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Dec 29, 2023 10 likes •543 views

tt t r trs s rts rts s

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SLIDE 1

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

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

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

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

❖♥t♦■❖♣ t❡❧❡❝♦♥❢❡r❡♥❝❡✱ ✷✵✶✹✲✵✶✲✷✾

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

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SLIDE 2

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

▼♦t✐✈❛t✐♦♥

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

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SLIDE 3

▼♦t✐✈❛t✐♦♥ ❖♥t♦■❖♣ ❉❖▲ ▼♦❞✉❧❛r ❛♥❞ ❍❡t❡r♦❣❡♥❡♦✉s ❖❙▼s ❖❙▼ ❞❡❝❧❛r❛t✐♦♥s ❛♥❞ r❡❧❛t✐♦♥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✦ ✭❋♦r♠❛❧✮ ♦♥t♦❧♦❣✐❡s✱ ✭❢♦r♠❛❧✮ s♣❡❝✐✜❝❛t✐♦♥s ❛♥❞ ✭❢♦r♠❛❧✮ ♠♦❞❡❧s ✇✐❧❧ ❤❡♥❝❡❢♦rt❤ ❜❡ ❛❜❜r❡✈✐❛t❡❞ ❛s ❖❙▼s✳

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

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SLIDE 4

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

❖♥t♦❧♦❣② ✉s❡ ❈❛s❡✿ ❖▼●✬s ❉❛t❡✲❚✐♠❡ ❱♦❝❛❜✉❧❛r②

❞❛t❡✲t✐♠❡ ✈♦❝❛❜✉❧❛r② ✐s ❢♦r♠✉❧❛t❡❞ ✐♥ ❞✐✛❡r❡♥t ❧❛♥❣✉❛❣❡s✿ ❙❇❱❘✱ ❈♦♠♠♦♥ ▲♦❣✐❝✱ ■❑▲✱ ❯▼▲✰❖❈▲✱ ❖❲▲ ❞✐✛❡r❡♥t ❧❛♥❣✉❛❣❡s ❛❞❞r❡ss ❞✐✛❡r❡♥t ❛✉❞✐❡♥❝❡s

❙❇❱❘✿ ❜✉s✐♥❡ss ✉s❡rs ❯▼▲✰❖❈▲✿ s♦❢t✇❛r❡ ✐♠♣❧❡♠❡♥t♦rs ❖❲▲✿ ♦♥t♦❧♦❣② ❞❡✈❡❧♦♣❡rs ❛♥❞ ✉s❡rs ❈♦♠♠♦♥ ▲♦❣✐❝✱ ■❑▲✿ ✭❢♦✉♥❞❛t✐♦♥❛❧✮ ♦♥t♦❧♦❣② ❞❡✈❡❧♦♣❡rs ❛♥❞ ✉s❡rs

❍♦✇ ❝❛♥ ✇❡

❢♦r♠❛❧❧② r❡❧❛t❡ t❤❡ ❞✐✛❡r❡♥t ❧♦❣✐❝❛❧ s♣❡❝✐✜❝❛t✐♦♥s❄ s♣❡❝✐❢② t❤❡ ❖❲▲ ✈❡rs✐♦♥ t♦ ❜❡ ❛♥ ❛♣♣r♦①✐♠❛t✐♦♥ ♦❢ t❤❡ ❈♦♠♠♦♥ ▲♦❣✐❝ ✈❡rs✐♦♥❄ ❡①tr❛❝t s✉❜♠♦❞✉❧❡s ❝♦✈❡r✐♥❣ s♣❡❝✐✜❝ ❛s♣❡❝ts❄

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

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SLIDE 5

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

❯s❡ ❈❛s❡✿ ❘❡✜♥❡♠❡♥t ♦❢ s♣❡❝✐✜❝❛t✐♦♥s

r❡✜♥❡♠❡♥t ❢r♦♠ r❡q✉✐r❡♠❡♥ts t♦ ❞❡s✐❣♥ t♦ ❝♦❞❡ ♠❛♥② ❞✐✛❡r❡♥t ❢♦r♠❛❧✐s♠s ❢♦r♠❛❧✐s♠ ♠❛② ❝❤❛♥❣❡ ❞✉r✐♥❣ ❢♦r♠❛❧ ❞❡✈❡❧♦♣♠❡♥t ②❡t✱ s♦♠❡ ❣❡♥❡r❛❧ ♠❡❝❤❛♥✐s♠ ♦❢ r❡✜♥❡♠❡♥ts ❛r❡ ❛❧✇❛②s t❤❡ s❛♠❡

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

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SLIDE 6

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

❯s❡ ❈❛s❡✿ ❈♦♥s✐st❡♥❝② ❛♥❞ s❛t✐s✜❛❜✐❧✐t② ❛♠♦♥❣ ❯▼▲ ♠♦❞❡❧s

❞♦❡s ❛♥ ♦❜❥❡❝t ❞✐❛❣r❛♠ s❛t✐s❢② ❛ ❝❧❛ss ❞✐❛❣r❛♠❄ ❉♦❡s ❛ st❛t❡ ♠❛❝❤✐♥❡ s❛t✐s❢② ❛♥ ❖❈▲ s♣❡❝✐✜❝❛t✐♦♥❄ ❉♦ t❤❡ ♣r♦t♦❝❛❧ st❛t❡ ♠❛❝❤✐♥❡s ❛t t❤❡ ❡♥❞s ♦❢ ❛ ❝♦♥♥❡❝t♦r ✜t t♦❣❡t❤❡r❄ ❉♦❡s ❛ st❛t❡ ♠❛❝❤✐♥❡ r❡✜♥❡ t❤❡ ♣r♦t♦❝♦❧ st❛t❡ ♠❛❝❤✐♥❡s ✐♥ ❛ str✉❝t✉r❡ ❞✐❛❣r❛♠❄

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

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SLIDE 7

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

❖♥t♦❧♦❣✐❡s✿ ❆♥ ■♥✐t✐❛❧ ▲♦❣✐❝ ●r❛♣❤

CL HOL Prop SROIQ (OWL 2 DL) FOL= FOLms= OBOOWL EL++ (OWL 2 EL) DL-LiteR (OWL 2 QL) DL-RL (OWL 2 RL) DDLOWL ECoOWL ECoFOL F-logic bRDF RDF RDFS OWL-Full EER

subinstitute theoroidal subinstitute simultaneously exact and model-expansive comorphisms model-expansive comorphisms grey: no fixed expressivity green: decidable ontology languages yellow: semi-decidable

  • range: some second-order constructs

red: full second-order logic

OBO 1.4 CASL UML-CD

CL-

Schema.org SKOS SKOS

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

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SLIDE 8

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

❙♣❡❝✐✜❝❛t✐♦♥s✿ ❆♥ ■♥✐t✐❛❧ ▲♦❣✐❝ ●r❛♣❤

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

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SLIDE 9

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

❯▼▲ ♠♦❞❡❧s✿ ❆♥ ■♥✐t✐❛❧ ▲♦❣✐❝ ●r❛♣❤

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

slide-10
SLIDE 10

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

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

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

♦❢ ♠❛♥② ❖❙▼s ❝♦✈❡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❡❞ ❖❙▼s

❜r✐❞❣❡s ❜❡t✇❡❡♥ ❞✐✛❡r❡♥t ♠♦❞❡❧❧✐♥❣s

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

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SLIDE 11

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

❖♥t♦■❖♣

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

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SLIDE 12

▼♦t✐✈❛t✐♦♥ ❖♥t♦■❖♣ ❉❖▲ ▼♦❞✉❧❛r ❛♥❞ ❍❡t❡r♦❣❡♥❡♦✉s ❖❙▼s ❖❙▼ ❞❡❝❧❛r❛t✐♦♥s ❛♥❞ r❡❧❛t✐♦♥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 ❛♠♦♥❣ ❖❙▼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✐♦♥ ▲❛♥❣✉❛❣❡ ✭❉❖▲✮ ✷✵✶✹✲✵✶✲✷✾ ✶✷

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SLIDE 13

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

❚❤❡ ❖♥t♦■❖♣ ✐♥✐t✐❛t✐✈❡

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✦

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

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SLIDE 14

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

❘❡q✉✐r❡♠❡♥ts ✐♥ t❤❡ ❖▼● ❘❋P ❖♥t♦■❖♣

♣r♦✈✐❞❡ ❛ ♠❡t❛✲❧❛♥❣✉❛❣❡ ❢♦r✿

❧♦❣✐❝❛❧❧② ❤❡t❡r♦❣❡♥❡♦✉s ❖❙▼s ♠♦❞✉❧❛r ❖❙▼s ♠♦❞✉❧❡ ❡①tr❛❝t✐♦♥✱ ❛♣♣r♦①✐♠❛t✐♦♥ ❧✐♥❦s ✭✐♥t❡r♣r❡t❛t✐♦♥s✱ ❛❧✐❣♥♠❡♥ts✮ ❜❡t✇❡❡♥ ❖❙▼s✴♠♦❞✉❧❡s ❝♦♠❜✐♥❛t✐♦♥ ♦❢ ❖❙▼s ❛❧♦♥❣ ❧✐♥❦s

♣r♦✈✐❞❡ ❛♥ ❛❜str❛❝t s②♥t❛① ❛s ▼❖❋ ♦r ❙▼❖❋ ♠♦❞❡❧ ♣r♦✈✐❞❡ ❛ ❝♦♥❝r❡t❡ s②♥t❛① ♣r♦✈✐❞❡ ❛ ❢♦r♠❛❧ s❡♠❛♥t✐❝s

❝r✐t❡r✐❛ ❢♦r ❧♦❣✐❝s t♦ ❝♦♥❢♦r♠ ✇✐t❤ ❖♥t♦■❖♣ tr❛♥s❧❛t✐♦♥s ❜❡t✇❡❡♥ t❤❡s❡ ❧♦❣✐❝s

❜❡ ❧♦❣✐❝✲❛❣♥♦st✐❝✱ ❡✳❣✳ ❖❙▼s ❝♦♥s✐st ♦❢ s②♠❜♦❧s ❛♥❞ ❛①✐♦♠s

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

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SLIDE 15

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

❉❖▲

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

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SLIDE 16

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

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

❤❛s ❜❡❡♥ ♣r❡♣❛r❡❞ ✇✐t❤✐♥ ■❙❖✴❚❈ ✸✼✴❙❈ ✸ ♥♦✇ ❝♦♥t✐♥✉❡❞ ❛s ❛ ♣r♦♣♦s❛❧ ❢♦r t❤❡ ❖▼● ❘❋P ❖♥t♦■❖♣

❉❖▲ ❂ ♦♥❡ s♣❡❝✐✜❝ ❛♥s✇❡r t♦ t❤❡ ❘❋P r❡q✉✐r❡♠❡♥ts t❤❡r❡ ♠❛② ❜❡ ♦t❤❡r ❛♥s✇❡rs t♦ t❤❡ ❘❋P ✭❜✉t ✉♥❧✐❦❡❧②✮

❉❖▲ ✐s ❜❛s❡❞ ♦♥ s♦♠❡ ❣r❛♣❤ ♦❢ ✐♥st✐t✉t✐♦♥s ❛♥❞ ✭❝♦✮♠♦r♣❤✐s♠s ❉❖▲ ❤❛s ❛ ♠♦❞❡❧✲❧❡✈❡❧ ❛♥❞ ❛ t❤❡♦r②✲❧❡✈❡❧ s❡♠❛♥t✐❝s

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

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SLIDE 17

▼♦t✐✈❛t✐♦♥ ❖♥t♦■❖♣ ❉❖▲ ▼♦❞✉❧❛r ❛♥❞ ❍❡t❡r♦❣❡♥❡♦✉s ❖❙▼s ❖❙▼ ❞❡❝❧❛r❛t✐♦♥s ❛♥❞ r❡❧❛t✐♦♥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✐♦♥ ▲❛♥❣✉❛❣❡ ✭❉❖▲✮ ✷✵✶✹✲✵✶✲✷✾ ✶✼

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SLIDE 18

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

❖✈❡r✈✐❡✇ ♦❢ ❉❖▲

✶ ♠♦❞✉❧❛r ❛♥❞ ❤❡t❡r♦❣❡♥❡♦✉s ❖❙▼s

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

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

✷ ❖❙▼ ❞❡❝❧❛r❛t✐♦♥s ❛♥❞ r❡❧❛t✐♦♥s ✭❜❛s❡❞ ♦♥ ✶✮

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

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

slide-19
SLIDE 19

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

▼♦❞✉❧❛r ❛♥❞ ❍❡t❡r♦❣❡♥❡♦✉s ❖❙▼s

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

slide-20
SLIDE 20

▼♦t✐✈❛t✐♦♥ ❖♥t♦■❖♣ ❉❖▲ ▼♦❞✉❧❛r ❛♥❞ ❍❡t❡r♦❣❡♥❡♦✉s ❖❙▼s ❖❙▼ ❞❡❝❧❛r❛t✐♦♥s ❛♥❞ r❡❧❛t✐♦♥s ❈♦♥❝❧✉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-21
SLIDE 21

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

❊①t❡♥s✐♦♥s

❖✶ t❤❡♥ ❖✷✿ ❡①t❡♥s✐♦♥ ♦❢ ❖✶ ❜② ♥❡✇ s②♠❜♦❧s ❛♥❞ ❛①✐♦♠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✐♦♥ ▲❛♥❣✉❛❣❡ ✭❉❖▲✮ ✷✵✶✹✲✵✶✲✷✾ ✷✶

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SLIDE 22

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

❘❡❢❡r❡♥❝❡s t♦ ◆❛♠❡❞ ❖❙▼s

❘❡❢❡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

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

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SLIDE 23

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

❯♥✐♦♥s

❖✶ ❛♥❞ ❖✷✿ ✉♥✐♦♥ ♦❢ t✇♦ st❛♥❞✲❛❧♦♥❡ ❖❙▼s ✭❢♦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✐♦♥ ▲❛♥❣✉❛❣❡ ✭❉❖▲✮ ✷✵✶✹✲✵✶✲✷✾ ✷✸

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SLIDE 24

▼♦t✐✈❛t✐♦♥ ❖♥t♦■❖♣ ❉❖▲ ▼♦❞✉❧❛r ❛♥❞ ❍❡t❡r♦❣❡♥❡♦✉s ❖❙▼s ❖❙▼ ❞❡❝❧❛r❛t✐♦♥s ❛♥❞ r❡❧❛t✐♦♥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✐♦♥ ▲❛♥❣✉❛❣❡ ✭❉❖▲✮ ✷✵✶✹✲✵✶✲✷✾ ✷✹

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SLIDE 25

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

❘❡❞✉❝t✐♦♥s

✐♥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♠

sort Elem

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

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

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

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SLIDE 26

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

■♥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 ♦❢ ❖

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

❞✉❛❧❧②

❖ ❢♦r❣❡t Σ ❖ ❢♦r❣❡t Σ ✇✐t❤ ■ sort Elem

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

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

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

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SLIDE 27

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

▼♦❞✉❧❡ ❊①tr❛❝t✐♦♥s

❖ ❡①tr❛❝t ❝ Σ ✇✐t❤ ♠ Σ✿ r❡str✐❝t✐♦♥ s✐❣♥❛t✉r❡ ✭s✉❜s✐❣♥❛t✉r❡ ♦❢ t❤❛t ♦❢ ❖✮ ❝✿ ♦♥❡ ♦❢ ✪♠❝♦♥s ❛♥❞ ✪❝❝♦♥s ♠✿ ♠♦❞✉❧❡ ❡①tr❛❝t✐♦♥ ♠❡t❤♦❞ ❖ ♠✉st ❜❡ ❛ ❝♦♥s❡r✈❛t✐✈❡ ❡①t❡♥s✐♦♥ ♦❢ t❤❡ r❡s✉❧t✐♥❣ ❡①tr❛❝t❡❞ ♠♦❞✉❧❡✳

co-ode:Pizza extract %mcons Class: VegetarianPizza Class: VegetableTopping ObjectProperty: hasTopping with locality

❉✉❛❧❧②✿ ❖ r❡♠♦✈❡ ❝ Σ ✇✐t❤ ♠

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

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SLIDE 28

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

❊①tr❛❝t ✕ ❋♦r❣❡t ✕ ❍✐❞❡

r❡♠♦✈❡✴❡①tr❛❝t ❢♦r❣❡t✴❦❡❡♣ ❤✐❞❡✴r❡✈❡❛❧ s❡♠❛♥t✐❝ ❜❛❝❦❣r♦✉♥❞ ❝♦♥s❡r✈❛t✐✈❡ ❡①t❡♥s✐♦♥ ✉♥✐❢♦r♠ ✐♥t❡r♣♦❧❛t✐♦♥ ♠♦❞❡❧ r❡❞✉❝t r❡❧❛t✐♦♥ t♦ ♦r✐❣✐♥❛❧ s✉❜t❤❡♦r② ✐♥t❡r♣r❡t❛❜❧❡ ✐♥t❡r♣r❡t❛❜❧❡ ❛♣♣r♦❛❝❤ t❤❡♦r② ❧❡✈❡❧ t❤❡♦r② ❧❡✈❡❧ ♠♦❞❡❧ ❧❡✈❡❧ t②♣❡ ♦❢ ♦♥t♦❧♦❣② ✢❛tt❡♥❛❜❧❡ ✢❛tt❡♥❛❜❧❡ ❡❧✉s✐✈❡ s✐❣♥❛t✉r❡ ♦❢ r❡s✉❧t ≥ Σ = Σ = Σ ❝❤❛♥❣❡ ♦❢ ❧♦❣✐❝ ♥♦t ♣♦ss✐❜❧❡ ♣♦ss✐❜❧❡ ♣♦ss✐❜❧❡

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

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SLIDE 29

▼♦t✐✈❛t✐♦♥ ❖♥t♦■❖♣ ❉❖▲ ▼♦❞✉❧❛r ❛♥❞ ❍❡t❡r♦❣❡♥❡♦✉s ❖❙▼s ❖❙▼ ❞❡❝❧❛r❛t✐♦♥s ❛♥❞ r❡❧❛t✐♦♥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✐♦♥ ▲❛♥❣✉❛❣❡ ✭❉❖▲✮ ✷✵✶✹✲✵✶✲✷✾ ✷✾

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SLIDE 30

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

❋r❡❡♥❡ss

❖✶ t❤❡♥ ❢r❡❡ ④ ❖✷ ⑥ ❢♦r❝❡s ✐♥✐t✐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✐♦♥ ▲❛♥❣✉❛❣❡ ✭❉❖▲✮ ✷✵✶✹✲✵✶✲✷✾ ✸✵

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SLIDE 31

▼♦t✐✈❛t✐♦♥ ❖♥t♦■❖♣ ❉❖▲ ▼♦❞✉❧❛r ❛♥❞ ❍❡t❡r♦❣❡♥❡♦✉s ❖❙▼s ❖❙▼ ❞❡❝❧❛r❛t✐♦♥s ❛♥❞ r❡❧❛t✐♦♥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✐♦♥ ▲❛♥❣✉❛❣❡ ✭❉❖▲✮ ✷✵✶✹✲✵✶✲✷✾ ✸✶

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SLIDE 32

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

❖❙▼ ❞❡❝❧❛r❛t✐♦♥s ❛♥❞ r❡❧❛t✐♦♥s

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

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SLIDE 33

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

❖❙▼ ❞❡✜♥✐t✐♦♥s

❖❙▼ ■❘■ ❂ ❖ ❡♥❞ ❛ss✐❣♥s ♥❛♠❡ ■❘■ t♦ ❖❙▼ ❖✱ ❢♦r ❧❛t❡r r❡❢❡r❡♥❝❡

  • ntology co-code:Pizza =

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

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

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SLIDE 34

▼♦t✐✈❛t✐♦♥ ❖♥t♦■❖♣ ❉❖▲ ▼♦❞✉❧❛r ❛♥❞ ❍❡t❡r♦❣❡♥❡♦✉s ❖❙▼s ❖❙▼ ❞❡❝❧❛r❛t✐♦♥s ❛♥❞ r❡❧❛t✐♦♥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✐♦♥ ▲❛♥❣✉❛❣❡ ✭❉❖▲✮ ✷✵✶✹✲✵✶✲✷✾ ✸✹

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SLIDE 35

▼♦t✐✈❛t✐♦♥ ❖♥t♦■❖♣ ❉❖▲ ▼♦❞✉❧❛r ❛♥❞ ❍❡t❡r♦❣❡♥❡♦✉s ❖❙▼s ❖❙▼ ❞❡❝❧❛r❛t✐♦♥s ❛♥❞ r❡❧❛t✐♦♥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✐♦♥ ▲❛♥❣✉❛❣❡ ✭❉❖▲✮ ✷✵✶✹✲✵✶✲✷✾ ✸✺

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SLIDE 36

▼♦t✐✈❛t✐♦♥ ❖♥t♦■❖♣ ❉❖▲ ▼♦❞✉❧❛r ❛♥❞ ❍❡t❡r♦❣❡♥❡♦✉s ❖❙▼s ❖❙▼ ❞❡❝❧❛r❛t✐♦♥s ❛♥❞ r❡❧❛t✐♦♥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✐♦♥ ▲❛♥❣✉❛❣❡ ✭❉❖▲✮ ✷✵✶✹✲✵✶✲✷✾ ✸✻

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SLIDE 37

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

❆❧✐❣♥♠❡♥ts

❛❧✐❣♥♠❡♥t ■❞ ❝❛r❞✶ ❝❛r❞✷ ✿ ❖✶ t♦ ❖✷ ❂ ❝✶✱✳ ✳ ✳ ❝♥ ❝❛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-38
SLIDE 38

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

❆❧✐❣♥♠❡♥t✿ ❆♥♦t❤❡r ❊①❛♠♣❧❡

  • ntology Onto1 =

Class: Person Class: Woman SubClassOf: Person Class: Bank end

  • ntology Onto2 =

Class: HumanBeing Class: Woman SubClassOf: HumanBeing Class: Bank end alignment VAlignment : Onto1 to Onto2 = Person = HumanBeing, Woman = Woman end

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

slide-39
SLIDE 39

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

❈♦♠❜✐♥❛t✐♦♥s

❝♦♠❜✐♥❡ ❖✶, . . . , ❖♥ ▲✶, . . . , ▲♠ ▲❥ ❛r❡ ❧✐♥❦s ✭✐♥t❡r♣r❡t❛t✐♦♥s✱ ❛❧✐❣♥♠❡♥ts✮ ❜❡t✇❡❡♥ ❖❙▼s ❚❤❡ ✐♥❞✐✈✐❞✉❛❧ ❖❙▼s ❝❛♥ ❜❡ ♣r❡✜①❡❞ ✇✐t❤ ❧❛❜❡❧s✱ ❧✐❦❡ ♥ : ❖ s❡♠❛♥t✐❝s ✐s ❛ ❝♦❧✐♠✐t

  • ntology AlignedOntology1 =

combine Alignment1

  • ntology VAlignedOntology =

combine 1 : Onto1, 2 : Onto2, VAlignment %% 1:Person is identified with 2:HumanBeing %% 1:Woman is identified with 2:Woman %% 1:Bank and 2:Bank are kept distinct

  • ntology VAlignedOntologyRenamed =

VAlignedOntology with 1:Bank |-> RiverBank, 2:Bank |-> FinancialBank, Person_HumanBeing |-> Person

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

slide-40
SLIDE 40

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

❉✐❛❣r❛♠ ❢♦r ❋✐rst ❆❧✐❣♥♠❡♥t

{❲♦♠❛♥} ❲♦♠❛♥ ⊑ P❡rs♦♥ {P❡rs♦♥} {❲♦♠❛♥}

  • {P❡rs♦♥}
  • ▼♦ss❛❦♦✇s❦✐

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

slide-41
SLIDE 41

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

❈♦❧✐♠✐t ❢♦r ❋✐rst ❆❧✐❣♥♠❡♥t

❲♦♠❛♥ ⊑ P❡rs♦♥ {❲♦♠❛♥}

  • ❲♦♠❛♥ ⊑ P❡rs♦♥
  • {P❡rs♦♥}
  • {❲♦♠❛♥}
  • {P❡rs♦♥}
  • ▼♦ss❛❦♦✇s❦✐

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

slide-42
SLIDE 42

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

❉✐❛❣r❛♠ ❢♦r ❙❡❝♦♥❞ ❆❧✐❣♥♠❡♥t

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

  • ▼♦ss❛❦♦✇s❦✐

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

slide-43
SLIDE 43

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

❈♦❧✐♠✐t ❢♦r ❙❡❝♦♥❞ ❆❧✐❣♥♠❡♥t

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

  • ❖♥t♦✷
  • {❲♦♠❛♥, P❡rs♦♥❴❍✉♠❛♥❇❡✐♥❣}
  • ▼♦ss❛❦♦✇s❦✐

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

slide-44
SLIDE 44

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

❈♦♥str✉❝t✐♦♥ ♦❢ ❉✐❛❣r❛♠s

❖✶ ❇ ❖✷ ❖′

✶

  • ❖′

✷

  • ❖✶❴❖✷

σ✷

  • σ✶
  • ❖✶❴❖✷ ❝♦♥t❛✐♥s✱ ❢♦r ❡❛❝❤ s✶ = s✷ ✐♥ ❆✱ ❛ s②♠❜♦❧ s✶❴s✷

❖′

✶ ❛♥❞ ❖′ ✷ ❝♦♥t❛✐♥ t❤❡ s②♠❜♦❧s ♦❢ ❖✶ ❛♥❞ ❖✷ ✱ r❡s♣❡❝t✐✈❡❧②✱

✇❤✐❝❤ ❛♣♣❡❛r ✐♥ ❆ ✐♥ ❛ ❝♦rr❡s♣♦♥❞❡♥❝❡ s✶ ❘ s✷ s✉❝❤ t❤❛t ❘ ✐s ♥♦t ❡q✉✐✈❛❧❡♥❝❡ ❛♥❞ ❇ ✐s ❛♥ ❖❙▼ ❝♦♥str✉❝t❡❞ t❤❡ s✐❣♥❛t✉r❡ ♠♦r♣❤✐s♠s σ✶ ❛♥❞ σ✷ ♠❛♣ ❡❛❝❤ s②♠❜♦❧ s✶❴s✷ t♦ s✶ ❛♥❞ r❡s♣❡❝t✐✈❡❧② s✷✳

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

slide-45
SLIDE 45

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

❖❙▼ ❇r✐❞❣❡s

❖✶ ❜r✐❞❣❡ ✇✐t❤ tr❛♥s❧❛t✐♦♥ t ❖✷ t ✐s ❛ ❧♦❣✐❝ tr❛♥s❧❛t✐♦♥ s❡♠❛♥t✐❝s✿ ❖✶ ✇✐t❤ tr❛♥s❧❛t✐♦♥ t t❤❡♥ ❖✷ t ✇✐❧❧ ❡✳❣✳ tr❛♥s❧❛t❡ ❖❲▲ t♦ s♦♠❡ ❉❉▲ ♦r E✲❝♦♥♥❡❝t✐♦♥s ❖✷✿ ❛①✐♦♠s ✐♥✈♦❧✈✐♥❣ t❤❡ r❡❧❛t✐♦♥s ✭✐♥tr♦❞✉❝❡❞ ❜② t✮ ❜❡t✇❡❡♥ ❖❙▼s ✐♥ ❖✶✳

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

slide-46
SLIDE 46

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

❖❙▼ ❇r✐❞❣❡ ❊①❛♠♣❧❡

  • ntology Publications1 =

Class: Publication Class: Article SubClassOf: Publication Class: InBook SubClassOf: Publication Class: Thesis SubClassOf: Publication ...

  • ntology Publications2 =

Class: Thing Class: Article SubClassOf: Thing Class: BookArticle SubClassOf: Thing Class: Publication SubClassOf: Thing Class: Thesis SubClassOf: Thing

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

slide-47
SLIDE 47

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

❖❙▼ ❇r✐❞❣❡ ❊①❛♠♣❧❡✱ ❝♦♥t✬❞

  • ntology Publications_Combined =

combine 1 : Publications1 with translation OWL2MS-OWL, 2 : Publications2 with translation OWL2MS-OWL %% implicitly: Article → 1:Article ... %% Article → 2:Article ... bridge with translation MS-OWL2DDL %% implicitly added my translation MS-OWL2DDL: binary 1:Publication

⊑

− → 2:Publication

1:PhdThesis

⊑

− → 2:Thesis

1:InBook

⊑

− → 2:BookArticle

1:Article

⊑

− → 2:Article

1:Article

⊒

− → 2:Article

end

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

slide-48
SLIDE 48

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

◗✉❛❧✐✜❝❛t✐♦♥s

◗✉❛❧✐✜❝❛t✐♦♥s ❝❤♦♦s❡ t❤❡ ❧♦❣✐❝✱ ❖❙▼ ❧❛♥❣✉❛❣❡ ❛♥❞✴♦r s❡r✐❛❧✐③❛t✐♦♥✿ ❧❛♥❣✉❛❣❡ ❧ ❧♦❣✐❝ ❧ s❡r✐❛❧✐③❛t✐♦♥ s ❚❤✐s ❛✛❡❝ts t❤❡ s✉❜s❡q✉❡♥t ❞❡❝❧❛r❛t✐♦♥s ❛♥❞ r❡❧❛t✐♦♥s ✐♥ t❤❡ ❞✐str✐❜✉t❡❞ ❖❙▼✳

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

slide-49
SLIDE 49

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

❈♦♥❝❧✉s✐♦♥

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

slide-50
SLIDE 50

▼♦t✐✈❛t✐♦♥ ❖♥t♦■❖♣ ❉❖▲ ▼♦❞✉❧❛r ❛♥❞ ❍❡t❡r♦❣❡♥❡♦✉s ❖❙▼s ❖❙▼ ❞❡❝❧❛r❛t✐♦♥s ❛♥❞ r❡❧❛t✐♦♥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✲❧✐❦❡ ❖❙▼s❄ ❈❛♥ 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-51
SLIDE 51

▼♦t✐✈❛t✐♦♥ ❖♥t♦■❖♣ ❉❖▲ ▼♦❞✉❧❛r ❛♥❞ ❍❡t❡r♦❣❡♥❡♦✉s ❖❙▼s ❖❙▼ ❞❡❝❧❛r❛t✐♦♥s ❛♥❞ r❡❧❛t✐♦♥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-52
SLIDE 52

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

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

❖♥t♦❤✉❜ ✐s ❛ ✇❡❜✲❜❛s❡❞ r❡♣♦s✐t♦r② ❡♥❣✐♥❡ ❢♦r ❞✐str✐❜✉t❡❞ ❤❡t❡r♦❣❡♥❡♦✉s ✭♠✉❧t✐✲❧❛♥❣✉❛❣❡✮ ❖❙▼s ♣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-53
SLIDE 53

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

❈♦♥❝❧✉s✐♦♥

❉❖▲ ✐s ❛ ♠❡t❛ ❧❛♥❣✉❛❣❡ ❢♦r ✭❢♦r♠❛❧✮ ♦♥t♦❧♦❣✐❡s✱ s♣❡❝✐✜❝❛t✐♦♥s ❛♥❞ ♠♦❞❡❧s ✭❖❙▼s✮ ❉❖▲ ❝♦✈❡rs ♠❛♥② ❛s♣❡❝ts ♦❢ ♠♦❞✉❧❛r✐t② ♦❢ ❛♥❞ r❡❧❛t✐♦♥s ❛♠♦♥❣ ❖❙▼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✐♦♥ ▲❛♥❣✉❛❣❡ ✭❉❖▲✮ ✷✵✶✹✲✵✶✲✷✾ ✺✸