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❚♦✇❛r❞s Pr❛❝t✐❝❛❧ ◗✉❡r② ❆♥s✇❡r✐♥❣ ❢♦r ❍♦r♥✲SHIQ

❚❤♦♠❛s ❊✐t❡r1 ▼❛❣❞❛❧❡♥❛ ❖rt✐③1 ▼❛♥t❛s ➆✐♠❦✉s1 ❚r✉♥❣✲❑✐❡♥ ❚r❛♥ 2

• ✉♦❤✉✐ ❳✐❛♦1

1■♥st✐t✉t❡ ♦❢ ■♥❢♦r♠❛t✐♦♥ ❙②st❡♠s✱ ❱✐❡♥♥❛ ❯♥✐✈❡rs✐t② ♦❢ ❚❡❝❤♥♦❧♦❣② 2❙❚❆❘▲❛❜✱ ❱r✐❥❡ ❯♥✐✈❡rs✐t❡✐t ❇r✉ss❡❧

✷✺t❤ ■♥t❡r♥❛t✐♦♥❛❧ ❲♦r❦s❤♦♣ ♦♥ ❉❡s❝r✐♣t✐♦♥ ▲♦❣✐❝s ✭❉▲ ✷✵✶✷✮

✶✴✶✽

❈◗ ❛♥s✇❡r✐♥❣ ❢♦r ❍♦r♥✲SHIQ ✶✳ ▼♦t✐✈❛t✐♦♥

◗✉❡r② ❆♥s✇❡r✐♥❣ ✐♥ ❉▲s

❖♥t♦❧♦❣② ❇❛s❡❞ ❉❛t❛ ❆❝❝❡ss ✐s ❛ ❦❡② ❛♣♣❧✐❝❛t✐♦♥ ♦❢ ❉▲s ❍❡♥❝❡✱ q✉❡r② ❛♥s✇❡r✐♥❣ ✐♥ ❉▲s ❛ ❝r✉❝✐❛❧ ♣r♦❜❧❡♠

❊✈❛❧✉❛t❡ ❛ ❝♦♥❥✉♥❝t✐✈❡ q✉❡r② q ♦✈❡r ❛♥ ❆❇♦① A✱ t❛❦✐♥❣ ✐♥t♦ ❛❝❝♦✉♥t t❤❡ ❝♦♥str❛✐♥ts ❡①♣r❡ss❡❞ ❜② ❛ ❉▲ ❚❇♦① T

❇r❛③✐❧ ❇r❛③✐❧ ❇r❛s✐❧✐❛ ❇r❛③✐❧ ❇r❛s✐❧✐❛ ❇r❛s✐❧✐❛ ❇r❛③✐❧ ❇r❛s✐❧✐❛ ❇r❛s✐❧✐❛ ❘❡❣✐ã♦❈❡♥tr♦❖❡st❡ ❘❡❣✐ã♦❈❡♥tr♦❖❡st❡ ❇r❛③✐❧ ❇r❛s✐❧✐❛

❉▲ ✷✵✶✷ ✷✴✶✽

❈◗ ❛♥s✇❡r✐♥❣ ❢♦r ❍♦r♥✲SHIQ ✶✳ ▼♦t✐✈❛t✐♦♥

◗✉❡r② ❆♥s✇❡r✐♥❣ ✐♥ ❉▲s

❖♥t♦❧♦❣② ❇❛s❡❞ ❉❛t❛ ❆❝❝❡ss ✐s ❛ ❦❡② ❛♣♣❧✐❝❛t✐♦♥ ♦❢ ❉▲s ❍❡♥❝❡✱ q✉❡r② ❛♥s✇❡r✐♥❣ ✐♥ ❉▲s ❛ ❝r✉❝✐❛❧ ♣r♦❜❧❡♠

❊✈❛❧✉❛t❡ ❛ ❝♦♥❥✉♥❝t✐✈❡ q✉❡r② q ♦✈❡r ❛♥ ❆❇♦① A✱ t❛❦✐♥❣ ✐♥t♦ ❛❝❝♦✉♥t t❤❡ ❝♦♥str❛✐♥ts ❡①♣r❡ss❡❞ ❜② ❛ ❉▲ ❚❇♦① T

hasDevelopedCapital(x) ← country(x), hasCapital(x, y), city(y), hasHDI(y, high) ❇r❛③✐❧ ❇r❛③✐❧ ❇r❛s✐❧✐❛ ❇r❛③✐❧ ❇r❛s✐❧✐❛ ❇r❛s✐❧✐❛ A country(❇r❛③✐❧) capital(❇r❛s✐❧✐❛) isLocatedIn(❇r❛s✐❧✐❛, ❘❡❣✐ã♦❈❡♥tr♦❖❡st❡) isLocatedIn(❘❡❣✐ã♦❈❡♥tr♦❖❡st❡, ❇r❛③✐❧) hasHDI(❇r❛s✐❧✐❛, high)

❉▲ ✷✵✶✷ ✷✴✶✽

❈◗ ❛♥s✇❡r✐♥❣ ❢♦r ❍♦r♥✲SHIQ ✶✳ ▼♦t✐✈❛t✐♦♥

◗✉❡r② ❆♥s✇❡r✐♥❣ ✐♥ ❉▲s

❖♥t♦❧♦❣② ❇❛s❡❞ ❉❛t❛ ❆❝❝❡ss ✐s ❛ ❦❡② ❛♣♣❧✐❝❛t✐♦♥ ♦❢ ❉▲s ❍❡♥❝❡✱ q✉❡r② ❛♥s✇❡r✐♥❣ ✐♥ ❉▲s ❛ ❝r✉❝✐❛❧ ♣r♦❜❧❡♠

❊✈❛❧✉❛t❡ ❛ ❝♦♥❥✉♥❝t✐✈❡ q✉❡r② q ♦✈❡r ❛♥ ❆❇♦① A✱ t❛❦✐♥❣ ✐♥t♦ ❛❝❝♦✉♥t t❤❡ ❝♦♥str❛✐♥ts ❡①♣r❡ss❡❞ ❜② ❛ ❉▲ ❚❇♦① T

hasDevelopedCapital(x) ← country(x), hasCapital(x, y), city(y), hasHDI(y, high) ❇r❛③✐❧ country(❇r❛③✐❧) hasHDI(❇r❛s✐❧✐❛, high) ❇r❛③✐❧ ❇r❛s✐❧✐❛ ❇r❛s✐❧✐❛ A country(❇r❛③✐❧) capital(❇r❛s✐❧✐❛) isLocatedIn(❇r❛s✐❧✐❛, ❘❡❣✐ã♦❈❡♥tr♦❖❡st❡) isLocatedIn(❘❡❣✐ã♦❈❡♥tr♦❖❡st❡, ❇r❛③✐❧) hasHDI(❇r❛s✐❧✐❛, high)

❉▲ ✷✵✶✷ ✷✴✶✽

❈◗ ❛♥s✇❡r✐♥❣ ❢♦r ❍♦r♥✲SHIQ ✶✳ ▼♦t✐✈❛t✐♦♥

◗✉❡r② ❆♥s✇❡r✐♥❣ ✐♥ ❉▲s

❖♥t♦❧♦❣② ❇❛s❡❞ ❉❛t❛ ❆❝❝❡ss ✐s ❛ ❦❡② ❛♣♣❧✐❝❛t✐♦♥ ♦❢ ❉▲s ❍❡♥❝❡✱ q✉❡r② ❛♥s✇❡r✐♥❣ ✐♥ ❉▲s ❛ ❝r✉❝✐❛❧ ♣r♦❜❧❡♠

❊✈❛❧✉❛t❡ ❛ ❝♦♥❥✉♥❝t✐✈❡ q✉❡r② q ♦✈❡r ❛♥ ❆❇♦① A✱ t❛❦✐♥❣ ✐♥t♦ ❛❝❝♦✉♥t t❤❡ ❝♦♥str❛✐♥ts ❡①♣r❡ss❡❞ ❜② ❛ ❉▲ ❚❇♦① T

hasDevelopedCapital(x) ← country(x), hasCapital(x, y), city(y), hasHDI(y, high) ❇r❛③✐❧ country(❇r❛③✐❧) hasHDI(❇r❛s✐❧✐❛, high) hasCapital(❇r❛③✐❧, ❇r❛s✐❧✐❛), city(❇r❛s✐❧✐❛), A T country(❇r❛③✐❧) capital(❇r❛s✐❧✐❛) isLocatedIn(❇r❛s✐❧✐❛, ❘❡❣✐ã♦❈❡♥tr♦❖❡st❡) isLocatedIn(❘❡❣✐ã♦❈❡♥tr♦❖❡st❡, ❇r❛③✐❧) hasHDI(❇r❛s✐❧✐❛, high) trans(isLocatedIn) country ⊑ ∃hasCapital.capital hasCapital ⊑ isLocatedIn country ⊑ 1 isLocatedIn−.capital country ⊑ ∀hasCapital.city

❉▲ ✷✵✶✷ ✷✴✶✽

❈◗ ❛♥s✇❡r✐♥❣ ❢♦r ❍♦r♥✲SHIQ ✶✳ ▼♦t✐✈❛t✐♦♥

◗✉❡r② ❆♥s✇❡r✐♥❣ ✐♥ ❉▲s

❖♥t♦❧♦❣② ❇❛s❡❞ ❉❛t❛ ❆❝❝❡ss ✐s ❛ ❦❡② ❛♣♣❧✐❝❛t✐♦♥ ♦❢ ❉▲s ❍❡♥❝❡✱ q✉❡r② ❛♥s✇❡r✐♥❣ ✐♥ ❉▲s ❛ ❝r✉❝✐❛❧ ♣r♦❜❧❡♠

❊✈❛❧✉❛t❡ ❛ ❝♦♥❥✉♥❝t✐✈❡ q✉❡r② q ♦✈❡r ❛♥ ❆❇♦① A✱ t❛❦✐♥❣ ✐♥t♦ ❛❝❝♦✉♥t t❤❡ ❝♦♥str❛✐♥ts ❡①♣r❡ss❡❞ ❜② ❛ ❉▲ ❚❇♦① T

hasDevelopedCapital(x) ← country(x), hasCapital(x, y), city(y), hasHDI(y, high) hasDevelopedCapital(❇r❛③✐❧) ← country(❇r❛③✐❧) hasHDI(❇r❛s✐❧✐❛, high) hasCapital(❇r❛③✐❧, ❇r❛s✐❧✐❛), city(❇r❛s✐❧✐❛), A T country(❇r❛③✐❧) capital(❇r❛s✐❧✐❛) isLocatedIn(❇r❛s✐❧✐❛, ❘❡❣✐ã♦❈❡♥tr♦❖❡st❡) isLocatedIn(❘❡❣✐ã♦❈❡♥tr♦❖❡st❡, ❇r❛③✐❧) hasHDI(❇r❛s✐❧✐❛, high) trans(isLocatedIn) country ⊑ ∃hasCapital.capital hasCapital ⊑ isLocatedIn country ⊑ 1 isLocatedIn−.capital country ⊑ ∀hasCapital.city

❉▲ ✷✵✶✷ ✷✴✶✽

❈◗ ❛♥s✇❡r✐♥❣ ❢♦r ❍♦r♥✲SHIQ ✶✳ ▼♦t✐✈❛t✐♦♥

❙t❛t❡ ♦❢ t❤❡ ❛rt

❋♦r ❧✐❣❤t✇❡✐❣❤t ❉▲s✱ s✉❝❝❡ss❢✉❧ q✉❡r② ❛♥s✇❡r✐♥❣ ✉s✐♥❣ ❞❛t❛❜❛s❡ t❡❝❤♥♦❧♦❣✐❡s

❋♦r DL✲▲✐t❡

◗✉❡r② r❡✇r✐t✐♥❣ ❝♦♠♣✐❧❡s q ❛♥❞ T ✐♥t♦ ❛ ❯❈◗✴❋❖ q✉❡r② qT qT ❝❛♥ ❜❡ ❡✈❛❧✉❛t❡❞ ♦✈❡r A ♦♥❧② ✇✐t❤ ♦✛✲t❤❡✲s❤❡❧❢ ❘❉❇▼❙s ▼❛♥② ♣❛♣❡rs ♦♥ ❜❡tt❡r ❛♥❞ s❤♦rt❡r r❡✇r✐t✐♥❣s

❋♦r EL

◗✉❡r② r❡✇r✐t✐♥❣ ✐♥t♦ ❉❛t❛❧♦❣ ✭❡✳❣✳✱✳ ❘❡q✉✐❡♠✮✱ ♥♦ ❋❖ r❡✇r✐t❛❜✐❧✐t② ❆❧t❡r♥❛t✐✈❡✿ t❤❡ ❝♦♠❜✐♥❡❞ ❛♣♣r♦❛❝❤

• ❚❇♦① ♣❛rt✐❛❧❧② ♠❛t❡r✐❛❧✐③❡❞ ✐♥ A ✭♣♦❧②♥♦♠✐❛❧ ❡①♣❛♥s✐♦♥✮
• q r❡✇r✐tt❡♥ ✐♥t♦ ❛ ❋❖ q✉❡r② ♦✈❡r t❤❡ ❡①♣❛♥❞❡❞ ❞❛t❛
• ❡✈❛❧✉❛t✐♦♥ ♣♦ss✐❜❧❡ ✇✐t❤ ♦✛✲t❤❡✲s❤❡❧❢ ❘❉❇▼❙s

❉▲ ✷✵✶✷ ✸✴✶✽

❈◗ ❛♥s✇❡r✐♥❣ ❢♦r ❍♦r♥✲SHIQ ✶✳ ▼♦t✐✈❛t✐♦♥

❙t❛t❡ ♦❢ t❤❡ ❛rt ✭❝♦♥t✬❞✮

❋♦r ♠♦r❡ ❡①♣r❡ss✐✈❡ ❉▲s

✭❢✉❧❧✮ ❈◗ ❛♥s✇❡r✐♥❣ ♥♦t s✉♣♣♦rt❡❞ ❜② r❡❛s♦♥❡rs ❛❧❣♦r✐t❤♠s ❞♦♥✬t s❡❡♠ ✐♠♣❧❡♠❡♥t❛❜❧❡ ♠❛♥② ❜❛❞ ❝♦♠♣❧❡①✐t② r❡s✉❧ts

• ALCI ❛♥❞ SH ❛r❡ ✷✲❊①♣❚✐♠❡✲❤❛r❞ ✐♥ ❝♦♠❜✐♥❡❞ ❝♦♠♣❧❡①✐t②
• ❛❧r❡❛❞② AL ✐♥tr❛❝t❛❜❧❡ ✐♥ ❞❛t❛ ❝♦♠♣❧❡①✐t②

❜❛❞ ♥❡✇s✦

■s q✉❡r② ❛♥s✇❡r✐♥❣ ❜❡②♦♥❞ ✲▲✐t❡ ❛♥❞ ♣r❛❝t✐❝❛❜❧❡❄ ❈❛♥ ✇❡ r❡❛❧✐③❡ ✐t ✉s✐♥❣ ❡①✐st✐♥❣ ❡✣❝✐❡♥t t❡❝❤♥♦❧♦❣✐❡s❄ ✭❘❉❇▼❙✱ ❉❛t❛❧♦❣ ❡♥❣✐♥❡s✱ ❡t❝✳✮

❉▲ ✷✵✶✷ ✹✴✶✽

❈◗ ❛♥s✇❡r✐♥❣ ❢♦r ❍♦r♥✲SHIQ ✶✳ ▼♦t✐✈❛t✐♦♥

❙t❛t❡ ♦❢ t❤❡ ❛rt ✭❝♦♥t✬❞✮

❋♦r ♠♦r❡ ❡①♣r❡ss✐✈❡ ❉▲s

✭❢✉❧❧✮ ❈◗ ❛♥s✇❡r✐♥❣ ♥♦t s✉♣♣♦rt❡❞ ❜② r❡❛s♦♥❡rs ❛❧❣♦r✐t❤♠s ❞♦♥✬t s❡❡♠ ✐♠♣❧❡♠❡♥t❛❜❧❡ ♠❛♥② ❜❛❞ ❝♦♠♣❧❡①✐t② r❡s✉❧ts

• ALCI ❛♥❞ SH ❛r❡ ✷✲❊①♣❚✐♠❡✲❤❛r❞ ✐♥ ❝♦♠❜✐♥❡❞ ❝♦♠♣❧❡①✐t②
• ❛❧r❡❛❞② AL ✐♥tr❛❝t❛❜❧❡ ✐♥ ❞❛t❛ ❝♦♠♣❧❡①✐t②

➥❜❛❞ ♥❡✇s✦

■s q✉❡r② ❛♥s✇❡r✐♥❣ ❜❡②♦♥❞ ✲▲✐t❡ ❛♥❞ ♣r❛❝t✐❝❛❜❧❡❄ ❈❛♥ ✇❡ r❡❛❧✐③❡ ✐t ✉s✐♥❣ ❡①✐st✐♥❣ ❡✣❝✐❡♥t t❡❝❤♥♦❧♦❣✐❡s❄ ✭❘❉❇▼❙✱ ❉❛t❛❧♦❣ ❡♥❣✐♥❡s✱ ❡t❝✳✮

❉▲ ✷✵✶✷ ✹✴✶✽

❈◗ ❛♥s✇❡r✐♥❣ ❢♦r ❍♦r♥✲SHIQ ✶✳ ▼♦t✐✈❛t✐♦♥

❙t❛t❡ ♦❢ t❤❡ ❛rt ✭❝♦♥t✬❞✮

❋♦r ♠♦r❡ ❡①♣r❡ss✐✈❡ ❉▲s

✭❢✉❧❧✮ ❈◗ ❛♥s✇❡r✐♥❣ ♥♦t s✉♣♣♦rt❡❞ ❜② r❡❛s♦♥❡rs ❛❧❣♦r✐t❤♠s ❞♦♥✬t s❡❡♠ ✐♠♣❧❡♠❡♥t❛❜❧❡ ♠❛♥② ❜❛❞ ❝♦♠♣❧❡①✐t② r❡s✉❧ts

• ALCI ❛♥❞ SH ❛r❡ ✷✲❊①♣❚✐♠❡✲❤❛r❞ ✐♥ ❝♦♠❜✐♥❡❞ ❝♦♠♣❧❡①✐t②
• ❛❧r❡❛❞② AL ✐♥tr❛❝t❛❜❧❡ ✐♥ ❞❛t❛ ❝♦♠♣❧❡①✐t②

➥❜❛❞ ♥❡✇s✦

• ■s q✉❡r② ❛♥s✇❡r✐♥❣ ❜❡②♦♥❞ DL✲▲✐t❡ ❛♥❞ EL ♣r❛❝t✐❝❛❜❧❡❄
• ❈❛♥ ✇❡ r❡❛❧✐③❡ ✐t ✉s✐♥❣ ❡①✐st✐♥❣ ❡✣❝✐❡♥t t❡❝❤♥♦❧♦❣✐❡s❄

✭❘❉❇▼❙✱ ❉❛t❛❧♦❣ ❡♥❣✐♥❡s✱ ❡t❝✳✮

❉▲ ✷✵✶✷ ✹✴✶✽

❈◗ ❛♥s✇❡r✐♥❣ ❢♦r ❍♦r♥✲SHIQ ✶✳ ▼♦t✐✈❛t✐♦♥

◗✉❡r② ❆♥s✇❡r✐♥❣ ✐♥ ❍♦r♥✲SHIQ

❍♦r♥ ❢r❛❣♠❡♥ts ♦❢ ❉▲s ❧✐❦❡ SHIQ s❡❡♠ ♣r♦♠✐s✐♥❣ ❝❛♥❞✐❞❛t❡s ❍♦r♥✲SHIQ ✐s tr❛❝t❛❜❧❡ ✐♥ ❞❛t❛ ❝♦♠♣❧❡①✐t② ✭P❚✐♠❡✲❝♦♠♣❧❡t❡✮ ❚❤❡ ❝♦♠❜✐♥❡❞ ❝♦♠♣❧❡①✐t② ✐s ♥♦t ❤✐❣❤❡r t❤❛♥ ❢♦r st❛♥❞❛r❞ r❡❛s♦♥✐♥❣

➤ ❊①♣❚✐♠❡✲❝♦♠♣❧❡t❡

■t ❤❛s ✉s❡❢✉❧ ❢❡❛t✉r❡s ♥♦t ♣r❡s❡♥t ✐♥ EL ❛♥❞ DL✲▲✐t❡

trans(isLocatedIn) country ⊑ ∀hasCapital.city country⊑ 1 isLocatedIn−.capital

❚❤❡s❡ ❢❡❛t✉r❡s ♠❛❦❡ t❤❡ ♣r♦❜❧❡♠ s✐❣♥✐✜❝❛♥t❧② ♠♦r❡ ❝♦♠♣❧❡① ■♥❝♦r♣♦r❛t✐♥❣ t❤❡♠ ✐♥t♦ ❡①✐st✐♥❣ t❡❝❤♥✐q✉❡s ✐s ♥♦t tr✐✈✐❛❧

❉▲ ✷✵✶✷ ✺✴✶✽

❈◗ ❛♥s✇❡r✐♥❣ ❢♦r ❍♦r♥✲SHIQ ✶✳ ▼♦t✐✈❛t✐♦♥

◗✉❡r② ❆♥s✇❡r✐♥❣ ✐♥ ❍♦r♥✲SHIQ

❍♦r♥ ❢r❛❣♠❡♥ts ♦❢ ❉▲s ❧✐❦❡ SHIQ s❡❡♠ ♣r♦♠✐s✐♥❣ ❝❛♥❞✐❞❛t❡s ❍♦r♥✲SHIQ ✐s tr❛❝t❛❜❧❡ ✐♥ ❞❛t❛ ❝♦♠♣❧❡①✐t② ✭P❚✐♠❡✲❝♦♠♣❧❡t❡✮ ❚❤❡ ❝♦♠❜✐♥❡❞ ❝♦♠♣❧❡①✐t② ✐s ♥♦t ❤✐❣❤❡r t❤❛♥ ❢♦r st❛♥❞❛r❞ r❡❛s♦♥✐♥❣

➤ ❊①♣❚✐♠❡✲❝♦♠♣❧❡t❡

■t ❤❛s ✉s❡❢✉❧ ❢❡❛t✉r❡s ♥♦t ♣r❡s❡♥t ✐♥ EL ❛♥❞ DL✲▲✐t❡

trans(isLocatedIn) country ⊑ ∀hasCapital.city country⊑ 1 isLocatedIn−.capital

❚❤❡s❡ ❢❡❛t✉r❡s ♠❛❦❡ t❤❡ ♣r♦❜❧❡♠ s✐❣♥✐✜❝❛♥t❧② ♠♦r❡ ❝♦♠♣❧❡① ■♥❝♦r♣♦r❛t✐♥❣ t❤❡♠ ✐♥t♦ ❡①✐st✐♥❣ t❡❝❤♥✐q✉❡s ✐s ♥♦t tr✐✈✐❛❧

❉▲ ✷✵✶✷ ✺✴✶✽

❈◗ ❛♥s✇❡r✐♥❣ ❢♦r ❍♦r♥✲SHIQ ✷✳ ❖✉r ❈♦♥tr✐❜✉t✐♦♥

◗✉❡r② ❆♥s✇❡r✐♥❣ ❢♦r ❍♦r♥✲SHIQ

❖✉r ❈♦♥tr✐❜✉t✐♦♥

❲❡ ♣r❡s❡♥t ❛ ♥♦✈❡❧ q✉❡r② r❡✇r✐t✐♥❣ ❛❧❣♦r✐t❤♠ ❢♦r ❍♦r♥✲SHIQ ❛♥❞ ❛ ♣r♦t♦t②♣❡ ✐♠♣❧❡♠❡♥t❛t✐♦♥ t❤❛t s❤♦✇s ♣r♦♠✐s✐♥❣ r❡s✉❧ts✳ ❲❡ r❡✇r✐t❡ q ✐♥t♦ ❛ ❯❈◗ rewT (q) ✭❞❡♣❡♥❞s ♦♥ t❤❡ ❚❇♦① T ✮ ❚❤❡ ✭♥♦♥✲❡①✐st❡♥t✐❛❧✮ ❛①✐♦♠s ♦❢ T ❛r❡ r❡✇r✐tt❡♥ ✐♥t♦ ❉❛t❛❧♦❣ r✉❧❡s cr(T ) ❆♥s✇❡r✐♥❣ q ♦✈❡r (T , A) ❛♠♦✉♥ts t♦ ❡✈❛❧✉❛t✐♥❣ t❤❡ ❉❛t❛❧♦❣ ♣r♦❣r❛♠ A ∪ cr(T ) ∪ rewT (q)

• ❲❡ ❝❛♥ ❛❧s♦ ❡✈❛❧✉❛t❡ rewT (q) ♦✈❡r t❤❡ ❝♦♠♣❧❡t✐♦♥ ♦❢ A ✭✇✐t❤ ♥♦

❛❞❞✐t✐♦♥❛❧ ✉♥♥❛♠❡❞ ♦❜❥❡❝ts✮

rewT (q) ❝❛♥ ❜❡ ❡①♣♦♥❡♥t✐❛❧✱ ❜✉t ❤❛s ♠❛♥❛❣❡❛❜❧❡ s✐③❡ ❢♦r r❡❛❧ q✉❡r✐❡s ❛♥❞ ♦♥t♦❧♦❣✐❡s

❉▲ ✷✵✶✷ ✻✴✶✽

❈◗ ❛♥s✇❡r✐♥❣ ❢♦r ❍♦r♥✲SHIQ ✷✳ ❖✉r ❈♦♥tr✐❜✉t✐♦♥

❚❤❡ r❡✇r✐t✐♥❣ ❛❧❣♦r✐t❤♠

▼❛✐♥ ✐❞❡❛✿

❊❧✐♠✐♥❛t❡ q✉❡r② ✈❛r✐❛❜❧❡s t❤❛t ❝❛♥ ❜❡ ♠❛t❝❤❡❞ ❛t ✉♥♥❛♠❡❞ ♦❜❥❡❝ts

• ◗✉❡r② ♠❛t❝❤❡s ❤❛✈❡ tr❡❡✲s❤❛♣❡❞ ♣❛rts
• ❲❡ ❝❧✐♣ ♦✛ t❤❡ ✈❛r✐❛❜❧❡s x t❤❛t ❝❛♥ ❜❡ ❧❡❛✈❡s
• ❘❡♣❧❛❝❡ t❤❡♠ ❜② ❝♦♥str❛✐♥ts D(y) ♦♥ t❤❡✐r ♣❛r❡♥t ✈❛r✐❛❜❧❡s y
• ❚❤❡ ❛❞❞❡❞ ❛t♦♠s D(y) ❡♥s✉r❡ t❤❡ ❡①✐st❡♥❝❡ ♦❢ ❛ ♠❛t❝❤ ❢♦r x

■♥ t❤❡ r❡s✉❧t✐♥❣ q✉❡r✐❡s ❛❧❧ ✈❛r✐❛❜❧❡s ❛r❡ ♠❛t❝❤❡❞ t♦ ♥❛♠❡❞ ♦❜❥❡❝ts

❉▲ ✷✵✶✷ ✼✴✶✽

❈◗ ❛♥s✇❡r✐♥❣ ❢♦r ❍♦r♥✲SHIQ ✷✳ ❖✉r ❈♦♥tr✐❜✉t✐♦♥

❖♥❡ st❡♣ ♦❢ q✉❡r② r❡✇r✐t✐♥❣

q(x1) ← r(x1, x2), r(x1, x4), r(x2, x3), s(x3, x4), A(x1), B(x4), B′(x2), C(x3)

x1 A x4 B r x2 B′ r x3 C r s

✶ ❙❡❧❡❝t t❤❡ ♥♦♥✲❞✐st✐♥❣✉✐s❤❡❞ ✈❛r✐❛❜❧❡ ✷ ❊♥s✉r❡ t❤❛t

❤❛s ♦♥❧② ✐♥❝♦♠✐♥❣ ❡❞❣❡s r❡♣❧❛❝❡ ❜② ❛s ♥❡❡❞❡❞

✸ ▼❡r❣❡ t❤❡ ♣r❡❞❡❝❡ss♦rs

✐❢ ✐s ❛ ❧❡❛❢ ♦❢ ❛ tr❡❡✱ t❤❡② ♠✉st ❜❡ ♠❛♣♣❡❞ t♦❣❡t❤❡r

✹ ❋✐♥❞ ❛♥ ❛①✐♦♠ t❤❛t ❡♥❢♦r❝❡s ❛♥

✲❝❤✐❧❞ t❤❛t ✐s ❢❛✐❧ ✐❢ ❞♦❡s ♥♦t ✐♠♣❧② s✉❝❤ ❛♥ ❛①✐♦♠

✺ ❉r♦♣

❛♥❞ ❛❞❞

❉▲ ✷✵✶✷ ✽✴✶✽

❈◗ ❛♥s✇❡r✐♥❣ ❢♦r ❍♦r♥✲SHIQ ✷✳ ❖✉r ❈♦♥tr✐❜✉t✐♦♥

❖♥❡ st❡♣ ♦❢ q✉❡r② r❡✇r✐t✐♥❣

x1 A x4 B r x2 B′ r x3 C r s x1 A x4 B r x2 B′ r x3 C r s ✶ ❙❡❧❡❝t t❤❡ ♥♦♥✲❞✐st✐♥❣✉✐s❤❡❞ ✈❛r✐❛❜❧❡ x3 ✷ ❊♥s✉r❡ t❤❛t

❤❛s ♦♥❧② ✐♥❝♦♠✐♥❣ ❡❞❣❡s

r❡♣❧❛❝❡ ❜② ❛s ♥❡❡❞❡❞

✸ ▼❡r❣❡ t❤❡ ♣r❡❞❡❝❡ss♦rs

✐❢ ✐s ❛ ❧❡❛❢ ♦❢ ❛ tr❡❡✱ t❤❡② ♠✉st ❜❡ ♠❛♣♣❡❞ t♦❣❡t❤❡r

✹ ❋✐♥❞ ❛♥ ❛①✐♦♠ t❤❛t ❡♥❢♦r❝❡s ❛♥

✲❝❤✐❧❞ t❤❛t ✐s

❢❛✐❧ ✐❢ ❞♦❡s ♥♦t ✐♠♣❧② s✉❝❤ ❛♥ ❛①✐♦♠

✺ ❉r♦♣

❛♥❞ ❛❞❞

❉▲ ✷✵✶✷ ✽✴✶✽

❈◗ ❛♥s✇❡r✐♥❣ ❢♦r ❍♦r♥✲SHIQ ✷✳ ❖✉r ❈♦♥tr✐❜✉t✐♦♥

❖♥❡ st❡♣ ♦❢ q✉❡r② r❡✇r✐t✐♥❣

x1 A x4 B r x2 B′ r x3 C r s x1 A x4 B r x2 B′ r x3 C r s− ✶ ❙❡❧❡❝t t❤❡ ♥♦♥✲❞✐st✐♥❣✉✐s❤❡❞ ✈❛r✐❛❜❧❡ x3 ✷ ❊♥s✉r❡ t❤❛t x3 ❤❛s ♦♥❧② ✐♥❝♦♠✐♥❣ ❡❞❣❡s

➤r❡♣❧❛❝❡ r(x, y) ❜② r−(y, x) ❛s ♥❡❡❞❡❞

✸ ▼❡r❣❡ t❤❡ ♣r❡❞❡❝❡ss♦rs

✐❢ ✐s ❛ ❧❡❛❢ ♦❢ ❛ tr❡❡✱ t❤❡② ♠✉st ❜❡ ♠❛♣♣❡❞ t♦❣❡t❤❡r

✹ ❋✐♥❞ ❛♥ ❛①✐♦♠ t❤❛t ❡♥❢♦r❝❡s ❛♥

✲❝❤✐❧❞ t❤❛t ✐s

❢❛✐❧ ✐❢ ❞♦❡s ♥♦t ✐♠♣❧② s✉❝❤ ❛♥ ❛①✐♦♠

✺ ❉r♦♣

❛♥❞ ❛❞❞

❉▲ ✷✵✶✷ ✽✴✶✽

❈◗ ❛♥s✇❡r✐♥❣ ❢♦r ❍♦r♥✲SHIQ ✷✳ ❖✉r ❈♦♥tr✐❜✉t✐♦♥

❖♥❡ st❡♣ ♦❢ q✉❡r② r❡✇r✐t✐♥❣

x1 A x4 B r x2 B′ r x3 C r s x1 A x3 C x2 B, B′ r r, s− ✶ ❙❡❧❡❝t t❤❡ ♥♦♥✲❞✐st✐♥❣✉✐s❤❡❞ ✈❛r✐❛❜❧❡ x3 ✷ ❊♥s✉r❡ t❤❛t x3 ❤❛s ♦♥❧② ✐♥❝♦♠✐♥❣ ❡❞❣❡s

➤r❡♣❧❛❝❡ r(x, y) ❜② r−(y, x) ❛s ♥❡❡❞❡❞

✸ ▼❡r❣❡ t❤❡ ♣r❡❞❡❝❡ss♦rs

➤✐❢ x3 ✐s ❛ ❧❡❛❢ ♦❢ ❛ tr❡❡✱ t❤❡② ♠✉st ❜❡ ♠❛♣♣❡❞ t♦❣❡t❤❡r

✹ ❋✐♥❞ ❛♥ ❛①✐♦♠ t❤❛t ❡♥❢♦r❝❡s ❛♥

✲❝❤✐❧❞ t❤❛t ✐s

❢❛✐❧ ✐❢ ❞♦❡s ♥♦t ✐♠♣❧② s✉❝❤ ❛♥ ❛①✐♦♠

✺ ❉r♦♣

❛♥❞ ❛❞❞

❉▲ ✷✵✶✷ ✽✴✶✽

❈◗ ❛♥s✇❡r✐♥❣ ❢♦r ❍♦r♥✲SHIQ ✷✳ ❖✉r ❈♦♥tr✐❜✉t✐♦♥

❖♥❡ st❡♣ ♦❢ q✉❡r② r❡✇r✐t✐♥❣

x1 A x4 B r x2 B′ r x3 C r s x1 A x3 C

T | = D ⊑ ∃(r ⊓ s−).C

x2 B, B′ r r, s− ✶ ❙❡❧❡❝t t❤❡ ♥♦♥✲❞✐st✐♥❣✉✐s❤❡❞ ✈❛r✐❛❜❧❡ x3 ✷ ❊♥s✉r❡ t❤❛t x3 ❤❛s ♦♥❧② ✐♥❝♦♠✐♥❣ ❡❞❣❡s

➤r❡♣❧❛❝❡ r(x, y) ❜② r−(y, x) ❛s ♥❡❡❞❡❞

✸ ▼❡r❣❡ t❤❡ ♣r❡❞❡❝❡ss♦rs

➤✐❢ x3 ✐s ❛ ❧❡❛❢ ♦❢ ❛ tr❡❡✱ t❤❡② ♠✉st ❜❡ ♠❛♣♣❡❞ t♦❣❡t❤❡r

✹ ❋✐♥❞ ❛♥ ❛①✐♦♠ t❤❛t ❡♥❢♦r❝❡s ❛♥ (r ⊓ s−)✲❝❤✐❧❞ t❤❛t ✐s C

➤❢❛✐❧ ✐❢ T ❞♦❡s ♥♦t ✐♠♣❧② s✉❝❤ ❛♥ ❛①✐♦♠

✺ ❉r♦♣

❛♥❞ ❛❞❞

❉▲ ✷✵✶✷ ✽✴✶✽

❈◗ ❛♥s✇❡r✐♥❣ ❢♦r ❍♦r♥✲SHIQ ✷✳ ❖✉r ❈♦♥tr✐❜✉t✐♦♥

❖♥❡ st❡♣ ♦❢ q✉❡r② r❡✇r✐t✐♥❣

x1 A x4 B r x2 B′ r x3 C r s x1 A x3 C

T | = D ⊑ ∃(r ⊓ s−).C

x2 B, B′, D r r, s− ✶ ❙❡❧❡❝t t❤❡ ♥♦♥✲❞✐st✐♥❣✉✐s❤❡❞ ✈❛r✐❛❜❧❡ x3 ✷ ❊♥s✉r❡ t❤❛t x3 ❤❛s ♦♥❧② ✐♥❝♦♠✐♥❣ ❡❞❣❡s

➤r❡♣❧❛❝❡ r(x, y) ❜② r−(y, x) ❛s ♥❡❡❞❡❞

✸ ▼❡r❣❡ t❤❡ ♣r❡❞❡❝❡ss♦rs

➤✐❢ x3 ✐s ❛ ❧❡❛❢ ♦❢ ❛ tr❡❡✱ t❤❡② ♠✉st ❜❡ ♠❛♣♣❡❞ t♦❣❡t❤❡r

✹ ❋✐♥❞ ❛♥ ❛①✐♦♠ t❤❛t ❡♥❢♦r❝❡s ❛♥ (r ⊓ s−)✲❝❤✐❧❞ t❤❛t ✐s C

➤❢❛✐❧ ✐❢ T ❞♦❡s ♥♦t ✐♠♣❧② s✉❝❤ ❛♥ ❛①✐♦♠

✺ ❉r♦♣ x3 ❛♥❞ ❛❞❞ D(x2)

❉▲ ✷✵✶✷ ✽✴✶✽

❈◗ ❛♥s✇❡r✐♥❣ ❢♦r ❍♦r♥✲SHIQ ✷✳ ❖✉r ❈♦♥tr✐❜✉t✐♦♥

❖♥❡ st❡♣ ♦❢ q✉❡r② r❡✇r✐t✐♥❣

x1 A x4 B r x2 B′ r x3 C r s x1 A

T | = D ⊑ ∃(r ⊓ s−).C

x2 B, B′, D r ✶ ❙❡❧❡❝t t❤❡ ♥♦♥✲❞✐st✐♥❣✉✐s❤❡❞ ✈❛r✐❛❜❧❡ x3 ✷ ❊♥s✉r❡ t❤❛t x3 ❤❛s ♦♥❧② ✐♥❝♦♠✐♥❣ ❡❞❣❡s

➤r❡♣❧❛❝❡ r(x, y) ❜② r−(y, x) ❛s ♥❡❡❞❡❞

✸ ▼❡r❣❡ t❤❡ ♣r❡❞❡❝❡ss♦rs

➤✐❢ x3 ✐s ❛ ❧❡❛❢ ♦❢ ❛ tr❡❡✱ t❤❡② ♠✉st ❜❡ ♠❛♣♣❡❞ t♦❣❡t❤❡r

✹ ❋✐♥❞ ❛♥ ❛①✐♦♠ t❤❛t ❡♥❢♦r❝❡s ❛♥ (r ⊓ s−)✲❝❤✐❧❞ t❤❛t ✐s C

➤❢❛✐❧ ✐❢ T ❞♦❡s ♥♦t ✐♠♣❧② s✉❝❤ ❛♥ ❛①✐♦♠

✺ ❉r♦♣ x3 ❛♥❞ ❛❞❞ D(x2)

❉▲ ✷✵✶✷ ✽✴✶✽

❈◗ ❛♥s✇❡r✐♥❣ ❢♦r ❍♦r♥✲SHIQ ✷✳ ❖✉r ❈♦♥tr✐❜✉t✐♦♥

❆♥♦t❤❡r st❡♣ ♦❢ q✉❡r② r❡✇r✐t✐♥❣

❚❤❡ q✉❡r② ✉s✐♥❣ t❤❡ ❛①✐♦♠ ✐s r❡✇r✐tt❡♥ t♦

x1 A1 x2 A2 r1 x3 A3 r2 x4 A4 r3

A ⊑ ∃r2.A3

x1 A1 x2 A2, A r1 x4 A4 r3

❚♦ ❤❛♥❞❧❡ tr❛♥s✐t✐✈❡ r♦❧❡s ✐♥ t❤❡ q✉❡r②✿ ✐♥tr♦❞✉❝❡ ❛ ♥❡✇ ✈❛r✐❛❜❧❡ ❜❡t✇❡❡♥ t❤❡ ❡❧✐♠✐♥❛t❡❞ ✈❛r✐❛❜❧❡ ❛♥❞ s♦♠❡ ♦❢ ✐ts ♣r❡❞❡❝❡ss♦rs ❡❧✐♠✐♥❛t❡ s❡ts ♦❢ ✈❛r✐❛❜❧❡s ✭❞✉❡ t♦ ✈❛r✐❛❜❧❡s ❝♦♥♥❡❝t❡❞ ✐♥ t❤❡ q✉❡r② t❤❛t ♠❛② ❜❡ ♠❛♣♣❡❞ t♦ t❤❡ s❛♠❡ ♦❜❥❡❝t✮

❉▲ ✷✵✶✷ ✾✴✶✽

❈◗ ❛♥s✇❡r✐♥❣ ❢♦r ❍♦r♥✲SHIQ ✷✳ ❖✉r ❈♦♥tr✐❜✉t✐♦♥

❆♥♦t❤❡r st❡♣ ♦❢ q✉❡r② r❡✇r✐t✐♥❣

❚❤❡ q✉❡r② ✉s✐♥❣ t❤❡ ❛①✐♦♠ ✐s r❡✇r✐tt❡♥ t♦

x1 A1 x2 A2 r1 x3 A3 r2 x4 A4 r3

A ⊑ ∃r2.A3

x1 A1 x2 A2, A r1 x4 A4 r3

❚♦ ❤❛♥❞❧❡ tr❛♥s✐t✐✈❡ r♦❧❡s ✐♥ t❤❡ q✉❡r②✿ ✐♥tr♦❞✉❝❡ ❛ ♥❡✇ ✈❛r✐❛❜❧❡ ❜❡t✇❡❡♥ t❤❡ ❡❧✐♠✐♥❛t❡❞ ✈❛r✐❛❜❧❡ ❛♥❞ s♦♠❡ ♦❢ ✐ts ♣r❡❞❡❝❡ss♦rs ❡❧✐♠✐♥❛t❡ s❡ts ♦❢ ✈❛r✐❛❜❧❡s ✭❞✉❡ t♦ ✈❛r✐❛❜❧❡s ❝♦♥♥❡❝t❡❞ ✐♥ t❤❡ q✉❡r② t❤❛t ♠❛② ❜❡ ♠❛♣♣❡❞ t♦ t❤❡ s❛♠❡ ♦❜❥❡❝t✮

❉▲ ✷✵✶✷ ✾✴✶✽

❈◗ ❛♥s✇❡r✐♥❣ ❢♦r ❍♦r♥✲SHIQ ✷✳ ❖✉r ❈♦♥tr✐❜✉t✐♦♥

❚❇♦① ❙❛t✉r❛t✐♦♥

❲❡ ❝♦♠♣✉t❡ ✐♥ ❛❞✈❛♥❝❡ ❛ s❡t Ξ(T ) ♦❢ r❡❧❡✈❛♥t ❛①✐♦♠s

• ❚❛✐❧♦r❡❞ r❡s♦❧✉t✐♦♥ ❝❛❧❝✉❧✉s ❢♦r ❍♦r♥✲ALCHIQ⊓
• ❆❞❛♣t❛t✐♦♥ ♦❢ ❡①✐st✐♥❣ ❝♦♥s❡q✉❡♥❝❡ ❞r✐✈❡♥ ♣r♦❝❡❞✉r❡s ❢♦r s❛t✐s✜❛❜✐❧✐t②

❊①❛♠♣❧❡ ❘✉❧❡s

M ⊑ ∃S.(N ⊓ N′) N ⊑ A M ⊑ ∃S.(N ⊓ N′ ⊓ A)

Rc

⊑

M ⊑ ∃(S ⊓ inv(r)).(N ⊓ A) A ⊑ ∀r.B M ⊑ B

R−

∀

❚❤❡ r❡✇r✐t✐♥❣ st❡♣ s✐♠♣❧② s❡❛r❝❤❡s ❢♦r ❛♥ ❛①✐♦♠ ✐♥ Ξ(T )

❉▲ ✷✵✶✷ ✶✵✴✶✽

❈◗ ❛♥s✇❡r✐♥❣ ❢♦r ❍♦r♥✲SHIQ ✷✳ ❖✉r ❈♦♥tr✐❜✉t✐♦♥

❚❤❡ ◗✉❡r② ❆♥s✇❡r✐♥❣ ❆❧❣♦r✐t❤♠

❆❧❣♦r✐t❤♠ ✶✿ ❆♥s✇❡r✐♥❣ ❈◗s ✈✐❛ ◗✉❡r② ❘❡✇r✐t✐♥❣

■♥♣✉t✿ ♥♦r♠❛❧ ❍♦r♥✲SHIQ ❑❇ K = (T , A)✱ ❈♦♥❥✉♥❝t✐✈❡ ◗✉❡r② q ❖✉t♣✉t✿ q✉❡r② ❛♥s✇❡rs Ξ(T ) ← ❙❛t✉r❛t❡(T )❀ rewT (q) ← ❘❡✇r✐t❡(q, Ξ(T ))❀ cr(T ) ← ❈♦♠♣❧❡t✐♦♥❘✉❧❡s(T )❀ P ← A ∪ cr(T ) ∪ rewT (q)❀ ans ← { u | q( u) ∈ ▼✐♥✐♠❛❧▼♦❞❡❧(P)}❀ ✄ ❝❛❧❧ ❉❛t❛❧♦❣ r❡❛s♦♥❡r

❚❤❡ ❝♦♠♣❧❡t✐♦♥ r✉❧❡s cr(T ) ❛r❡ str❛✐❣❤t❢♦r✇❛r❞✱ ❡✳❣✳ B(y) ← A(x), r(x, y) ❢♦r ❡❛❝❤ A ⊑ ∀r.B ∈ T r(x, y) ← r1(x, y), . . . , rn(x, y) ❢♦r ❡❛❝❤ r1 ⊓ . . . ⊓ rn ⊑ r ∈ T

❉▲ ✷✵✶✷ ✶✶✴✶✽

❈◗ ❛♥s✇❡r✐♥❣ ❢♦r ❍♦r♥✲SHIQ ✷✳ ❖✉r ❈♦♥tr✐❜✉t✐♦♥

❙②st❡♠ ❆r❝❤✐t❡❝t✉r❡✿ ❈❧✐♣♣❡r

❲❡ ❤❛✈❡ ✐♠♣❧❡♠❡♥t❡❞ ❛ ♣r♦t♦t②♣❡ s②st❡♠ ❝❛❧❧❡❞ ❈❧✐♣♣❡r

✭❤tt♣✿✴✴✇✇✇✳❦r✳t✉✇✐❡♥✳❛❝✳❛t✴r❡s❡❛r❝❤✴s②st❡♠s✴❝❧✐♣♣❡r✮

❙❛t✉r❛t✐♦♥ ❖♥t♦❧♦❣② Pr❡♣r♦✲ ❝❡ss✐♥❣ O ◗✉❡r② Pr❡♣r♦✲ ❝❡ss✐♥❣ ✭✶✮ q ◗✉❡r② ❘❡✇r✐t✐♥❣ ❉❛t❛❧♦❣ ❚r❛♥s❧❛t✐♦♥ ✭✺✮ ❉❛t❛❧♦❣ ❊♥❣✐♥❡ ✭❉▲❱✱ ❈❧✐♥❣♦✮ ❛♥s A ✭✷✮ T rewT (q) ✭✹✮ ✭✸✮ q P ✭✶✮ ❈◗ ✇✐t❤ s✐♠♣❧❡ r♦❧❡s ♦♥❧② ✭✷✮ ◆♦r♠❛❧✐③❡❞ ❚❇♦① ✭✸✮ ❊①✐st❡♥t✐❛❧ ❛①✐♦♠s ✐♥ Ξ(T ) ✭✹✮ ❆①✐♦♠s ❢♦r ❆❇♦① ❝♦♠♣❧❡t✐♦♥ ✭✺✮ P ← A ∪ cr(T ) ∪ rewT (q)

❉▲ ✷✵✶✷ ✶✷✴✶✽

❈◗ ❛♥s✇❡r✐♥❣ ❢♦r ❍♦r♥✲SHIQ ✸✳ ❊①♣❡r✐♠❡♥ts

❊①♣❡r✐♠❡♥ts

❲❡ ❝❛rr✐❡❞ ♦✉t t❤❡ ❢♦❧❧♦✇✐♥❣ ❡①♣❡r✐♠❡♥ts✿ ❉♦✇♥s❝❛❧✐♥❣ t❡st

• ❲❡ ❝♦♠♣❛r❡❞ ❈❧✐♣♣❡r ✇✐t❤ st❛t❡ ♦❢ t❤❡ ❛rt q✉❡r② r❡✇r✐t✐♥❣ s②st❡♠s

♦✈❡r DL✲▲✐t❡ ♦♥t♦❧♦❣✐❡s

❋✉❧❧ ❍♦r♥✲ t❡st

❲❡ t❡st❡❞ ❈❧✐♣♣❡r ♦✈❡r ❛ ❢✉❧❧ ❍♦r♥✲ ♦♥t♦❧♦❣②

❉▲ ✷✵✶✷ ✶✸✴✶✽

❈◗ ❛♥s✇❡r✐♥❣ ❢♦r ❍♦r♥✲SHIQ ✸✳ ❊①♣❡r✐♠❡♥ts

❊①♣❡r✐♠❡♥ts

❲❡ ❝❛rr✐❡❞ ♦✉t t❤❡ ❢♦❧❧♦✇✐♥❣ ❡①♣❡r✐♠❡♥ts✿ ❉♦✇♥s❝❛❧✐♥❣ t❡st

• ❲❡ ❝♦♠♣❛r❡❞ ❈❧✐♣♣❡r ✇✐t❤ st❛t❡ ♦❢ t❤❡ ❛rt q✉❡r② r❡✇r✐t✐♥❣ s②st❡♠s

♦✈❡r DL✲▲✐t❡ ♦♥t♦❧♦❣✐❡s

❋✉❧❧ ❍♦r♥✲SHIQ t❡st

• ❲❡ t❡st❡❞ ❈❧✐♣♣❡r ♦✈❡r ❛ ❢✉❧❧ ❍♦r♥✲SHIQ ♦♥t♦❧♦❣②

❉▲ ✷✵✶✷ ✶✸✴✶✽

❈◗ ❛♥s✇❡r✐♥❣ ❢♦r ❍♦r♥✲SHIQ ✸✳ ❊①♣❡r✐♠❡♥ts

❉♦✇♥s❝❛❧✐♥❣ t❡st

❲❡ ✉s❡❞ t❤❡ ♦♥t♦❧♦❣✐❡s ♦❢ t❤❡ ❘❡q✉✐❡♠ t❡st s✉✐t❡ ❆❞♦❧❡♥❛ ✭❆✮✱ ❙t♦❝❦ ❊①❝❤❛♥❣❡ ✭❙✮✱ ❱✐❝♦❞✐ ✭❱✮ ❛♥❞ ❯♥✐✈❡rs✐t② ✭❯✮ ❲❡ ❛❞❞❡❞ ✷ q✉❡r✐❡s t♦ t❤❡ ✺ ❡①✐st✐♥❣ ♦♥❡s ❢♦r ❡❛❝❤ ♦♥t♦❧♦❣② ❲❡ ❝♦♠♣❛r❡❞ ❈❧✐♣♣❡r ✇✐t❤ Pr❡st♦ ❛♥❞ ❘❡q✉✐❡♠ ❲❡ ❝♦♠♣❛r❡❞ r❡✇r✐t✐♥❣ t✐♠❡s ❛♥❞ s✐③❡ ♦❢ t❤❡ r❡✇r✐tt❡♥ q✉❡r✐❡s ❋♦r ❯✱ ✇❡ ❛❧s♦ ❡✈❛❧✉❛t❡❞ t❤❡ r❡s✉❧t✐♥❣ ❉❛t❛❧♦❣ ♣r♦❣r❛♠ ♦✈❡r ✹ ❆❇♦①❡s✱ ✻✼❦ t♦ ✸✷✵❦

❉▲ ✷✵✶✷ ✶✹✴✶✽

❈◗ ❛♥s✇❡r✐♥❣ ❢♦r ❍♦r♥✲SHIQ ✸✳ ❊①♣❡r✐♠❡♥ts

❉♦✇♥s❝❛❧✐♥❣ t❡st ✭✷✮

O ◗✉❡r② ★ ❘✉❧❡s✴❈◗s ❘❡✇r✐t✐♥❣ t✐♠❡✱ ♠s ✭❛✈❣✳ ❡✈❛❧✳ t✐♠❡✱ ❉▲❱✮ ❘❡q✉✐❡♠● Pr❡st♦ ❈❧✐♣♣❡r ❘❡q✉✐❡♠● Pr❡st♦ ❈❧✐♣♣❡r ◗✶ ✷✼ ✺✸ ✹✷ ✷✽✶ ✹✺ ✺✵ ◗✷ ✺✵ ✸✷ ✸✶ ✶✽✹ ✹✻ ✻✷ ◗✸ ✶✵✹ ✸✷ ✸✶ ✷✾✷ ✷✼ ✻✺ ❆ ◗✹ ✷✷✹ ✹✸ ✸✻ ✺✷✸ ✸✷ ✼✶ ◗✺ ✻✷✹ ✸✼ ✸✻ ✶✶✼✼ ✷✺ ✼✵ ◗✻ ✸✻✹ ✸✺ ✸✵ ✺✷✸ ✸✶ ✻✺ ◗✼ ✷✺✹✽ ✹✸ ✸✷ ✼✼✹✶ ✻✶ ✻✹ ◗✶ ✻ ✼ ✶✵ ✶✹ ✼ ✶✾ ◗✷ ✷ ✸ ✷✷ ✷✻✸ ✾ ✷✷ ◗✸ ✹ ✹ ✾ ✶✼✶✼ ✶✵ ✷✶ ❙ ◗✹ ✹ ✹ ✷✹ ✶✻✶✶ ✾ ✷✸ ◗✺ ✽ ✺ ✶✵ ✶✽✾✹✶ ✶✵ ✷✷ ◗✻ ✹ ✽ ✺ ✷✵✹ ✶✶ ✷✶ ◗✼ ✽ ✻ ✼ ✶✼✸✸ ✶✶ ✶✼ ◗✶ ✷ ✹ ✷ ✶✹ ✭ ✶✷✹✼ ✮ ✶✷ ✭ ✶✷✺✷ ✮ ✷✼ ✭ ✶✷✺✺ ✮ ◗✷ ✶ ✷ ✹✺ ✷✵✶ ✭ ✶✷✹✼ ✮ ✷✸ ✭ ✶✷✻✷ ✮ ✸✻ ✭ ✶✻✸✼ ✮ ◗✸ ✹ ✽ ✶✼ ✹✼✼ ✭ ✷✵✺✺ ✮ ✷✻ ✭ ✷✶✼✷ ✮ ✷✾ ✭ ✶✽✾✵ ✮ ❯ ◗✹ ✷ ✺✻ ✻✸ ✷✹✸✶ ✭ ✶✷✻✵ ✮ ✷✵ ✭ ✶✷✸✺ ✮ ✷✽ ✭ ✶✼✸✺ ✮ ◗✺ ✶✵ ✽ ✶✻ ✼✷✶✻ ✭ ✶✷✻✼ ✮ ✷✻ ✭ ✶✸✵✺ ✮ ✸✻ ✭ ✶✸✼✷ ✮ ◗✻ ✶✵ ✶✸ ✶✵ ✶✸ ✭ ✶✷✼✷ ✮ ✶✹ ✭ ✶✷✻✵ ✮ ✷✼ ✭ ✶✷✻✷ ✮ ◗✼ ✾✻✵ ✷✹ ✶✾ ✶✽✾✵ ✭ ✶✼✸✵ ✮ ✶✺ ✭ ✶✸✶✵ ✮ ✸✺ ✭ ✶✸✷✷ ✮

❉▲ ✷✵✶✷ ✶✺✴✶✽

❈◗ ❛♥s✇❡r✐♥❣ ❢♦r ❍♦r♥✲SHIQ ✸✳ ❊①♣❡r✐♠❡♥ts

❋✉❧❧ ❍♦r♥✲SHIQ t❡st

❲❡ ♠♦❞✐✜❡❞ t❤❡ SHOIN(D) ♦♥t♦❧♦❣② ❯❖❇▼ ❲❡ ❞r♦♣♣❡❞ ♦r str❡♥❣t❤❡♥❡❞ ✭✐♥ ❝❛s❡ ♦❢ ❞✐s❥✉♥❝t✐♦♥s✮ ♥♦♥✲❍♦r♥✲SHIQ ❚❇♦① ❛①✐♦♠s ❚❤❡ ✜♥❛❧ ♦♥t♦❧♦❣② ❤❛s ✶✾✻ ❚❇♦① ❛①✐♦♠s ❲❡ ✉s❡❞ ❆❇♦①❡s ✇✐t❤ ✷✵❦✱ ✽✵❦✱ ✶✹✵❦ ❛♥❞ ✷✵✵❦ ❛ss❡rt✐♦♥s✳ ✶✵ s♠❛❧❧✱ ❤❛♥❞✲t❛✐❧♦r❡❞ q✉❡r✐❡s✱ ✇✐t❤ ❛♥ ❛✈❡r❛❣❡ ♦❢ ✺ ❛t♦♠s

❉▲ ✷✵✶✷ ✶✻✴✶✽

❈◗ ❛♥s✇❡r✐♥❣ ❢♦r ❍♦r♥✲SHIQ ✸✳ ❊①♣❡r✐♠❡♥ts

❋✉❧❧ ❍♦r♥✲SHIQ t❡st ✭✷✮

◗✉❡r② ★ ❘✉❧❡s ❘❡✇r✐t✐♥❣ ❚✐♠❡ ✭♠s✮ ❉❛t❛❧♦❣ ✭❉▲❱✮ ❚✐♠❡ ✭♠s✮ ◗✶ ✷ ✻✽ ✽✵ ✴ ✸✷✵ ✴ ✺✻✵ ✴ ✽✸✵ ◗✷ ✸ ✻✸ ✾✵ ✴ ✸✸✵ ✴ ✺✻✵ ✴ ✽✸✵ ◗✸ ✾ ✾✻ ✾✵ ✴ ✸✷✵ ✴ ✺✼✵ ✴ ✽✶✵ ◗✹ ✶✼✷ ✶✹✸ ✷✸✵ ✴ ✽✸✵ ✴ ✶✹✸✵ ✴ ✶✺✽✵ ◗✺ ✶✻ ✾✶ ✾✵ ✴ ✸✸✵ ✴ ✺✼✵ ✴ ✽✷✵ ◗✻ ✷✺✺ ✶✼✼ ✷✺✵ ✴ ✽✾✵ ✴ ✶✺✸✵ ✴ ✶✽✵✵ ◗✼ ✽ ✽✾ ✽✵ ✴ ✸✷✵ ✴ ✺✼✵ ✴ ✽✷✵ ◗✽ ✶✼✺ ✶✹✻ ✷✸✵ ✴ ✽✸✵ ✴ ✶✹✸✵ ✴ ✶✺✽✵ ◗✾ ✶✼✺ ✶✹✺ ✷✸✵ ✴ ✽✷✵ ✴ ✶✹✵✵ ✴ ✶✻✵✵ ◗✶✵ ✷ ✻✹ ✽✵ ✴ ✸✸✵ ✴ ✺✼✵ ✴ ✽✸✵

❉▲ ✷✵✶✷ ✶✼✴✶✽

❈◗ ❛♥s✇❡r✐♥❣ ❢♦r ❍♦r♥✲SHIQ ✹✳ ❈♦♥❝❧✉s✐♦♥s

❈♦♥❝❧✉s✐♦♥s

❲❡ ❤❛✈❡ ♣r♦♣♦s❡❞ ❛ q✉❡r② r❡✇r✐t✐♥❣ t❡❝❤♥✐q✉❡ ❢♦r ❍♦r♥✲SHIQ ■t ❛❧❧♦✇s ✉s t♦ r❡❞✉❝❡ ❈◗s ❛♥s✇❡r✐♥❣ ♦✈❡r ❍♦r♥✲SHIQ t♦ ❡✈❛❧✉❛t✐♥❣ ❛ ❉❛t❛❧♦❣ ♣r♦❣r❛♠ ♦✈❡r t❤❡ ❆❇♦① ❚❤❡ ♣r♦t♦t②♣❡ s②st❡♠ ❈❧✐♣♣❡r s❤♦✇s ♣r♦♠✐s✐♥❣ r❡s✉❧ts

❱❡rs✐♦♥ ✇✐t❤ tr❛♥s✐t✐✈❡ r♦❧❡s ♠❛② ❜❡ ❛✈❛✐❧❛❜❧❡ s♦♦♥✦

P♦ss✐❜❧❡ ❡①t❡♥s✐♦♥s✿

✇❡❛❦❧② ❉▲✲s❛❢❡ r✉❧❡s ✭❛❧❣♦r✐t❤♠ ❞❡✈❡❧♦♣❡❞✱ ✐♠♣❧❡♠❡♥t❛t✐♦♥ ♣❡♥❞✐♥❣✮ ♦t❤❡r ❉▲s✿ r❡❣✉❧❛r ✱ ❍♦r♥✲ ❀ ❞❛t❛t②♣❡s ♦t❤❡r q✉❡r② ❧❛♥❣✉❛❣❡s✿ r❡❣✉❧❛r ♣❛t❤ q✉❡r✐❡s

❋❛r ♠♦r❡ t❡st✐♥❣ ♥❡❡❞❡❞ ❜✉t ❧❛❝❦ ♦❢ r❡❛❧✐st✐❝ t❡st ❝❛s❡s ✐s ❛ ❜✐❣ ✐ss✉❡✦

❉▲ ✷✵✶✷ ✶✽✴✶✽

❈◗ ❛♥s✇❡r✐♥❣ ❢♦r ❍♦r♥✲SHIQ ✹✳ ❈♦♥❝❧✉s✐♦♥s

❈♦♥❝❧✉s✐♦♥s

❲❡ ❤❛✈❡ ♣r♦♣♦s❡❞ ❛ q✉❡r② r❡✇r✐t✐♥❣ t❡❝❤♥✐q✉❡ ❢♦r ❍♦r♥✲SHIQ ■t ❛❧❧♦✇s ✉s t♦ r❡❞✉❝❡ ❈◗s ❛♥s✇❡r✐♥❣ ♦✈❡r ❍♦r♥✲SHIQ t♦ ❡✈❛❧✉❛t✐♥❣ ❛ ❉❛t❛❧♦❣ ♣r♦❣r❛♠ ♦✈❡r t❤❡ ❆❇♦① ❚❤❡ ♣r♦t♦t②♣❡ s②st❡♠ ❈❧✐♣♣❡r s❤♦✇s ♣r♦♠✐s✐♥❣ r❡s✉❧ts

❱❡rs✐♦♥ ✇✐t❤ tr❛♥s✐t✐✈❡ r♦❧❡s ♠❛② ❜❡ ❛✈❛✐❧❛❜❧❡ s♦♦♥✦

P♦ss✐❜❧❡ ❡①t❡♥s✐♦♥s✿

✇❡❛❦❧② ❉▲✲s❛❢❡ r✉❧❡s ✭❛❧❣♦r✐t❤♠ ❞❡✈❡❧♦♣❡❞✱ ✐♠♣❧❡♠❡♥t❛t✐♦♥ ♣❡♥❞✐♥❣✮ ♦t❤❡r ❉▲s✿ r❡❣✉❧❛r ✱ ❍♦r♥✲ ❀ ❞❛t❛t②♣❡s ♦t❤❡r q✉❡r② ❧❛♥❣✉❛❣❡s✿ r❡❣✉❧❛r ♣❛t❤ q✉❡r✐❡s

❋❛r ♠♦r❡ t❡st✐♥❣ ♥❡❡❞❡❞ ❜✉t ❧❛❝❦ ♦❢ r❡❛❧✐st✐❝ t❡st ❝❛s❡s ✐s ❛ ❜✐❣ ✐ss✉❡✦

❉▲ ✷✵✶✷ ✶✽✴✶✽

❈◗ ❛♥s✇❡r✐♥❣ ❢♦r ❍♦r♥✲SHIQ ✹✳ ❈♦♥❝❧✉s✐♦♥s

❈♦♥❝❧✉s✐♦♥s

❲❡ ❤❛✈❡ ♣r♦♣♦s❡❞ ❛ q✉❡r② r❡✇r✐t✐♥❣ t❡❝❤♥✐q✉❡ ❢♦r ❍♦r♥✲SHIQ ■t ❛❧❧♦✇s ✉s t♦ r❡❞✉❝❡ ❈◗s ❛♥s✇❡r✐♥❣ ♦✈❡r ❍♦r♥✲SHIQ t♦ ❡✈❛❧✉❛t✐♥❣ ❛ ❉❛t❛❧♦❣ ♣r♦❣r❛♠ ♦✈❡r t❤❡ ❆❇♦① ❚❤❡ ♣r♦t♦t②♣❡ s②st❡♠ ❈❧✐♣♣❡r s❤♦✇s ♣r♦♠✐s✐♥❣ r❡s✉❧ts

➤❱❡rs✐♦♥ ✇✐t❤ tr❛♥s✐t✐✈❡ r♦❧❡s ♠❛② ❜❡ ❛✈❛✐❧❛❜❧❡ s♦♦♥✦

P♦ss✐❜❧❡ ❡①t❡♥s✐♦♥s✿

✇❡❛❦❧② ❉▲✲s❛❢❡ r✉❧❡s ✭❛❧❣♦r✐t❤♠ ❞❡✈❡❧♦♣❡❞✱ ✐♠♣❧❡♠❡♥t❛t✐♦♥ ♣❡♥❞✐♥❣✮ ♦t❤❡r ❉▲s✿ r❡❣✉❧❛r ✱ ❍♦r♥✲ ❀ ❞❛t❛t②♣❡s ♦t❤❡r q✉❡r② ❧❛♥❣✉❛❣❡s✿ r❡❣✉❧❛r ♣❛t❤ q✉❡r✐❡s

❋❛r ♠♦r❡ t❡st✐♥❣ ♥❡❡❞❡❞ ❜✉t ❧❛❝❦ ♦❢ r❡❛❧✐st✐❝ t❡st ❝❛s❡s ✐s ❛ ❜✐❣ ✐ss✉❡✦

❉▲ ✷✵✶✷ ✶✽✴✶✽

❈◗ ❛♥s✇❡r✐♥❣ ❢♦r ❍♦r♥✲SHIQ ✹✳ ❈♦♥❝❧✉s✐♦♥s

❈♦♥❝❧✉s✐♦♥s

❲❡ ❤❛✈❡ ♣r♦♣♦s❡❞ ❛ q✉❡r② r❡✇r✐t✐♥❣ t❡❝❤♥✐q✉❡ ❢♦r ❍♦r♥✲SHIQ ■t ❛❧❧♦✇s ✉s t♦ r❡❞✉❝❡ ❈◗s ❛♥s✇❡r✐♥❣ ♦✈❡r ❍♦r♥✲SHIQ t♦ ❡✈❛❧✉❛t✐♥❣ ❛ ❉❛t❛❧♦❣ ♣r♦❣r❛♠ ♦✈❡r t❤❡ ❆❇♦① ❚❤❡ ♣r♦t♦t②♣❡ s②st❡♠ ❈❧✐♣♣❡r s❤♦✇s ♣r♦♠✐s✐♥❣ r❡s✉❧ts

➤❱❡rs✐♦♥ ✇✐t❤ tr❛♥s✐t✐✈❡ r♦❧❡s ♠❛② ❜❡ ❛✈❛✐❧❛❜❧❡ s♦♦♥✦

P♦ss✐❜❧❡ ❡①t❡♥s✐♦♥s✿

• ✇❡❛❦❧② ❉▲✲s❛❢❡ r✉❧❡s ✭❛❧❣♦r✐t❤♠ ❞❡✈❡❧♦♣❡❞✱ ✐♠♣❧❡♠❡♥t❛t✐♦♥ ♣❡♥❞✐♥❣✮
• ♦t❤❡r ❉▲s✿ r❡❣✉❧❛r EL++✱ ❍♦r♥✲SRIQ❀ ❞❛t❛t②♣❡s
• ♦t❤❡r q✉❡r② ❧❛♥❣✉❛❣❡s✿ r❡❣✉❧❛r ♣❛t❤ q✉❡r✐❡s

❋❛r ♠♦r❡ t❡st✐♥❣ ♥❡❡❞❡❞ ❜✉t ❧❛❝❦ ♦❢ r❡❛❧✐st✐❝ t❡st ❝❛s❡s ✐s ❛ ❜✐❣ ✐ss✉❡✦

❉▲ ✷✵✶✷ ✶✽✴✶✽

❈◗ ❛♥s✇❡r✐♥❣ ❢♦r ❍♦r♥✲SHIQ ✹✳ ❈♦♥❝❧✉s✐♦♥s

❈♦♥❝❧✉s✐♦♥s

❲❡ ❤❛✈❡ ♣r♦♣♦s❡❞ ❛ q✉❡r② r❡✇r✐t✐♥❣ t❡❝❤♥✐q✉❡ ❢♦r ❍♦r♥✲SHIQ ■t ❛❧❧♦✇s ✉s t♦ r❡❞✉❝❡ ❈◗s ❛♥s✇❡r✐♥❣ ♦✈❡r ❍♦r♥✲SHIQ t♦ ❡✈❛❧✉❛t✐♥❣ ❛ ❉❛t❛❧♦❣ ♣r♦❣r❛♠ ♦✈❡r t❤❡ ❆❇♦① ❚❤❡ ♣r♦t♦t②♣❡ s②st❡♠ ❈❧✐♣♣❡r s❤♦✇s ♣r♦♠✐s✐♥❣ r❡s✉❧ts

➤❱❡rs✐♦♥ ✇✐t❤ tr❛♥s✐t✐✈❡ r♦❧❡s ♠❛② ❜❡ ❛✈❛✐❧❛❜❧❡ s♦♦♥✦

P♦ss✐❜❧❡ ❡①t❡♥s✐♦♥s✿

• ✇❡❛❦❧② ❉▲✲s❛❢❡ r✉❧❡s ✭❛❧❣♦r✐t❤♠ ❞❡✈❡❧♦♣❡❞✱ ✐♠♣❧❡♠❡♥t❛t✐♦♥ ♣❡♥❞✐♥❣✮
• ♦t❤❡r ❉▲s✿ r❡❣✉❧❛r EL++✱ ❍♦r♥✲SRIQ❀ ❞❛t❛t②♣❡s
• ♦t❤❡r q✉❡r② ❧❛♥❣✉❛❣❡s✿ r❡❣✉❧❛r ♣❛t❤ q✉❡r✐❡s

❋❛r ♠♦r❡ t❡st✐♥❣ ♥❡❡❞❡❞ ❜✉t ❧❛❝❦ ♦❢ r❡❛❧✐st✐❝ t❡st ❝❛s❡s ✐s ❛ ❜✐❣ ✐ss✉❡✦

❉▲ ✷✵✶✷ ✶✽✴✶✽

❈◗ ❛♥s✇❡r✐♥❣ ❢♦r ❍♦r♥✲SHIQ ✹✳ ❈♦♥❝❧✉s✐♦♥s

❈♦♥❝❧✉s✐♦♥s

❲❡ ❤❛✈❡ ♣r♦♣♦s❡❞ ❛ q✉❡r② r❡✇r✐t✐♥❣ t❡❝❤♥✐q✉❡ ❢♦r ❍♦r♥✲SHIQ ■t ❛❧❧♦✇s ✉s t♦ r❡❞✉❝❡ ❈◗s ❛♥s✇❡r✐♥❣ ♦✈❡r ❍♦r♥✲SHIQ t♦ ❡✈❛❧✉❛t✐♥❣ ❛ ❉❛t❛❧♦❣ ♣r♦❣r❛♠ ♦✈❡r t❤❡ ❆❇♦① ❚❤❡ ♣r♦t♦t②♣❡ s②st❡♠ ❈❧✐♣♣❡r s❤♦✇s ♣r♦♠✐s✐♥❣ r❡s✉❧ts

➤❱❡rs✐♦♥ ✇✐t❤ tr❛♥s✐t✐✈❡ r♦❧❡s ♠❛② ❜❡ ❛✈❛✐❧❛❜❧❡ s♦♦♥✦

P♦ss✐❜❧❡ ❡①t❡♥s✐♦♥s✿

• ✇❡❛❦❧② ❉▲✲s❛❢❡ r✉❧❡s ✭❛❧❣♦r✐t❤♠ ❞❡✈❡❧♦♣❡❞✱ ✐♠♣❧❡♠❡♥t❛t✐♦♥ ♣❡♥❞✐♥❣✮
• ♦t❤❡r ❉▲s✿ r❡❣✉❧❛r EL++✱ ❍♦r♥✲SRIQ❀ ❞❛t❛t②♣❡s
• ♦t❤❡r q✉❡r② ❧❛♥❣✉❛❣❡s✿ r❡❣✉❧❛r ♣❛t❤ q✉❡r✐❡s

❋❛r ♠♦r❡ t❡st✐♥❣ ♥❡❡❞❡❞ ❜✉t ❧❛❝❦ ♦❢ r❡❛❧✐st✐❝ t❡st ❝❛s❡s ✐s ❛ ❜✐❣ ✐ss✉❡✦

❉▲ ✷✵✶✷ ✶✽✴✶✽