❡r r❡❢❡r❡♥❝❡Γ(■❘■) := [ [❖] ]Γ

ntology co-code:Pizza =

Class: VegetarianPizza Class: VegetableTopping ObjectProperty: hasTopping ... end

▼♦ss❛❦♦✇s❦✐ ❉✐str✐❜✉t❡❞ ❖♥t♦❧♦❣②✱ ▼♦❞❡❧✐♥❣ ❛♥❞ ❙♣❡❝✐✜❝❛t✐♦♥ ▲❛♥❣✉❛❣❡ ✭❉❖▲✮ ✷✵✶✹✲✶✶✲✶✷ ✹✾

SLIDE 50

▼♦t✐✈❛t✐♦♥ ❖♥t♦■❖♣ ❉❖▲ ❋♦❝✉s❡❞ ❖▼❙ ❖▼❙ ▲✐❜r❛r✐❡s ❈♦♥❝❧✉s✐♦♥

MappingDefn ::= IntprDefn | EquivDefn | ModuleRelDefn | AlignDefn IntprDefn ::= IntprKeyword IntprName [Conservative] ’:’ [’end’] | IntprKeyword IntprName [Conservative] ’:’ ’=’ LogicTranslation* [SymbolMapItems] IntprKeyword ::= ’interpretation’ | ’view’ IntprName ::= IRI IntprType ::= GroupOMS ’to’ GroupOMS

▼♦ss❛❦♦✇s❦✐ ❉✐str✐❜✉t❡❞ ❖♥t♦❧♦❣②✱ ▼♦❞❡❧✐♥❣ ❛♥❞ ❙♣❡❝✐✜❝❛t✐♦♥ ▲❛♥❣✉❛❣❡ ✭❉❖▲✮ ✷✵✶✹✲✶✶✲✶✷ ✺✵

SLIDE 51

▼♦t✐✈❛t✐♦♥ ❖♥t♦■❖♣ ❉❖▲ ❋♦❝✉s❡❞ ❖▼❙ ❖▼❙ ▲✐❜r❛r✐❡s ❈♦♥❝❧✉s✐♦♥

■♥t❡r♣r❡t❛t✐♦♥s

✐♥t❡r♣r❡t❛t✐♦♥ ■❞ ✿ ❖✶ t♦ ❖✷ ❂ σ σ ✐s ❛ s✐❣♥❛t✉r❡ ♠♦r♣❤✐s♠ ♦r ❛ ❧♦❣✐❝ tr❛♥s❧❛t✐♦♥ ❡①♣r❡ss❡s t❤❛t ❖✷ ❧♦❣✐❝❛❧❧② ✐♠♣❧✐❡s σ(❖✶)

interpretation i : TotalOrder to Nat = Elem → Nat interpretation geometry_of_time %mcons : %% Interpretation of linearly ordered time intervals.. int:owltime_le %% ... that begin and end with an instant as lines %% that are incident with linearly ... to { ord:linear_ordering and bi:complete_graphical %% ... ordered points in a special geometry, ... and int:mappings/owltime_interval_reduction } = ProperInterval → Interval end

▼♦ss❛❦♦✇s❦✐ ❉✐str✐❜✉t❡❞ ❖♥t♦❧♦❣②✱ ▼♦❞❡❧✐♥❣ ❛♥❞ ❙♣❡❝✐✜❝❛t✐♦♥ ▲❛♥❣✉❛❣❡ ✭❉❖▲✮ ✷✵✶✹✲✶✶✲✶✷ ✺✶

SLIDE 52

▼♦t✐✈❛t✐♦♥ ❖♥t♦■❖♣ ❉❖▲ ❋♦❝✉s❡❞ ❖▼❙ ❖▼❙ ▲✐❜r❛r✐❡s ❈♦♥❝❧✉s✐♦♥

OMSOrMappingorNetworkRef ::= IRI NetworkElements ::= NetworkElement ( ’,’ NetworkElement )* NetworkElement ::= [Id ’:’] OMSOrMappingorNetworkRef ExcludeExtensions ::= ’excluding’ ExtensionRef ( ’,’ ExtensionRef )*

▼♦ss❛❦♦✇s❦✐ ❉✐str✐❜✉t❡❞ ❖♥t♦❧♦❣②✱ ▼♦❞❡❧✐♥❣ ❛♥❞ ❙♣❡❝✐✜❝❛t✐♦♥ ▲❛♥❣✉❛❣❡ ✭❉❖▲✮ ✷✵✶✹✲✶✶✲✶✷ ✺✷

SLIDE 53

▼♦t✐✈❛t✐♦♥ ❖♥t♦■❖♣ ❉❖▲ ❋♦❝✉s❡❞ ❖▼❙ ❖▼❙ ▲✐❜r❛r✐❡s ❈♦♥❝❧✉s✐♦♥

❆♥ ✐♥t❡r♣r❡t❛t✐♦♥ ✐♥ ❯▼▲

%prefix( : <http://www.example.org/uml#> uml: <http://www.uml.org/spec/UML/> %% descriptions of logics ... log: <http://www.omg.org/spec/DOL/logics/> logic log:uml interpretation abstract_to_concrete_atm : psm to { atm with Idle |-> Idle, CardEntered |-> Idle, PINEntered |-> Idle, Verified |-> Idle, Verifying |-> Verifying hide card, PIN } end

▼♦ss❛❦♦✇s❦✐ ❉✐str✐❜✉t❡❞ ❖♥t♦❧♦❣②✱ ▼♦❞❡❧✐♥❣ ❛♥❞ ❙♣❡❝✐✜❝❛t✐♦♥ ▲❛♥❣✉❛❣❡ ✭❉❖▲✮ ✷✵✶✹✲✶✶✲✶✷ ✺✸

SLIDE 54

▼♦t✐✈❛t✐♦♥ ❖♥t♦■❖♣ ❉❖▲ ❋♦❝✉s❡❞ ❖▼❙ ❖▼❙ ▲✐❜r❛r✐❡s ❈♦♥❝❧✉s✐♦♥

❆♥ ✐♥t❡r♣r❡t❛t✐♦♥ ✐♥ ❈❆❙▲

spec InsertSort = List then

ps insert : Elem*List[Elem] -> List[Elem];

insert_sort : List[Elem]->List[Elem] vars x,y:Elem; L:List[Elem] . insert(x,[]) = x::[] . insert(x,y::L) = x::insert(y,L) when x<=y else y::i . insert_sort([]) = [] . insert_sort(x::L) = insert(x,insert_sort(L)) hide insert interpretation InsertSortCorrectness : Sorting to InsertSort = sorter |-> insert_sort

▼♦ss❛❦♦✇s❦✐ ❉✐str✐❜✉t❡❞ ❖♥t♦❧♦❣②✱ ▼♦❞❡❧✐♥❣ ❛♥❞ ❙♣❡❝✐✜❝❛t✐♦♥ ▲❛♥❣✉❛❣❡ ✭❉❖▲✮ ✷✵✶✹✲✶✶✲✶✷ ✺✹

SLIDE 55

▼♦t✐✈❛t✐♦♥ ❖♥t♦■❖♣ ❉❖▲ ❋♦❝✉s❡❞ ❖▼❙ ❖▼❙ ▲✐❜r❛r✐❡s ❈♦♥❝❧✉s✐♦♥

❖▼❙ ♥❡t✇♦r❦s ✭❞✐❛❣r❛♠s✮

network N =

◆✶, . . . , ◆♠, ❖✶, . . . , ❖♥, ▼✶, . . . , ▼♣

excluding ◆′

✶, . . . , ◆′ ✐ , ❖′ ✶, . . . , ❖′ ❥ , ▼′ ✶, . . . , ▼′ ❦

◆✐ ❛r❡ ♦t❤❡r ♥❡t✇♦r❦s ❖✐ ❛r❡ ❖▼❙ ✭♣♦ss✐❜❧② ♣r❡✜①❡❞ ✇✐t❤ ❧❛❜❡❧s✱ ❧✐❦❡ ♥ : ❖✮ ▼✐ ❛r❡ ♠❛♣♣✐♥❣s ✭✈✐❡✇s✱ ✐♥t❡r♣r❡t❛t✐♦♥s✮

▼♦ss❛❦♦✇s❦✐ ❉✐str✐❜✉t❡❞ ❖♥t♦❧♦❣②✱ ▼♦❞❡❧✐♥❣ ❛♥❞ ❙♣❡❝✐✜❝❛t✐♦♥ ▲❛♥❣✉❛❣❡ ✭❉❖▲✮ ✷✵✶✹✲✶✶✲✶✷ ✺✺

SLIDE 56

▼♦t✐✈❛t✐♦♥ ❖♥t♦■❖♣ ❉❖▲ ❋♦❝✉s❡❞ ❖▼❙ ❖▼❙ ▲✐❜r❛r✐❡s ❈♦♥❝❧✉s✐♦♥

❈♦♠❜✐♥❛t✐♦♥s

❝♦♠❜✐♥❡ ◆ ◆ ✐s ❛ ♥❡t✇♦r❦ s❡♠❛♥t✐❝s ✐s t❤❡ ✭❛✮ ❝♦❧✐♠✐t ♦❢ t❤❡ ❞✐❛❣r❛♠ ◆

ntology AlignedOntology1 =

combine N

❚❤❡r❡ ✐s ❛ ♥❛t✉r❛❧ s❡♠❛♥t✐❝s ♦❢ ❞✐❛❣r❛♠s✿ ❝♦♠♣❛t✐❜❧❡ ❢❛♠✐❧✐❡s ♦❢ ♠♦❞❡❧s✳ ❚❤❡♥ ✐♥ ❡①❛❝t ✐♥st✐t✉t✐♦♥s✱ ♠♦❞❡❧s ♦❢ ❞✐❛❣r❛♠s ❛r❡ ✐♥ ❜✐❥❡❝t✐✈❡ ❝♦rr❡s♣♦♥❞❡♥❝❡ t♦ ♠♦❞❡❧s ♦❢ t❤❡ ❝♦❧✐♠✐t✳

▼♦ss❛❦♦✇s❦✐ ❉✐str✐❜✉t❡❞ ❖♥t♦❧♦❣②✱ ▼♦❞❡❧✐♥❣ ❛♥❞ ❙♣❡❝✐✜❝❛t✐♦♥ ▲❛♥❣✉❛❣❡ ✭❉❖▲✮ ✷✵✶✹✲✶✶✲✶✷ ✺✻

SLIDE 57

▼♦t✐✈❛t✐♦♥ ❖♥t♦■❖♣ ❉❖▲ ❋♦❝✉s❡❞ ❖▼❙ ❖▼❙ ▲✐❜r❛r✐❡s ❈♦♥❝❧✉s✐♦♥

❙❛♠♣❧❡ ❝♦♠❜✐♥❛t✐♦♥

ntology Source =

Class: Person Class: Woman SubClassOf: Person

ntology Onto1 =

Class: Person Class: Bank Class: Woman SubClassOf: Person interpretation I1 : Source to Onto1 = Person |-> Person, Woman |-> Woman

ntology Onto2 =

Class: HumanBeing Class: Bank Class: Woman SubClassOf: HumanBeing interpretation I2 : Source to Onto2 = Person |-> HumanBeing, Woman |-> Woman

ntology CombinedOntology =

combine Source, Onto1, Onto2, I1, I2

▼♦ss❛❦♦✇s❦✐ ❉✐str✐❜✉t❡❞ ❖♥t♦❧♦❣②✱ ▼♦❞❡❧✐♥❣ ❛♥❞ ❙♣❡❝✐✜❝❛t✐♦♥ ▲❛♥❣✉❛❣❡ ✭❉❖▲✮ ✷✵✶✹✲✶✶✲✶✷ ✺✼

SLIDE 58

▼♦t✐✈❛t✐♦♥ ❖♥t♦■❖♣ ❉❖▲ ❋♦❝✉s❡❞ ❖▼❙ ❖▼❙ ▲✐❜r❛r✐❡s ❈♦♥❝❧✉s✐♦♥

❘❡s✉❧t✐♥❣ ❝♦❧✐♠✐t

{❲♦♠❛♥, P❡rs♦♥❴❍✉♠❛♥❇❡✐♥❣, ✶ : ❇❛♥❦, ✷ : ❇❛♥❦} ❖♥t♦✶

❖♥t♦✷
{❲♦♠❛♥, P❡rs♦♥}
▼♦ss❛❦♦✇s❦✐

❉✐str✐❜✉t❡❞ ❖♥t♦❧♦❣②✱ ▼♦❞❡❧✐♥❣ ❛♥❞ ❙♣❡❝✐✜❝❛t✐♦♥ ▲❛♥❣✉❛❣❡ ✭❉❖▲✮ ✷✵✶✹✲✶✶✲✶✷ ✺✽

SLIDE 59

▼♦t✐✈❛t✐♦♥ ❖♥t♦■❖♣ ❉❖▲ ❋♦❝✉s❡❞ ❖▼❙ ❖▼❙ ▲✐❜r❛r✐❡s ❈♦♥❝❧✉s✐♦♥

AlignDefn ::= ’alignment’ AlignName [AlignCards] ’:’ [’end’] | ’alignment’ AlignName [AlignCards] ’:’ ’=’ Correspondence ( ’,’ Correspondence )* AlignName ::= IRI AlignCards ::= AlignCardForward AlignCardBackward AlignCardForward ::= AlignCard AlignCardBackward ::= AlignCard AlignCard ::= ’1’ | ’?’ | ’+’ | ’*’ AlignType ::= GroupOMS ’to’ GroupOMS<\CLnote[type=q-aut]{would it make sense Correspondence ::= CorrespondenceBlock | SingleCorrespondence | ’*’ CorrespondenceBlock ::= ’relation’ [RelationRef] [Confidence] ’{’ ( ’,’ Correspondence )* ’}’ SingleCorrespondence ::= SymbolRef [RelationRef] [Confidence] [CorrespondenceId] CorrespondenceId ::= ’%(’ IRI ’)%’ SymbolRef ::= IRI TermOrSymbolRef ::= Term | SymbolRef RelationRef ::= ’<\greaterthan>’ | ’<\lessthan>’ | ’=’ | ’%’ | ’$\ni$’ | ’$\in$’ | ’$\mapsto$’ | IRI Confidence ::= Double Double ::= ($<$ a number $\in [0,1]$ $>$)

▼♦ss❛❦♦✇s❦✐ ❉✐str✐❜✉t❡❞ ❖♥t♦❧♦❣②✱ ▼♦❞❡❧✐♥❣ ❛♥❞ ❙♣❡❝✐✜❝❛t✐♦♥ ▲❛♥❣✉❛❣❡ ✭❉❖▲✮ ✷✵✶✹✲✶✶✲✶✷ ✺✾

SLIDE 60

▼♦t✐✈❛t✐♦♥ ❖♥t♦■❖♣ ❉❖▲ ❋♦❝✉s❡❞ ❖▼❙ ❖▼❙ ▲✐❜r❛r✐❡s ❈♦♥❝❧✉s✐♦♥

❆❧✐❣♥♠❡♥ts

❛❧✐❣♥♠❡♥t ■❞ ❝❛r❞✶ ❝❛r❞✷ ✿ ❖✶ t♦ ❖✷ ❂ ❝✶✱✳ ✳ ✳ ❝♥ ❛ss✉♠✐♥❣ ❙✐♥❣❧❡❉♦♠❛✐♥ ⑤ ●❧♦❜❛❧❉♦♠❛✐♥ ⑤ ❈♦♥t❡①t✉❛❧✐③❡❞❉♦♠❛✐♥ ❝❛r❞✐ ✐s ✭♦♣t✐♦♥❛❧❧②✮ ♦♥❡ ♦❢ ✶✱ ❄✱ ✰✱ ✯ t❤❡ ❝✐ ❛r❡ ❝♦rr❡s♣♦♥❞❡♥❝❡s ♦❢ ❢♦r♠ s②♠✶ r❡❧ ❝♦♥❢ s②♠✷

s②♠✐ ✐s ❛ s②♠❜♦❧ ❢r♦♠ ❖✐ r❡❧ ✐s ♦♥❡ ♦❢ >✱ <✱ ❂✱ ✪✱ ∋✱ ∈✱ →✱ ♦r ❛♥ ■❞ ❝♦♥❢ ✐s ❛♥ ✭♦♣t✐♦♥❛❧✮ ❝♦♥✜❞❡♥❝❡ ✈❛❧✉❡ ❜❡t✇❡❡♥ ✵ ❛♥❞ ✶

❙②♥t❛① ♦❢ ❛❧✐❣♥♠❡♥ts ❢♦❧❧♦✇s t❤❡ ❛❧✐❣♥♠❡♥t ❆P■

http://alignapi.gforge.inria.fr

alignment Alignment1 : { Class: Woman } to { Class: Person } = Woman < Person end

▼♦ss❛❦♦✇s❦✐ ❉✐str✐❜✉t❡❞ ❖♥t♦❧♦❣②✱ ▼♦❞❡❧✐♥❣ ❛♥❞ ❙♣❡❝✐✜❝❛t✐♦♥ ▲❛♥❣✉❛❣❡ ✭❉❖▲✮ ✷✵✶✹✲✶✶✲✶✷ ✻✵

SLIDE 61

▼♦t✐✈❛t✐♦♥ ❖♥t♦■❖♣ ❉❖▲ ❋♦❝✉s❡❞ ❖▼❙ ❖▼❙ ▲✐❜r❛r✐❡s ❈♦♥❝❧✉s✐♦♥

❆❧✐❣♥♠❡♥t✿ ❊①❛♠♣❧❡

ntology S =

Class: Person Individual: alex Types: Person Class: Child

ntology T =

Class: HumanBeing Class: Male SubClassOf: HumanBeing Class: Employee alignment A : S to T = Person = HumanBeing alex in Male Child < not Employee assuming GlobalDomain

▼♦ss❛❦♦✇s❦✐ ❉✐str✐❜✉t❡❞ ❖♥t♦❧♦❣②✱ ▼♦❞❡❧✐♥❣ ❛♥❞ ❙♣❡❝✐✜❝❛t✐♦♥ ▲❛♥❣✉❛❣❡ ✭❉❖▲✮ ✷✵✶✹✲✶✶✲✶✷ ✻✶

SLIDE 62

▼♦t✐✈❛t✐♦♥ ❖♥t♦■❖♣ ❉❖▲ ❋♦❝✉s❡❞ ❖▼❙ ❖▼❙ ▲✐❜r❛r✐❡s ❈♦♥❝❧✉s✐♦♥

❉✐str✐❜✉t❡❞ ❖▼❙ ✭❞✐❛❣r❛♠s✮✱ r❡✈✐s✐t❡❞

network N =

◆✶, . . . , ◆♠, ❖✶, . . . , ❖♥, ▼✶, . . . , ▼♣, ❆✶, . . . , ❆r

excluding ◆′

✶, . . . , ◆′ ✐ , ❖′ ✶, . . . , ❖′ ❥ , ▼′ ✶, . . . , ▼′ ❦

◆✐ ❛r❡ ♦t❤❡r ♥❡t✇♦r❦s ❖✐ ❛r❡ ❖▼❙ ✭♣♦ss✐❜❧② ♣r❡✜①❡❞ ✇✐t❤ ❧❛❜❡❧s✱ ❧✐❦❡ ♥ : ❖✮ ▼✐ ❛r❡ ♠❛♣♣✐♥❣s ✭✈✐❡✇s✱ ❡q✉✐✈❛❧❡♥❝❡s✮ ❆✐ ❛r❡ ❛❧✐❣♥♠❡♥ts ❚❤❡ r❡s✉❧t✐♥❣ ❞✐❛❣r❛♠ ◆ ✐♥❝❧✉❞❡s ✭✐♥st✐t✉t✐♦♥✲s♣❡❝✐✜❝✮ ❲✲❛❧✐❣♥♠❡♥t ❞✐❛❣r❛♠s ❢♦r ❡❛❝❤ ❛❧✐❣♥♠❡♥t ❆✐✳ ❯s✐♥❣ ❛ss✉♠✐♥❣✱ ❛ss✉♠♣t✐♦♥s ❛❜♦✉t t❤❡ ❞♦♠❛✐♥s ♦❢ ❛❧❧ ❖▼❙ ❝❛♥ ❜❡ s♣❡❝✐✜❡❞✿ ❙✐♥❣❧❡❉♦♠❛✐♥ ❛❧✐❣♥❡❞ s②♠❜♦❧s ❛r❡ ♠❛♣♣❡❞ t♦ ❡❛❝❤ ♦t❤❡r

❧♦❜❛❧❉♦♠❛✐♥ ❛❧✐❣♥❡❞ ❖▼❙ ❛ r❡❧❛t✐✈✐③❡❞

❈♦♥t❡①t✉❛❧✐③❡❞❉♦♠❛✐♥ ❛❧✐❣♥♠❡♥ts ❛r❡ r❡✐✜❡❞ ❛s ❜✐♥❛r② r❡❧❛t✐♦♥s

▼♦ss❛❦♦✇s❦✐ ❉✐str✐❜✉t❡❞ ❖♥t♦❧♦❣②✱ ▼♦❞❡❧✐♥❣ ❛♥❞ ❙♣❡❝✐✜❝❛t✐♦♥ ▲❛♥❣✉❛❣❡ ✭❉❖▲✮ ✷✵✶✹✲✶✶✲✶✷ ✻✷

SLIDE 63

▼♦t✐✈❛t✐♦♥ ❖♥t♦■❖♣ ❉❖▲ ❋♦❝✉s❡❞ ❖▼❙ ❖▼❙ ▲✐❜r❛r✐❡s ❈♦♥❝❧✉s✐♦♥

❉✐❛❣r❛♠ ♦❢ ❛ ❙✐♥❣❧❡❉♦♠❛✐♥ ❛❧✐❣♥♠❡♥t

❙ ❇ ❚ {P❡rs♦♥, ❛❧❡①, ❈❤✐❧❞}

σ✶

ι✶
{▼❛❧❡, ❍✉♠❛♥❇❡✐♥❣, ❊♠♣❧♦②❡❡}

ι✷

σ✷
✇❤❡r❡

♦♥t♦❧♦❣② ❇ = ❈❧❛ss✿ P❡rs♦♥❴❍✉♠❛♥❇❡✐♥❣ ❈❧❛ss✿ ❊♠♣❧♦②❡❡ ❈❧❛ss✿ ❈❤✐❧❞ ❙✉❜❈❧❛ss❖❢✿ ¬ ❊♠♣❧♦②❡❡ ■♥❞✐✈✐❞✉❛❧✿ ❛❧❡① ❚②♣❡s✿ ▼❛❧❡

▼♦ss❛❦♦✇s❦✐ ❉✐str✐❜✉t❡❞ ❖♥t♦❧♦❣②✱ ▼♦❞❡❧✐♥❣ ❛♥❞ ❙♣❡❝✐✜❝❛t✐♦♥ ▲❛♥❣✉❛❣❡ ✭❉❖▲✮ ✷✵✶✹✲✶✶✲✶✷ ✻✸

SLIDE 64

▼♦t✐✈❛t✐♦♥ ❖♥t♦■❖♣ ❉❖▲ ❋♦❝✉s❡❞ ❖▼❙ ❖▼❙ ▲✐❜r❛r✐❡s ❈♦♥❝❧✉s✐♦♥

❘❡s✉❧t✐♥❣ ❝♦❧✐♠✐t

❚❤❡ ❝♦❧✐♠✐t ♦♥t♦❧♦❣② ♦❢ t❤❡ ❞✐❛❣r❛♠ ♦❢ t❤❡ ❛❧✐❣♥♠❡♥t ❛❜♦✈❡ ✐s✿ ♦♥t♦❧♦❣② ❇ = ❈❧❛ss✿ P❡rs♦♥❴❍✉♠❛♥❇❡✐♥❣ ❈❧❛ss✿ ❊♠♣❧♦②❡❡ ❈❧❛ss✿ ▼❛❧❡ ❙✉❜❈❧❛ss❖❢✿ P❡rs♦♥❴❍✉♠❛♥❇❡✐♥❣ ❈❧❛ss✿ ❈❤✐❧❞ ❙✉❜❈❧❛ss❖❢✿ ¬ ❊♠♣❧♦②❡❡ ■♥❞✐✈✐❞✉❛❧✿ ❛❧❡① ❚②♣❡s✿ ▼❛❧❡, P❡rs♦♥❴❍✉♠❛♥❇❡✐♥❣

▼♦ss❛❦♦✇s❦✐ ❉✐str✐❜✉t❡❞ ❖♥t♦❧♦❣②✱ ▼♦❞❡❧✐♥❣ ❛♥❞ ❙♣❡❝✐✜❝❛t✐♦♥ ▲❛♥❣✉❛❣❡ ✭❉❖▲✮ ✷✵✶✹✲✶✶✲✶✷ ✻✹

SLIDE 65

▼♦t✐✈❛t✐♦♥ ❖♥t♦■❖♣ ❉❖▲ ❋♦❝✉s❡❞ ❖▼❙ ❖▼❙ ▲✐❜r❛r✐❡s ❈♦♥❝❧✉s✐♦♥

❇❛❝❦❣r♦✉♥❞ ❙✐♠♣❧❡ s❡♠❛♥t✐❝s ♦❢ ❞✐❛❣r❛♠s

❋r❛♠❡✇♦r❦✿ ✐♥st✐t✉t✐♦♥s ❧✐❦❡ ❖❲▲✱ ❋❖▲✱ ✳ ✳ ✳ ❖♥t♦❧♦❣✐❡s ❛r❡ ✐♥t❡r♣r❡t❡❞ ♦✈❡r t❤❡ s❛♠❡ ❞♦♠❛✐♥ ❖✶

♠✶

❖✷

♠✷

. . .

❖♥

♠♥

♠♦❞❡❧ ❢♦r ❆✿ (♠✶, ♠✷) s✉❝❤ t❤❛t ♠✶(s) ❘ ♠✷(t) ❢♦r ❡❛❝❤ s ❘ t ✐♥ ❆ ♠♦❞❡❧ ❢♦r ❛ ❞✐❛❣r❛♠✿ ❢❛♠✐❧② (♠✐) ♦❢ ♠♦❞❡❧s s✉❝❤ t❤❛t (♠✐, ♠❥) ✐s ❛ ♠♦❞❡❧ ❢♦r ❆✐❥ ❧♦❝❛❧ ♠♦❞❡❧s ♦❢ ❖❥ ♠♦❞✉❧♦ ❛ ❞✐❛❣r❛♠✿ ❥t❤✲♣r♦❥❡❝t✐♦♥ ♦♥ ♠♦❞❡❧s ♦❢ t❤❡ ❞✐❛❣r❛♠

▼♦ss❛❦♦✇s❦✐ ❉✐str✐❜✉t❡❞ ❖♥t♦❧♦❣②✱ ▼♦❞❡❧✐♥❣ ❛♥❞ ❙♣❡❝✐✜❝❛t✐♦♥ ▲❛♥❣✉❛❣❡ ✭❉❖▲✮ ✷✵✶✹✲✶✶✲✶✷ ✻✺

SLIDE 66

▼♦t✐✈❛t✐♦♥ ❖♥t♦■❖♣ ❉❖▲ ❋♦❝✉s❡❞ ❖▼❙ ❖▼❙ ▲✐❜r❛r✐❡s ❈♦♥❝❧✉s✐♦♥

■♥t❡❣r❛t❡❞ s❡♠❛♥t✐❝s ♦❢ ❞✐❛❣r❛♠s

❋r❛♠❡✇♦r❦✿ ❞✐✛❡r❡♥t ❞♦♠❛✐♥s r❡❝♦♥❝✐❧❡❞ ✐♥ ❛ ❣❧♦❜❛❧ ❞♦♠❛✐♥ ❖✶

♠

❖✷

♠✷

. . .

❖♥

♠♥

❉✶

γ✶

❉✷

γ✷

. . .

❉♥

γ♥

♠♦❞❡❧ ❢♦r ❛ ❞✐❛❣r❛♠✿ ❢❛♠✐❧② (♠✐) ♦❢ ♠♦❞❡❧s ✇✐t❤ ❡q✉❛❧✐③✐♥❣ ❢✉♥❝t✐♦♥ γ s✉❝❤ t❤❛t (γ✐♠✐, γ❥♠❥) ✐s ❛ ♠♦❞❡❧ ❢♦r ❆✐❥

▼♦ss❛❦♦✇s❦✐ ❉✐str✐❜✉t❡❞ ❖♥t♦❧♦❣②✱ ▼♦❞❡❧✐♥❣ ❛♥❞ ❙♣❡❝✐✜❝❛t✐♦♥ ▲❛♥❣✉❛❣❡ ✭❉❖▲✮ ✷✵✶✹✲✶✶✲✶✷ ✻✻

SLIDE 67

▼♦t✐✈❛t✐♦♥ ❖♥t♦■❖♣ ❉❖▲ ❋♦❝✉s❡❞ ❖▼❙ ❖▼❙ ▲✐❜r❛r✐❡s ❈♦♥❝❧✉s✐♦♥

❘❡❧❛t✐✈✐③❛t✐♦♥ ♦❢ ❛♥ ❖❲▲ ♦♥t♦❧♦❣②

▲❡t ❖ ❜❡ ❛♥ ♦♥t♦❧♦❣②✱ ❞❡✜♥❡ ✐ts r❡❧❛t✐✈✐③❛t✐♦♥ ˜ ❖✿ ❝♦♥❝❡♣ts ❛r❡ ❝♦♥❝❡♣ts ♦❢ ❖ ✇✐t❤ ❛ ♥❡✇ ❝♦♥❝❡♣t ⊤❖❀ r♦❧❡s ❛♥❞ ✐♥❞✐✈✐❞✉❛❧s ❛r❡ t❤❡ s❛♠❡ ❛①✐♦♠s✿

❡❛❝❤ ❝♦♥❝❡♣t ❈ ✐s s✉❜s✉♠❡❞ ❜② ⊤❖✱ ❡❛❝❤ ✐♥❞✐✈✐❞✉❛❧ ✐ ✐s ❛♥ ✐♥st❛♥❝❡ ♦❢ ⊤❖✱ ❡❛❝❤ r♦❧❡ r ❤❛s ❞♦♠❛✐♥ ❛♥❞ r❛♥❣❡ ⊤❖✳

❛♥❞ t❤❡ ❛①✐♦♠s ♦❢ ❖ ✇❤❡r❡ t❤❡ ❢♦❧❧♦✇✐♥❣ r❡♣❧❛❝❡♠❡♥t ♦❢ ❝♦♥❝❡♣t ✐s ♠❛❞❡✿

❡❛❝❤ ♦❝❝✉r❡♥❝❡ ♦❢ ⊤ ✐s r❡♣❧❛❝❡❞ ❜② ⊤❖✱ ❡❛❝❤ ❝♦♥❝❡♣t ¬❈ ✐s r❡♣❧❛❝❡❞ ❜② ⊤❖ \ ❈✱ ❛♥❞ ❡❛❝❤ ❝♦♥❝❡♣t ∀❘.❈ ✐s r❡♣❧❛❝❡❞ ❜② ⊤❖ ⊓ ∀❘.❈✳

▼♦ss❛❦♦✇s❦✐ ❉✐str✐❜✉t❡❞ ❖♥t♦❧♦❣②✱ ▼♦❞❡❧✐♥❣ ❛♥❞ ❙♣❡❝✐✜❝❛t✐♦♥ ▲❛♥❣✉❛❣❡ ✭❉❖▲✮ ✷✵✶✹✲✶✶✲✶✷ ✻✼

SLIDE 68

▼♦t✐✈❛t✐♦♥ ❖♥t♦■❖♣ ❉❖▲ ❋♦❝✉s❡❞ ❖▼❙ ❖▼❙ ▲✐❜r❛r✐❡s ❈♦♥❝❧✉s✐♦♥

❊①❛♠♣❧❡✿ ✐♥t❡❣r❛t❡❞ s❡♠❛♥t✐❝s

❈ ˜ ❙

❚

{P❡rs♦♥, ❛❧❡①, ❈❤✐❧❞}

σ✶

ι✶
{▼❛❧❡, ❍✉♠❛♥❇❡✐♥❣, ❊♠♣❧♦②❡❡}

ι✷

σ✷
✇❤❡r❡

♦♥t♦❧♦❣② ❇ = ❈❧❛ss✿ ❚❤✐♥❣❙ ❈❧❛ss✿ ❚❤✐♥❣❚ ❈❧❛ss✿ P❡rs♦♥❴❍✉♠❛♥❇❡✐♥❣ ❙✉❜❈❧❛ss❖❢✿ ❚❤✐♥❣❙✱ ❚❤✐♥❣❚ ❈❧❛ss✿ ▼❛❧❡ ❈❧❛ss✿ ❊♠♣❧♦②❡❡ ❈❧❛ss✿ ❈❤✐❧❞ ❙✉❜❈❧❛ss❖❢✿ ❚❤✐♥❣❚ ❛♥❞ ¬ ❊♠♣❧♦②❡❡ ■♥❞✐✈✐❞✉❛❧✿ ❛❧❡① ❚②♣❡s✿ ▼❛❧❡

▼♦ss❛❦♦✇s❦✐ ❉✐str✐❜✉t❡❞ ❖♥t♦❧♦❣②✱ ▼♦❞❡❧✐♥❣ ❛♥❞ ❙♣❡❝✐✜❝❛t✐♦♥ ▲❛♥❣✉❛❣❡ ✭❉❖▲✮ ✷✵✶✹✲✶✶✲✶✷ ✻✽

SLIDE 69

▼♦t✐✈❛t✐♦♥ ❖♥t♦■❖♣ ❉❖▲ ❋♦❝✉s❡❞ ❖▼❙ ❖▼❙ ▲✐❜r❛r✐❡s ❈♦♥❝❧✉s✐♦♥

❊①❛♠♣❧❡✿ ✐♥t❡❣r❛t❡❞ s❡♠❛♥t✐❝s ✭❝♦♥t✬❞✮

♦♥t♦❧♦❣② ❈ = ❈❧❛ss✿ ❚❤✐♥❣❙ ❈❧❛ss✿ ❚❤✐♥❣❚ ❈❧❛ss✿ P❡rs♦♥❴❍✉♠❛♥❇❡✐♥❣ ❙✉❜❈❧❛ss❖❢✿ ❚❤✐♥❣❙✱ ❚❤✐♥❣❈ ❈❧❛ss✿ ▼❛❧❡ ❙✉❜❈❧❛ss❖❢✿ P❡rs♦♥❴❍✉♠❛♥❇❡✐♥❣ ❈❧❛ss✿ ❊♠♣❧♦②❡❡ ❙✉❜❈❧❛ss❖❢✿ ❚❤✐♥❣❚ ❈❧❛ss✿ ❈❤✐❧❞ ❙✉❜❈❧❛ss❖❢✿ ❚❤✐♥❣❙ ❈❧❛ss✿ ❈❤✐❧❞ ❙✉❜❈❧❛ss❖❢✿ ❚❤✐♥❣❚ ❛♥❞ ¬ ❊♠♣❧♦②❡❡ ■♥❞✐✈✐❞✉❛❧✿ ❛❧❡① ❚②♣❡s✿ ▼❛❧❡✱ P❡rs♦♥❴❍✉♠❛♥❇❡✐♥❣

▼♦ss❛❦♦✇s❦✐ ❉✐str✐❜✉t❡❞ ❖♥t♦❧♦❣②✱ ▼♦❞❡❧✐♥❣ ❛♥❞ ❙♣❡❝✐✜❝❛t✐♦♥ ▲❛♥❣✉❛❣❡ ✭❉❖▲✮ ✷✵✶✹✲✶✶✲✶✷ ✻✾

SLIDE 70

▼♦t✐✈❛t✐♦♥ ❖♥t♦■❖♣ ❉❖▲ ❋♦❝✉s❡❞ ❖▼❙ ❖▼❙ ▲✐❜r❛r✐❡s ❈♦♥❝❧✉s✐♦♥

❈♦♥t❡①t✉❛❧✐③❡❞ s❡♠❛♥t✐❝s ♦❢ ❞✐❛❣r❛♠s

❋r❛♠❡✇♦r❦✿ ❞✐✛❡r❡♥t ❞♦♠❛✐♥s r❡❧❛t❡❞ ❜② ❝♦❤❡r❡♥t r❡❧❛t✐♦♥s ❖✶

♠

❖✷

♠✷

. . .

❖♥

♠♥

❉✶

r✶,✷ r✶,✸

❉✷

r✷,✸ . . .

❉♥

r♥,✶

s✉❝❤ t❤❛t

r✐❥ ✐s ❢✉♥❝t✐♦♥❛❧ ❛♥❞ ✐♥❥❡❝t✐✈❡✱ r✐✐ ✐s t❤❡ ✐❞❡♥t✐t② ✭❞✐❛❣♦♥❛❧✮ r❡❧❛t✐♦♥✱ r❥✐ ✐s t❤❡ ❝♦♥✈❡rs❡ ♦❢ r✐❥✱ ❛♥❞ r✐❦ ✐s t❤❡ r❡❧❛t✐♦♥❛❧ ❝♦♠♣♦s✐t✐♦♥ ♦❢ r✐❥ ❛♥❞ r❥❦ ♠♦❞❡❧ ❢♦r ❛ ❞✐❛❣r❛♠✿ ❢❛♠✐❧② (♠✐) ♦❢ ♠♦❞❡❧s ✇✐t❤ ❝♦❤❡r❡♥t r❡❧❛t✐♦♥s (r✐❥) s✉❝❤ t❤❛t (♠✐, r❥✐♠❥) ✐s ❛ ♠♦❞❡❧ ❢♦r ❆✐❥

▼♦ss❛❦♦✇s❦✐ ❉✐str✐❜✉t❡❞ ❖♥t♦❧♦❣②✱ ▼♦❞❡❧✐♥❣ ❛♥❞ ❙♣❡❝✐✜❝❛t✐♦♥ ▲❛♥❣✉❛❣❡ ✭❉❖▲✮ ✷✵✶✹✲✶✶✲✶✷ ✼✵

SLIDE 71

▼♦t✐✈❛t✐♦♥ ❖♥t♦■❖♣ ❉❖▲ ❋♦❝✉s❡❞ ❖▼❙ ❖▼❙ ▲✐❜r❛r✐❡s ❈♦♥❝❧✉s✐♦♥

❈♦♥t❡①t✉❛❧✐③❡❞ s❡♠❛♥t✐❝s ♦❢ ❞✐❛❣r❛♠s✱ r❡✈✐s✐t❡❞

˜ ❙ ❇ ˜ ❚ ❖✶

σ✶

ι✶
❖✷

ι✷

σ✷
✇❤❡r❡ ❇ ♠♦❞✐✜❡s ❇ ❛s ❢♦❧❧♦✇s✿

r✐❥ ❛r❡ ❛❞❞❡❞ t♦ ❇ ❛s r♦❧❡s ✇✐t❤ ❞♦♠❛✐♥ ⊤❙ ❛♥❞ r❛♥❣❡ ⊤❚ t❤❡ ❝♦rr❡s♣♦♥❞❡♥❝❡s ❛r❡ tr❛♥s❧❛t❡❞ t♦ ❛①✐♦♠s ✐♥✈♦❧✈✐♥❣ t❤❡s❡ r♦❧❡s✿

s✐ = t❥ ❜❡❝♦♠❡s s✐ r✐❥ t❥ ❛✐ ∈ ❝❥ ❜❡❝♦♠❡s ❛✐ ∈ ∃r✐❥.❝❥ . . .

t❤❡ ♣r♦♣❡rt✐❡s ♦❢ t❤❡ r♦❧❡s ❛r❡ ❛❞❞❡❞ ❛s ❛①✐♦♠s ✐♥ ❇

▼♦ss❛❦♦✇s❦✐ ❉✐str✐❜✉t❡❞ ❖♥t♦❧♦❣②✱ ▼♦❞❡❧✐♥❣ ❛♥❞ ❙♣❡❝✐✜❝❛t✐♦♥ ▲❛♥❣✉❛❣❡ ✭❉❖▲✮ ✷✵✶✹✲✶✶✲✶✷ ✼✶

SLIDE 72

▼♦t✐✈❛t✐♦♥ ❖♥t♦■❖♣ ❉❖▲ ❋♦❝✉s❡❞ ❖▼❙ ❖▼❙ ▲✐❜r❛r✐❡s ❈♦♥❝❧✉s✐♦♥

❆❞❞✐♥❣ ❞♦♠❛✐♥ r❡❧❛t✐♦♥s t♦ t❤❡ ❜r✐❞❣❡

♦♥t♦❧♦❣② ❇ = ❈❧❛ss✿ ❚❤✐♥❣❙ ❈❧❛ss✿ ❚❤✐♥❣❚ ❖❜❥❡❝tPr♦♣❡r②✿ r❙❚ ❉♦♠❛✐♥✿ ❚❤✐♥❣❙ ❘❛♥❣❡✿ ❚❤✐♥❣❚ ❈❧❛ss✿ P❡rs♦♥ ❊q✉✐✈❛❧❡♥t❚♦✿ r❙❚ s♦♠❡ ❍✉♠❛♥❇❡✐♥❣ ❈❧❛ss✿ ❊♠♣❧♦②❡❡ ❈❧❛ss✿ ❈❤✐❧❞ ❙✉❜❈❧❛ss❖❢✿ r❙❚ s♦♠❡ ¬ ❊♠♣❧♦②❡❡ ■♥❞✐✈✐❞✉❛❧✿ ❛❧❡① ❚②♣❡s✿ r❙❚ s♦♠❡ ▼❛❧❡

▼♦ss❛❦♦✇s❦✐ ❉✐str✐❜✉t❡❞ ❖♥t♦❧♦❣②✱ ▼♦❞❡❧✐♥❣ ❛♥❞ ❙♣❡❝✐✜❝❛t✐♦♥ ▲❛♥❣✉❛❣❡ ✭❉❖▲✮ ✷✵✶✹✲✶✶✲✶✷ ✼✷

SLIDE 73

▼♦t✐✈❛t✐♦♥ ❖♥t♦■❖♣ ❉❖▲ ❋♦❝✉s❡❞ ❖▼❙ ❖▼❙ ▲✐❜r❛r✐❡s ❈♦♥❝❧✉s✐♦♥

❊①❛♠♣❧❡✿ ❝♦♥t❡①t✉❛❧✐③❡❞ s❡♠❛♥t✐❝s

❈ ❙

❇
❚
{P❡rs♦♥, ❛❧❡①, ❈❤✐❧❞, ⊤s}

σ✶

ι✶
{▼❛❧❡, ❍✉♠❛♥❇❡✐♥❣, ❊♠♣❧♦②❡❡, ⊤❚ }

ι✷

σ✷
✇❤❡r❡

♦♥t♦❧♦❣② ❈ = ❈❧❛ss✿ ❚❤✐♥❣❙ ❈❧❛ss✿ ❚❤✐♥❣❚ ❖❜❥❡❝tPr♦♣❡r②✿ r❙❚ ❉♦♠❛✐♥✿ ❚❤✐♥❣❙ ❘❛♥❣❡✿ ❚❤✐♥❣❚ ❈❧❛ss✿ P❡rs♦♥ ❊q✉✐✈❛❧❡♥t❚♦✿ r❙❚ s♦♠❡ ❍✉♠❛♥❇❡✐♥❣ ❈❧❛ss✿ ❊♠♣❧♦②❡❡ ❈❧❛ss✿ ❈❤✐❧❞ ❙✉❜❈❧❛ss❖❢✿ r❙❚ s♦♠❡ ¬ ❊♠♣❧♦②❡❡ ■♥❞✐✈✐❞✉❛❧✿ ❛❧❡① ❚②♣❡s✿ r❙❚ s♦♠❡ ▼❛❧❡✱ P❡rs♦♥

▼♦ss❛❦♦✇s❦✐ ❉✐str✐❜✉t❡❞ ❖♥t♦❧♦❣②✱ ▼♦❞❡❧✐♥❣ ❛♥❞ ❙♣❡❝✐✜❝❛t✐♦♥ ▲❛♥❣✉❛❣❡ ✭❉❖▲✮ ✷✵✶✹✲✶✶✲✶✷ ✼✸

SLIDE 74

▼♦t✐✈❛t✐♦♥ ❖♥t♦■❖♣ ❉❖▲ ❋♦❝✉s❡❞ ❖▼❙ ❖▼❙ ▲✐❜r❛r✐❡s ❈♦♥❝❧✉s✐♦♥

QueryRelatedDefn ::= QueryDefn | SubstDefn | ResultDefn QueryDefn ::= ’query’ QueryName ’=’ ’select’ Vars ’where’ Sentence OMS [’along’ Translation] SubstDefn ::= ’substitution’ SubstName ’:’ OMS ’to’ OMS ’=’ SymbolMap ResultDefn ::= ’result’ ResultName SubstName ( ’,’ SubstName )* QueryName [’%complete’] QueryName ::= IRI SubstName ::= IRI ResultName ::= IRI Vars ::= Symbol ( ’,’ Symbol )*

▼♦ss❛❦♦✇s❦✐ ❉✐str✐❜✉t❡❞ ❖♥t♦❧♦❣②✱ ▼♦❞❡❧✐♥❣ ❛♥❞ ❙♣❡❝✐✜❝❛t✐♦♥ ▲❛♥❣✉❛❣❡ ✭❉❖▲✮ ✷✵✶✹✲✶✶✲✶✷ ✼✹

SLIDE 75

▼♦t✐✈❛t✐♦♥ ❖♥t♦■❖♣ ❉❖▲ ❋♦❝✉s❡❞ ❖▼❙ ❖▼❙ ▲✐❜r❛r✐❡s ❈♦♥❝❧✉s✐♦♥

◗✉❡r✐❡s

❉❖▲ ✐s ❛ ❧♦❣✐❝❛❧ ✭♠❡t❛✮ ❧❛♥❣✉❛❣❡ ❢♦❝✉s ♦♥ ♦♥t♦❧♦❣✐❡s✱ ♠♦❞❡❧s✱ s♣❡❝✐✜❝❛t✐♦♥s✱ ❛♥❞ t❤❡✐r ❧♦❣✐❝❛❧ r❡❧❛t✐♦♥s✿ ❧♦❣✐❝❛❧ ❝♦♥s❡q✉❡♥❝❡✱ ✐♥t❡r♣r❡t❛t✐♦♥s✱ ✳ ✳ ✳ ◗✉❡r✐❡s ❛r❡ ❞✐✛❡r❡♥t✿ ❛♥s✇❡r ✐s ♥♦t ✏②❡s✑ ♦r ✏♥♦✑✱ ❜✉t ❛♥ ❛♥s✇❡r s✉❜st✐t✉t✐♦♥ q✉❡r② ❧❛♥❣✉❛❣❡ ♠❛② ❞✐✛❡r ❢r♦♠ ❧❛♥❣✉❛❣❡ ♦❢ ❖▼❙ t❤❛t ✐s q✉❡r✐❡❞

▼♦ss❛❦♦✇s❦✐ ❉✐str✐❜✉t❡❞ ❖♥t♦❧♦❣②✱ ▼♦❞❡❧✐♥❣ ❛♥❞ ❙♣❡❝✐✜❝❛t✐♦♥ ▲❛♥❣✉❛❣❡ ✭❉❖▲✮ ✷✵✶✹✲✶✶✲✶✷ ✼✺

SLIDE 76

▼♦t✐✈❛t✐♦♥ ❖♥t♦■❖♣ ❉❖▲ ❋♦❝✉s❡❞ ❖▼❙ ❖▼❙ ▲✐❜r❛r✐❡s ❈♦♥❝❧✉s✐♦♥

❙❛♠♣❧❡ q✉❡r② ❧❛♥❣✉❛❣❡s

❝♦♥❥✉♥❝t✐✈❡ q✉❡r✐❡s ✐♥ ❖❲▲ Pr♦❧♦❣✴▲♦❣✐❝ Pr♦❣r❛♠♠✐♥❣ ❙P❆❘◗▲

▼♦ss❛❦♦✇s❦✐ ❉✐str✐❜✉t❡❞ ❖♥t♦❧♦❣②✱ ▼♦❞❡❧✐♥❣ ❛♥❞ ❙♣❡❝✐✜❝❛t✐♦♥ ▲❛♥❣✉❛❣❡ ✭❉❖▲✮ ✷✵✶✹✲✶✶✲✶✷ ✼✻

SLIDE 77

▼♦t✐✈❛t✐♦♥ ❖♥t♦■❖♣ ❉❖▲ ❋♦❝✉s❡❞ ❖▼❙ ❖▼❙ ▲✐❜r❛r✐❡s ❈♦♥❝❧✉s✐♦♥

❙②♥t❛① ♦❢ q✉❡r✐❡s ✐♥ ❉❖▲

◆❡✇ ❖▼❙ ❞❡❝❧❛r❛t✐♦♥s ❛♥❞ r❡❧❛t✐♦♥s✿

query qname = select vars where sentence in OMS [along language-translation] substitution sname : OMS1 to OMS2 = derived-symbol-map result rname = sname_1, ..., sname_n for qname %% result is a substitution

◆❡✇ s❡♥t❡♥❝❡s ✭❤♦✇❡✈❡r✱ ❛s str✉❝t✉r❡❞ ❖▼❙✦✮✿

apply(sname,sentence) %% apply substition

❖♣❡♥ q✉❡st✐♦♥✿ ❤♦✇ t♦ ❞❡❛❧ ✇✐t❤ ✏❝♦♥str✉❝t✑ q✉❡r✐❡s❄

▼♦ss❛❦♦✇s❦✐ ❉✐str✐❜✉t❡❞ ❖♥t♦❧♦❣②✱ ▼♦❞❡❧✐♥❣ ❛♥❞ ❙♣❡❝✐✜❝❛t✐♦♥ ▲❛♥❣✉❛❣❡ ✭❉❖▲✮ ✷✵✶✹✲✶✶✲✶✷ ✼✼

SLIDE 78

▼♦t✐✈❛t✐♦♥ ❖♥t♦■❖♣ ❉❖▲ ❋♦❝✉s❡❞ ❖▼❙ ❖▼❙ ▲✐❜r❛r✐❡s ❈♦♥❝❧✉s✐♦♥

❈♦♥❝❧✉s✐♦♥

▼♦ss❛❦♦✇s❦✐ ❉✐str✐❜✉t❡❞ ❖♥t♦❧♦❣②✱ ▼♦❞❡❧✐♥❣ ❛♥❞ ❙♣❡❝✐✜❝❛t✐♦♥ ▲❛♥❣✉❛❣❡ ✭❉❖▲✮ ✷✵✶✹✲✶✶✲✶✷ ✼✽

SLIDE 79

▼♦t✐✈❛t✐♦♥ ❖♥t♦■❖♣ ❉❖▲ ❋♦❝✉s❡❞ ❖▼❙ ❖▼❙ ▲✐❜r❛r✐❡s ❈♦♥❝❧✉s✐♦♥

❈❤❛❧❧❡♥❣❡s

❲❤❛t ✐s ❛ s✉✐t❛❜❧❡ ❛❜str❛❝t ♠❡t❛ ❢r❛♠❡✇♦r❦ ❢♦r ♥♦♥✲♠♦♥♦t♦♥✐❝ ❧♦❣✐❝s ❛♥❞ r✉❧❡ ❧❛♥❣✉❛❣❡s ❧✐❦❡ ❘■❋ ❛♥❞ ❘✉❧❡▼▲❄ ❆r❡ ✐♥st✐t✉t✐♦♥s s✉✐t❛❜❧❡ ❤❡r❡❄ ❞✐✛❡r❡♥t ❢r♦♠ t❤♦s❡ ❢♦r ❖❲▲❄ ❲❤❛t ✐s ❛ ✉s❡❢✉❧ ❛❜str❛❝t ♥♦t✐♦♥ ♦❢ q✉❡r② ✭❧❛♥❣✉❛❣❡✮ ❛♥❞ ❛♥s✇❡r s✉❜st✐t✉t✐♦♥❄ ❍♦✇ t♦ ✐♥t❡❣r❛t❡ ❚❇♦①✲❧✐❦❡ ❛♥❞ ❆❇♦①✲❧✐❦❡ ❖▼❙❄ ❈❛♥ t❤❡ ♥♦t✐♦♥s ♦❢ ❝❧❛ss ❤✐❡r❛r❝❤② ❛♥❞ ♦❢ s❛t✐s✜❛❜✐❧✐t② ♦❢ ❛ ❝❧❛ss ❜❡ ❣❡♥❡r❛❧✐s❡❞ ❢r♦♠ ❖❲▲ t♦ ♦t❤❡r ❧❛♥❣✉❛❣❡s❄ ❍♦✇ t♦ ✐♥t❡r♣r❡t ❛❧✐❣♥♠❡♥t ❝♦rr❡s♣♦♥❞❡♥❝❡s ✇✐t❤ ❝♦♥✜❞❡♥❝❡ ♦t❤❡r t❤❛t ✶ ✐♥ ❛ ❝♦♠❜✐♥❛t✐♦♥❄ ❈❛♥ ❧♦❣✐❝❛❧ ❢r❛♠❡✇♦r❦s ❜❡ ✉s❡❞ ❢♦r t❤❡ s♣❡❝✐✜❝❛t✐♦♥ ♦❢ ❖▼❙ ❧❛♥❣✉❛❣❡s ❛♥❞ tr❛♥s❧❛t✐♦♥s❄ Pr♦♦❢ s✉♣♣♦rt

▼♦ss❛❦♦✇s❦✐ ❉✐str✐❜✉t❡❞ ❖♥t♦❧♦❣②✱ ▼♦❞❡❧✐♥❣ ❛♥❞ ❙♣❡❝✐✜❝❛t✐♦♥ ▲❛♥❣✉❛❣❡ ✭❉❖▲✮ ✷✵✶✹✲✶✶✲✶✷ ✼✾

SLIDE 80

▼♦t✐✈❛t✐♦♥ ❖♥t♦■❖♣ ❉❖▲ ❋♦❝✉s❡❞ ❖▼❙ ❖▼❙ ▲✐❜r❛r✐❡s ❈♦♥❝❧✉s✐♦♥

❚♦♦❧ s✉♣♣♦rt✿ ❍❡t❡r♦❣❡♥❡♦✉s ❚♦♦❧ ❙❡t ✭❍❡ts✮

❛✈❛✐❧❛❜❧❡ ❛t hets.dfki.de s♣❡❛❦s ❉❖▲✱ ❍❡t❈❆❙▲✱ ❈♦❈❆❙▲✱ ❈s♣❈❆❙▲✱ ▼❖❋✱ ◗❱❚✱ ❖❲▲✱ ❈♦♠♠♦♥ ▲♦❣✐❝✱ ❛♥❞ ♦t❤❡r ❧❛♥❣✉❛❣❡s ❛♥❛❧②s✐s ❝♦♠♣✉t❛t✐♦♥ ♦❢ ❝♦❧✐♠✐ts ♠❛♥❛❣❡♠❡♥t ♦❢ ♣r♦♦❢ ♦❜❧✐❣❛t✐♦♥s ✐♥t❡r❢❛❝❡s t♦ t❤❡♦r❡♠ ♣r♦✈❡rs✱ ♠♦❞❡❧ ❝❤❡❝❦❡rs✱ ♠♦❞❡❧ ✜♥❞❡rs

▼♦ss❛❦♦✇s❦✐ ❉✐str✐❜✉t❡❞ ❖♥t♦❧♦❣②✱ ▼♦❞❡❧✐♥❣ ❛♥❞ ❙♣❡❝✐✜❝❛t✐♦♥ ▲❛♥❣✉❛❣❡ ✭❉❖▲✮ ✷✵✶✹✲✶✶✲✶✷ ✽✵

SLIDE 81

▼♦t✐✈❛t✐♦♥ ❖♥t♦■❖♣ ❉❖▲ ❋♦❝✉s❡❞ ❖▼❙ ❖▼❙ ▲✐❜r❛r✐❡s ❈♦♥❝❧✉s✐♦♥

❚♦♦❧ s✉♣♣♦rt✿ ❖♥t♦❤✉❜ ✇❡❜ ♣♦rt❛❧ ❛♥❞ r❡♣♦s✐t♦r②

❖♥t♦❤✉❜ ✐s ❛ ✇❡❜✲❜❛s❡❞ r❡♣♦s✐t♦r② ❡♥❣✐♥❡ ❢♦r ❞✐str✐❜✉t❡❞ ❤❡t❡r♦❣❡♥❡♦✉s ✭♠✉❧t✐✲❧❛♥❣✉❛❣❡✮ ❖▼❙ ♣r♦t♦t②♣❡ ❛✈❛✐❧❛❜❧❡ ❛t ontohub.org s♣❡❛❦s ❉❖▲✱ ❖❲▲✱ ❈♦♠♠♦♥ ▲♦❣✐❝✱ ❛♥❞ ♦t❤❡r ❧❛♥❣✉❛❣❡s ♠✐❞✲t❡r♠ ❣♦❛❧✿ ❢♦❧❧♦✇ t❤❡ ❖♣❡♥ ❖♥t♦❧♦❣② ❘❡♣♦s✐t♦r② ■♥✐t✐❛t✐✈❡ ✭❖❖❘✮ ❛r❝❤✐t❡❝t✉r❡ ❛♥❞ ❆P■ ❆P■ ✐s ❞✐s❝✉ss❡❞ ❛t

https://github.com/ontohub/OOR_Ontohub_API

❛♥♥✉❛❧ ❖♥t♦❧♦❣② s✉♠♠✐t ❛s ❛ ✈❡♥✉❡ ❢♦r r❡✈✐❡✇✱ ❛♥❞ ❞✐s❝✉ss✐♦♥

▼♦ss❛❦♦✇s❦✐ ❉✐str✐❜✉t❡❞ ❖♥t♦❧♦❣②✱ ▼♦❞❡❧✐♥❣ ❛♥❞ ❙♣❡❝✐✜❝❛t✐♦♥ ▲❛♥❣✉❛❣❡ ✭❉❖▲✮ ✷✵✶✹✲✶✶✲✶✷ ✽✶

SLIDE 82

▼♦t✐✈❛t✐♦♥ ❖♥t♦■❖♣ ❉❖▲ ❋♦❝✉s❡❞ ❖▼❙ ❖▼❙ ▲✐❜r❛r✐❡s ❈♦♥❝❧✉s✐♦♥

EquivKeyword ::= ’equivalence’ EquivName ::= IRI EquivType ::= GroupOMS ’<\lessthan>-<\greaterthan>’ GroupOMS

▼♦ss❛❦♦✇s❦✐ ❉✐str✐❜✉t❡❞ ❖♥t♦❧♦❣②✱ ▼♦❞❡❧✐♥❣ ❛♥❞ ❙♣❡❝✐✜❝❛t✐♦♥ ▲❛♥❣✉❛❣❡ ✭❉❖▲✮ ✷✵✶✹✲✶✶✲✶✷ ✽✷

SLIDE 83

▼♦t✐✈❛t✐♦♥ ❖♥t♦■❖♣ ❉❖▲ ❋♦❝✉s❡❞ ❖▼❙ ❖▼❙ ▲✐❜r❛r✐❡s ❈♦♥❝❧✉s✐♦♥

❊q✉✐✈❛❧❡♥❝❡s

❡q✉✐✈❛❧❡♥❝❡ ■❞ ✿ ❖✶ ↔ ❖✷ ❂ ❖✸ ✭❢r❛❣♠❡♥t✮ ❖▼❙ ❖✸ ✐s s✉❝❤ t❤❛t ❖✐ t❤❡♥ ✪❞❡❢ ❖✸ ✐s ❛ ❞❡✜♥✐t✐♦♥❛❧ ❡①t❡♥s✐♦♥ ♦❢ ❖✐ ❢♦r ✐ = ✶, ✷❀ t❤✐s ✐♠♣❧✐❡s t❤❛t ❖✶ ❛♥❞ ❖✷ ❤❛✈❡ ♠♦❞❡❧ ❝❧❛ss❡s t❤❛t ❛r❡ ✐♥ ❜✐❥❡❝t✐✈❡ ❝♦rr❡s♣♦♥❞❡♥❝❡

equivalence e : algebra:BooleanAlgebra

↔ algebra:BooleanRing =

x∧y = x·y x∨y = x+y+x·y

¬x = 1+x

x·y = x∧y x+y = (x∨y) ∧ ¬(x∧y) end

▼♦ss❛❦♦✇s❦✐ ❉✐str✐❜✉t❡❞ ❖♥t♦❧♦❣②✱ ▼♦❞❡❧✐♥❣ ❛♥❞ ❙♣❡❝✐✜❝❛t✐♦♥ ▲❛♥❣✉❛❣❡ ✭❉❖▲✮ ✷✵✶✹✲✶✶✲✶✷ ✽✸

SLIDE 84

▼♦t✐✈❛t✐♦♥ ❖♥t♦■❖♣ ❉❖▲ ❋♦❝✉s❡❞ ❖▼❙ ❖▼❙ ▲✐❜r❛r✐❡s ❈♦♥❝❧✉s✐♦♥

ModuleRelDefn ::= ’module’ ModuleName [Conservative] ’:’ ’for’ InterfaceSignature ModuleName ::= IRI ModuleType ::= OMS ’of’ OMS

▼♦ss❛❦♦✇s❦✐ ❉✐str✐❜✉t❡❞ ❖♥t♦❧♦❣②✱ ▼♦❞❡❧✐♥❣ ❛♥❞ ❙♣❡❝✐✜❝❛t✐♦♥ ▲❛♥❣✉❛❣❡ ✭❉❖▲✮ ✷✵✶✹✲✶✶✲✶✷ ✽✹

SLIDE 85

▼♦t✐✈❛t✐♦♥ ❖♥t♦■❖♣ ❉❖▲ ❋♦❝✉s❡❞ ❖▼❙ ❖▼❙ ▲✐❜r❛r✐❡s ❈♦♥❝❧✉s✐♦♥

▼♦❞✉❧❡ ❘❡❧❛t✐♦♥s

♠♦❞✉❧❡ ■❞ ❝ ✿ ❖✶ ♦❢ ❖✷ ❢♦r Σ ❖✶ ✐s ❛ ♠♦❞✉❧❡ ♦❢ ❖✷ ✇✐t❤ r❡str✐❝t✐♦♥ s✐❣♥❛t✉r❡ Σ ❛♥❞ ❝♦♥s❡r✈❛t✐✈✐t② ❝ ❝❂✪♠❝♦♥s ❡✈❡r② Σ✲r❡❞✉❝t ♦❢ ❛♥ ❖✶✲♠♦❞❡❧ ❝❛♥ ❜❡ ❡①♣❛♥❞❡❞ t♦ ❛♥ ❖✷✲♠♦❞❡❧ ❝❂✪❝❝♦♥s ❡✈❡r② Σ✲s❡♥t❡♥❝❡ ϕ ❢♦❧❧♦✇✐♥❣ ❢r♦♠ ❖✶ ❛❧r❡❛❞② ❢♦❧❧♦✇s ❢r♦♠ ❖✶ ❚❤✐s r❡❧❛t✐♦♥ s❤❛❧❧ ❤♦❧❞ ❢♦r ❛♥② ♠♦❞✉❧❡ ❖✶ ❡①tr❛❝t❡❞ ❢r♦♠ ❖✷ ✉s✐♥❣ t❤❡ ❡①tr❛❝t ❝♦♥str✉❝t✳

▼♦ss❛❦♦✇s❦✐ ❉✐str✐❜✉t❡❞ ❖♥t♦❧♦❣②✱ ▼♦❞❡❧✐♥❣ ❛♥❞ ❙♣❡❝✐✜❝❛t✐♦♥ ▲❛♥❣✉❛❣❡ ✭❉❖▲✮ ✷✵✶✹✲✶✶✲✶✷ ✽✺

SLIDE 86

▼♦t✐✈❛t✐♦♥ ❖♥t♦■❖♣ ❉❖▲ ❋♦❝✉s❡❞ ❖▼❙ ❖▼❙ ▲✐❜r❛r✐❡s ❈♦♥❝❧✉s✐♦♥

❈♦♥❝❧✉s✐♦♥

❉❖▲ ✐s ❛ ♠❡t❛ ❧❛♥❣✉❛❣❡ ❢♦r ✭❢♦r♠❛❧✮ ♦♥t♦❧♦❣✐❡s✱ s♣❡❝✐✜❝❛t✐♦♥s ❛♥❞ ♠♦❞❡❧s ✭❖▼❙✮ ❉❖▲ ❝♦✈❡rs ♠❛♥② ❛s♣❡❝ts ♦❢ ♠♦❞✉❧❛r✐t② ♦❢ ❛♥❞ r❡❧❛t✐♦♥s ❛♠♦♥❣ ❖▼❙ ✭✏❖▼❙✲✐♥✲t❤❡ ❧❛r❣❡✑✮ ❉❖▲ ✇✐❧❧ ❜❡ s✉❜♠✐tt❡❞ t♦ t❤❡ ❖▼● ❛s ❛♥ ❛♥s✇❡r t♦ t❤❡ ❖♥t♦■❖♣ ❘❋P ②♦✉ ❝❛♥ ❤❡❧♣ ✇✐t❤ ❥♦✐♥✐♥❣ t❤❡ ❖♥t♦■❖♣ ❞✐s❝✉ss✐♦♥

s❡❡ ontoiop.org

▼♦ss❛❦♦✇s❦✐ ❉✐str✐❜✉t❡❞ ❖♥t♦❧♦❣②✱ ▼♦❞❡❧✐♥❣ ❛♥❞ ❙♣❡❝✐✜❝❛t✐♦♥ ▲❛♥❣✉❛❣❡ ✭❉❖▲✮ ✷✵✶✹✲✶✶✲✶✷ ✽✻

SLIDE 87

▼♦t✐✈❛t✐♦♥ ❖♥t♦■❖♣ ❉❖▲ ❋♦❝✉s❡❞ ❖▼❙ ❖▼❙ ▲✐❜r❛r✐❡s ❈♦♥❝❧✉s✐♦♥

❘❡❧❛t❡❞ ✇♦r❦

❙tr✉❝t✉r❡❞ s♣❡❝✐✜❝❛t✐♦♥s ❛♥❞ t❤❡✐r s❡♠❛♥t✐❝s ✭❈❧❡❛r✱ ❆❙▲✱ ❈❆❙▲✱ ✳ ✳ ✳ ✮ ❍❡t❡r♦❣❡♥❡♦✉s s♣❡❝✐✜❝❛t✐♦♥ ✭❍❡t❈❆❙▲✮ ♠♦❞✉❧❛r ♦♥t♦❧♦❣✐❡s ✭❲♦▼♦ ✇♦r❦s❤♦♣ s❡r✐❡s✮

▼♦ss❛❦♦✇s❦✐ ❉✐str✐❜✉t❡❞ ❖♥t♦❧♦❣②✱ ▼♦❞❡❧✐♥❣ ❛♥❞ ❙♣❡❝✐✜❝❛t✐♦♥ ▲❛♥❣✉❛❣❡ ✭❉❖▲✮ ✷✵✶✹✲✶✶✲✶✷ ✽✼