❯◆■❱❊❘❙■❉❆❉❊ ❋❊❉❊❘❆▲ ❉❖ ❈❊❆❘➪
❉➱❇❖❘❆ ❋❆❘■❆❙ ❋❘❖❚❆
❯▼❆ ▲Ó●■❈❆ ❉❊ ❉❊❙❈❘■➬➹❖ ❉❊❋❆❯▲❚
❉➱❇❖❘❆ ❋❆❘■❆❙ ❋❘❖❚❆
❯▼❆ ▲Ó●■❈❆ ❉❊ ❉❊❙❈❘■➬➹❖ ❉❊❋❆❯▲❚
❉✐ss❡rt❛çã♦ ❞❡ ▼❡str❛❞♦ ❛♣r❡s❡♥t❛❞❛ à ❈♦✲ ♦r❞❡♥❛çã♦ ❞♦ Pr♦❣r❛♠❛ ❞❡ Pós✲❣r❛❞✉❛çã♦ ❡♠ ❈♦♠♣✉t❛çã♦ ❞❛ ❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞♦ ❈❡❛rá ❝♦♠♦ ♣❛rt❡ ❞♦s r❡q✉✐s✐t♦s ♣❛r❛ ♦❜t❡♥çã♦ ❞♦ ❣r❛✉ ❞❡ ▼❡str❡ ❡♠ ❈♦♠✲ ♣✉t❛çã♦✳
➪r❡❛ ❞❡ ❈♦♥❝❡♥tr❛çã♦✿■♥t❡❧✐❣ê♥❝✐❛ ❆rt✐✜❝✐❛❧
❖r✐❡♥t❛❞♦r❛✿ ❆♥❛ ❚❡r❡s❛ ▼❛rt✐♥s
❈♦✲❖r✐❡♥t❛❞♦r✿ ❏♦ã♦ ❋❡r♥❛♥❞♦ ❆❧❝â♥t❛r❛
❉➱❇❖❘❆ ❋❆❘■❆❙ ❋❘❖❚❆
❯▼❆ ▲Ó●■❈❆ ❉❊ ❉❊❙❈❘■➬➹❖ ❉❊❋❆❯▲❚
❉✐ss❡rt❛çã♦ ❞❡ ▼❡str❛❞♦ ❛♣r❡s❡♥t❛❞❛ à ❈♦♦r❞❡♥❛çã♦ ❞♦ Pr♦❣r❛♠❛ ❞❡ Pós✲❣r❛❞✉❛çã♦ ❡♠ ❈♦♠♣✉t❛çã♦ ❞❛ ❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞♦ ❈❡❛rá ❝♦♠♦ ♣❛rt❡ ❞♦s r❡q✉✐s✐t♦s ♣❛r❛ ♦❜t❡♥çã♦ ❞♦ ❣r❛✉ ❞❡ ▼❡str❡ ❡♠ ❈♦♠♣✉t❛çã♦✳
❆♣r♦✈❛❞❛ ❡♠✿ ❴❴✴❴❴✴❴❴❴❴
❇❛♥❝❛ ❊①❛♠✐♥❛❞♦r❛
Pr♦❢❛✳ ❉r❛✳ ❆♥❛ ❚❡r❡s❛ ▼❛rt✐♥s ❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞♦ ❈❡❛rá ✲ ❯❋❈
❖r✐❡♥t❛❞♦r
Pr♦❢✳ ❉r✳ ❏♦ã♦ ❋❡r♥❛♥❞♦ ❆❧❝â♥t❛r❛ ❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞♦ ❈❡❛rá ✲ ❯❋❈
❈♦✲♦r✐❡♥t❛❞♦r
Pr♦❢✳ ❉r✳ ▼❛r❝❡❧✐♥♦ ❈❛✈❛❧❝❛♥t❡ P❡q✉❡♥♦ ❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞♦ ❈❡❛rá ✲ ❯❋❈
Pr♦❢✳ ❉r✳ ❊❞✇❛r❞ ❍❡r♠❛♥♥ ❍❛❡✉s❧❡r P♦♥t✐❢í❝✐❛ ❯♥✐✈❡rs✐❞❛❞❡ ❈❛tó❧✐❝❛ ❞♦ ❘✐♦ ❞❡
❆●❘❆❉❊❈■▼❊◆❚❖❙
❘❊❙❯▼❖
❆ ❢♦r♠❛❧✐③❛çã♦ ❞♦ ❝♦♥❤❡❝✐♠❡♥t♦ ❡ ❛ ❛✉t♦♠❛t✐③❛çã♦ ❞♦ r❛❝✐♦❝í♥✐♦ sã♦ ❛ss✉♥t♦s ❝❡♥tr❛✐s ❞❡ ♣❡sq✉✐s❛ ❞❛ ■♥t❡❧✐❣ê♥❝✐❛ ❆rt✐✜❝✐❛❧✳ ❆ ▲ó❣✐❝❛ ❞❡ Pr✐♠❡✐r❛ ❖r❞❡♠ t❡♠ s✐❞♦ tr❛❞✐❝✐♦♥❛❧✲ ♠❡♥t❡ ✉t✐❧✐③❛❞❛ ♣❛r❛ t❛✐s ♣r♦♣ós✐t♦s✳ ◆♦ ❡♥t❛♥t♦✱ ❡❧❛ é ♠❛✐s ❛❞❡q✉❛❞❛ ♣❛r❛ ❧✐❞❛r ❝♦♠ ❝♦♥❤❡❝✐♠❡♥t♦ ❝♦♠♣❧❡t♦ ❡♠ ❝✐r❝✉♥stâ♥❝✐❛s ✐❞❡❛✐s✳ ❊♠ s✐t✉❛çõ❡s r❡❛✐s✱ ♥❛s q✉❛✐s ♦ ❝♦♥❤❡✲ ❝✐♠❡♥t♦ é ♣❛r❝✐❛❧✱ ❛ ▲ó❣✐❝❛ ❞❡ Pr✐♠❡✐r❛ ❖r❞❡♠ ♥ã♦ é s✉✜❝✐❡♥t❡✳ ▲ó❣✐❝❛s ♥ã♦✲♠♦♥♦tô♥✐❝❛s tê♠ s✐❞♦ ♣r♦♣♦st❛s ♣❛r❛ ♠❡❧❤♦r ❧✐❞❛r ❝♦♠ ♦ r❛❝✐♦❝í♥✐♦ ♣rát✐❝♦✳ ❯♠❛ ❢♦r♠❛❧✐③❛çã♦ ❞♦ r❛❝✐♦❝í♥✐♦ ♥ã♦✲♠♦♥♦tô♥✐❝♦ ❜❡♠✲s✉❝❡❞✐❞❛ é ❛ ▲ó❣✐❝❛ ❉❡❢❛✉❧t ❞❡ ❘❡✐t❡r q✉❡ ❡st❡♥❞❡ ❛ ▲ó✲ ❣✐❝❛ ❞❡ Pr✐♠❡✐r❛ ❖r❞❡♠ ❝♦♠ r❡❣r❛s ❞❡❢❛✉❧t✳ ■♥❢❡❧✐③♠❡♥t❡✱ ❛ ▲ó❣✐❝❛ ❉❡❢❛✉❧t é ✐♥❞❡❝✐❞í✈❡❧✳ ◆❡st❛ ❞✐ss❡rt❛çã♦✱ ♣r♦♣♦♠♦s ✉♠❛ ▲ó❣✐❝❛ ❞❡ ❉❡s❝r✐çã♦ ❉❡❢❛✉❧t ❡①♣r❡ss✐✈❛ ♦ s✉✜❝✐❡♥t❡ ♣❛r❛ ❢♦r♠❛❧✐③❛r ♦ r❛❝✐♦❝í♥✐♦ ♣rát✐❝♦ s♦❜r❡ ❜❛s❡s ❞❡ ❝♦♥❤❡❝✐♠❡♥t♦✳ ❊❧❛ t❡♠ ❝♦♠♦ ❜❛s❡ ♠♦♥♦tô♥✐❝❛ ❛ ▲ó❣✐❝❛ ❞❡ ❉❡s❝r✐çã♦ALC✳ ❆❞✐❝✐♦♥❛♠♦s ❛❧❣✉♠❛s r❡str✐çõ❡s à ❛♣❧✐❝❛çã♦ ❞♦s ❞❡❢❛✉❧ts ❛ ✜♠ ❞❡ ♦❜t❡r ♣r♦♣r✐❡❞❛❞❡s ✐♥t❡r❡ss❛♥t❡s✱ t❛✐s ❝♦♠♦ ❛ ❝♦❡rê♥❝✐❛ ❡ ❛ ❡❧✐♠✐♥❛çã♦ ❞❡ ❡①t❡♥sõ❡s ❛♥ô♠❛❧❛s✳ ❆♣r❡s❡♥t❛♠♦s ♦s ♣r✐♥❝✐♣❛✐s ❛❧❣♦r✐t♠♦s ✉s❛❞♦s ♣❛r❛ ❝♦♥str✉✐r ✉♠❛ ❡①t❡♥sã♦ ❝♦♠ ✉♠ ♣❛ss♦✲❛✲♣❛ss♦ ❡ s✉❛s ❛♥á❧✐s❡ ❞❡ ❝♦♠♣❧❡①✐❞❛❞❡✳
❆❇❙❚❘❆❈❚
❑♥♦✇❧❡❞❣❡ ❢♦r♠❛❧✐③❛t✐♦♥ ❛♥❞ r❡❛s♦♥✐♥❣ ❛✉t♦♠❛t✐③❛t✐♦♥ ❛r❡ ❝❡♥tr❛❧ ✇✐t❤✐♥ ❆rt✐✜❝✐❛❧ ■♥t❡❧✲ ❧✐❣❡♥❝❡✳ ❋✐rst ❖r❞❡r ▲♦❣✐❝ ❤❛s ❜❡❡♥ tr❛❞✐t✐♦♥❛❧❧② ✉s❡❞ ❢♦r s✉❝❤ ♣✉r♣♦s❡s✳ ❍♦✇❡✈❡r✱ ✐t ✐s ❜❡tt❡r s✉✐t❡❞ t♦ ❞❡❛❧ ✇✐t❤ ❝♦♠♣❧❡t❡ ❦♥♦✇❧❡❞❣❡ ✐♥ ✐❞❡❛❧ ❝✐r❝✉♠st❛♥❝❡s✳ ■♥ r❡❛❧ s✐t✉❛t✐♦♥s✱ ✐♥ ✇❤✐❝❤ t❤❡ ❦♥♦✇❧❡❞❣❡ ✐s ♣❛rt✐❛❧✱ ❋✐rst ❖r❞❡r ▲♦❣✐❝ ✐s ♥♦t s✉✣❝✐❡♥t✳ ◆♦♥♠♦♥♦t♦♥✐❝ ❧♦❣✲ ✐❝s ❤❛✈❡ ❜❡❡♥ ♣r♦♣♦s❡❞ t♦ ❜❡tt❡r ❝♦♣❡ ✇✐t❤ ♣r❛❝t✐❝❛❧ r❡❛s♦♥✐♥❣✳ ❆ s✉❝❝❡ss❢✉❧ ❢♦r♠❛❧✐③❛t✐♦♥ ♦❢ ♥♦♥♠♦♥♦t♦♥✐❝ r❡❛s♦♥✐♥❣ ✐s t❤❡ ❘❡✐t❡r✬s ❞❡❢❛✉❧t ❧♦❣✐❝ ✇❤✐❝❤ ❡①t❡♥❞s ❝❧❛ss✐❝❛❧ ❧♦❣✐❝ ✇✐t❤ ❞❡❢❛✉❧t r✉❧❡s✳ ❯♥❢♦rt✉♥❛t❡❧②✱ ❞❡❢❛✉❧t ❧♦❣✐❝ ✐s ✉♥❞❡❝✐❞❛❜❧❡✳ ■♥ t❤✐s ✇♦r❦✱ ✇❡ ♣r♦♣♦s❡ ❛ ❞❡s❝r✐♣t✐♦♥ ❞❡❢❛✉❧t ❧♦❣✐❝ ❡①♣r❡ss✐❜❧❡ ❡♥♦✉❣❤ t♦ ❢♦r♠❛❧✐③❡ ♣r❛❝t✐❝❛❧ r❡❛s♦♥✐♥❣ ✐♥ ❦♥♦✇❧❡❞❣❡ ❜❛s❡s✳ ■t ❤❛s ❛s ✐ts ♠♦♥♦t♦♥✐❝ ❜❛s✐s t❤❡ALC ❉❡s❝r✐♣t✐♦♥ ▲♦❣✐❝✳ ❲❡ ❛❞❞ s♦♠❡ r❡str✐❝t✐♦♥s t♦ t❤❡ ❛♣♣❧✐❝❛t✐♦♥ ♦❢ ❞❡❢❛✉❧ts ✐♥ ♦r❞❡r t♦ ♦❜t❛✐♥ ♥✐❝❡ ♣r♦♣❡rt✐❡s s✉❝❤ ❛s ❝♦❤❡r❡♥❝❡ ❛♥❞ t❤❡ ❡❧✐♠✐♥❛t✐♦♥ ♦❢ ❛♥♦♠❛❧♦✉s ❡①t❡♥s✐♦♥s✳ ❲❡ ♣r❡s❡♥t t❤❡ ♠❛✐♥ ❛❧❣♦r✐t❤♠s ✉s❡❞ t♦ ❜✉✐❧❞ ❛♥ ❡①t❡♥s✐♦♥ ✇✐t❤ ❛ st❡♣ ❜② st❡♣ ❝♦♠♣❧❡①✐t② ❛♥❛❧②s✐s✳
▲■❙❚❆ ❉❊ ❋■●❯❘❆❙
❋✐❣✉r❛ ✶ ❲❡❜ ❙❡♠â♥t✐❝❛ ✲ ❘❡♣r❡s❡♥t❛çã♦ ❡♠ ❈❛♠❛❞❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶
▲■❙❚❆ ❉❊ ❚❆❇❊▲❆❙
❚❛❜❡❧❛ ✶ ❊①❡♠♣❧♦s ❞❡ ▲ó❣✐❝❛s ❞❡ ❉❡s❝r✐çã♦ ❡ s✉❛s ♥♦✈❛s ❢✉♥❝✐♦♥❛❧✐❞❛❞❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✶
❚❛❜❡❧❛ ✷ ❈♦rr❡s♣♦♥❞ê♥❝✐❛ ❡♥tr❡ ❛❧❣✉♠❛s ❢ór♠✉❧❛s ❞❡ ❉▲ ❡ ❋❖▲ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✷
❚❛❜❡❧❛ ✸ ◆♦t❛çã♦ ❯♥✐❢♦r♠❡ α ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✹
❚❛❜❡❧❛ ✹ ◆♦t❛çã♦ ❯♥✐❢♦r♠❡ β ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✹
❚❛❜❡❧❛ ✺ ◆♦t❛çã♦ ❯♥✐❢♦r♠❡ neg ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✹
❚❛❜❡❧❛ ✻ ◆♦t❛çã♦ ❯♥✐❢♦r♠❡ v(R) ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✹
❚❛❜❡❧❛ ✼ ◆♦t❛çã♦ ❯♥✐❢♦r♠❡ π(R) ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✹
❙❯▼➪❘■❖
✶ ■♥tr♦❞✉çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵ ✶✳✶ ▼♦t✐✈❛çã♦ ❡ ❈❛r❛❝t❡r✐③❛çã♦ ❞♦ Pr♦❜❧❡♠❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵ ✶✳✷ ❖❜❥❡t✐✈♦s ❞❛ ❉✐ss❡rt❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸ ✶✳✸ ❖r❣❛♥✐③❛çã♦ ❞❛ ❉✐ss❡rt❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹
✷ ▲ó❣✐❝❛s ❞❡ ❉❡s❝r✐çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺ ✷✳✶ ❚❜♦① ❡ ❆❜♦①✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺ ✷✳✷ ❉❡✜♥✐çã♦ ❞❛ ❙✐♥t❛①❡ ❡ ❞❛ ❙❡♠â♥t✐❝❛ ❞❡AL✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼ ✷✳✷✳✶ ❙✐♥t❛①❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼ ✷✳✷✳✷ ❙ê♠❛♥t✐❝❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✾ ✷✳✸ ❊①t❡♥sõ❡s ❞❛ ▲✐♥❣✉❛❣❡♠ AL✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✵ ✷✳✹ AL❝♦♠♦ ✉♠ ❢r❛❣♠❡♥t♦ ❞❡ ❋❖▲ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✶ ✷✳✺ ❚❛r❡❢❛s ❞❡ ❘❛❝✐♦❝í♥✐♦ ♦✉ ■♥❢❡rê♥❝✐❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✶ ✷✳✺✳✶ ❚❛r❡❢❛s ❞❡ ❘❛❝✐♦❝í♥✐♦ ♣❛r❛ ❚❜♦① ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✸ ✷✳✺✳✷ ❚❛r❡❢❛s ❞❡ ❘❛❝✐♦❝í♥✐♦ ♣❛r❛ ❆❜♦① ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✼ ✷✳✻ ❆❧❣♦r✐t♠♦s ❞❡ ❚❛❜❧❡❛✉① ♣❛r❛ALC ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✽ ✷✳✻✳✶ ❊st❡♥❞❡♥❞♦ ♦ ❚❛❜❧❡❛✉① ♣❛r❛ ❚❜♦① ❝í❝❧✐❝♦s ❡ ❝♦♠ ❛①✐♦♠❛s ❞❡ ✐♥❝❧✉sã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✷ ✷✳✻✳✷ ❯♠ ❚❛❜❧❡❛✉① ❊❳P❚■▼❊ ♣❛r❛ ALC ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✸
✸ ❆ ▲ó❣✐❝❛ ❉❡❢❛✉❧t ❞❡ ❘❡✐t❡r✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✶ ✸✳✶ ❚❡♦r✐❛ ❉❡❢❛✉❧t ❡ ❉❡✜♥✐çã♦ ❞❡ ❊①t❡♥sõ❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✶ ✸✳✷ ❉❡✜♥✐çõ❡s ❆❧t❡r♥❛t✐✈❛s ♣❛r❛ ❊①t❡♥sõ❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✸ ✸✳✸ ❖s Pr♦❜❧❡♠❛s ❞❛ ■♥❡①✐stê♥❝✐❛ ❞❡ ❊①t❡♥sõ❡s ❡ ❞❛s ❊①t❡♥sõ❡s ❆♥ô♠❛❧❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✹ ✸✳✹ ❖r❞❡♥❛çã♦ ❞❡ ❉❡❢❛✉❧ts ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✾ ✸✳✺ ❆❧❣♦r✐t♠♦s ❞❡ ❈♦♥str✉çã♦ ❞❡ ❊①t❡♥sõ❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✵
✹✳✶ ❚❡♦r✐❛ ❞❡ ❉❡s❝r✐çã♦ ❉❡❢❛✉❧t ❡ ❉❡✜♥✐çã♦ ❞❡ ❊①t❡♥sõ❡s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✸ ✹✳✷ Pré✲❝♦♠♣✐❧❛çã♦ ♣❛r❛ ❈♦♥str✉çã♦ ❞❡ ❊①t❡♥sõ❡s ❞❡ ❉❉▲✿ ❉❡✜♥✐çã♦✱ ❆❧❣♦r✐t♠♦s
❡ ❈♦♠♣❧❡①✐❞❛❞❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✹ ✹✳✷✳✶ ❚r❛♥s❢♦r♠❛çã♦ ♣❛r❛ ❛ ❋♦r♠❛ ◆♦r♠❛❧ ❈❧❛✉s❛❧✿ ❉❡✜♥✐çã♦✱ ❆❧❣♦r✐t♠♦s ❡ ❈♦♠✲
♣❧❡①✐❞❛❞❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✼ ✹✳✷✳✷ ❖r❞❡♥❛çã♦ ❞❡ ❉❡❢❛✉❧ts✿ ❉❡✜♥✐çã♦✱ ❆❧❣♦r✐t♠♦s ❡ ❈♦♠♣❧❡①✐❞❛❞❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✾ ✹✳✷✳✸ ❖r❣❛♥✐③❛çã♦ ❞♦s ❉❡❢❛✉❧ts ❡♠ P❛rt✐çõ❡s✿ ❉❡✜♥✐çã♦✱ ❆❧❣♦r✐t♠♦s ❡ ❈♦♠♣❧❡①✐❞❛❞❡ ✻✺ ✹✳✸ ❯♠❛ ❉❡✜♥✐çã♦ ❈♦♥str✉t✐✈❛ ❞❡ ❊①t❡♥sã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✸ ✹✳✹ ❆ ❈♦♥str✉çã♦ ❞❡ ❊①t❡♥sõ❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✹
✺ ❈♦♥❝❧✉sã♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✻ ✺✳✶ ❈♦♥❝❧✉sõ❡s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✻ ✺✳✷ ❈♦♠♣❛r❛çã♦ ❝♦♠ ❚r❛❜❛❧❤♦s ❘❡❧❛❝✐♦♥❛❞♦s ❡ ❚r❛❜❛❧❤♦s ❋✉t✉r♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✻
❘❡❢❡rê♥❝✐❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✽
✶ ■◆❚❘❖❉❯➬➹❖
✶✳✶ ▼♦t✐✈❛çã♦ ❡ ❈❛r❛❝t❡r✐③❛çã♦ ❞♦ Pr♦❜❧❡♠❛
❈♦♠ ♦ ❛❞✈❡♥t♦ ❞❛s ♥♦✈❛s t❡❝♥♦❧♦❣✐❛s✱ ❛ ■♥t❡r♥❡t ✈❡♠ s❡ ♣♦♣✉❧❛r✐③❛♥❞♦ ❝❛❞❛ ❞✐❛ ♠❛✐s ❡ t♦r♥❛♥❞♦✲s❡ ❢❡rr❛♠❡♥t❛ ❡ss❡♥❝✐❛❧ ♥♦ ❝♦t✐❞✐❛♥♦ ❞♦ s❡r ❤✉♠❛♥♦✳ ❆ ❲♦r❧❞ ❲✐❞❡ ❲❡❜ ✭t❛♠❜é♠ ❝♦♥❤❡❝✐❞❛ ❝♦♠♦ ❲❡❜ ❡ ❲❲❲✮ é ✉♠ s✐st❡♠❛ ❞❡ ❞♦❝✉♠❡♥t♦s ❡♠ ❤✐♣❡r♠í❞✐❛ q✉❡ sã♦ ✐♥t❡r❧✐❣❛❞♦s ❡ ❡①❡❝✉t❛❞♦s ♥❛ ■♥t❡r♥❡t✳ ❖s ❞♦❝✉♠❡♥t♦s ♣♦❞❡♠ ❡st❛r ♥❛ ❢♦r♠❛ ❞❡ ✈í❞❡♦s✱ s♦♥s✱ ❤✐♣❡rt❡①t♦s ❡ ✜❣✉r❛s✳ P❛r❛ ✈✐s✉❛❧✐③❛r ❛ ✐♥❢♦r♠❛çã♦✱ ♣♦❞❡✲s❡ ✉s❛r ✉♠ ♣r♦❣r❛♠❛ ❞❡ ❝♦♠♣✉t❛❞♦r ❝❤❛♠❛❞♦ ♥❛✈❡❣❛❞♦r ♣❛r❛ ❞❡s❝❛rr❡❣❛r ✐♥❢♦r♠❛çõ❡s ✭❝❤❛♠❛❞❛s ✏❞♦❝✉♠❡♥t♦s✑ ♦✉ ✏♣á❣✐♥❛s✑✮ ❞❡ s❡r✈✐❞♦r❡s ❲❡❜ ✭♦✉ ✏s✐t❡s✑✮ ❡ ♠♦strá✲❧♦s ♥❛ t❡❧❛ ❞♦ ✉s✉ár✐♦✳ ❖ ✉s✉ár✐♦ ♣♦❞❡ ❡♥tã♦ s❡❣✉✐r ❛s ❤✐♣❡r❧✐❣❛çõ❡s ♥❛ ♣á❣✐♥❛ ♣❛r❛ ♦✉tr♦s ❞♦❝✉♠❡♥t♦s ♦✉ ♠❡s♠♦ ❡♥✈✐❛r ✐♥❢♦r♠❛çõ❡s ❞❡ ✈♦❧t❛ ♣❛r❛ ♦ s❡r✈✐❞♦r ♣❛r❛ ✐♥t❡r❛❣✐r ❝♦♠ ❡❧❡✳
❆ ❲❡❜ ❛t✉❛❧♠❡♥t❡ ♣♦ss✉✐ ♠✉✐t❛s ♣á❣✐♥❛s✱ ❝❛❞❛ q✉❛❧ ❝❛rr❡❣❛❞❛ ❝♦♠ ✐♥❢♦r♠❛çõ❡s ❡ ❞❛❞♦s q✉❡ s❡rã♦ ❞❡ ✉t✐❧✐❞❛❞❡ ♣❛r❛ ❛❧❣✉♠ ✉s✉ár✐♦ ♥♦ ♠✉♥❞♦✳ ❘❡st❛✲♥♦s s❛❜❡r✿ t❛❧ ✉s✉ár✐♦ ❝♦♥s❡❣✉✐rá ❡♥❝♦♥tr❛r ❡ss❛ ✐♥❢♦r♠❛çã♦❄ ❈♦♠♦ ❡❧❡ ❡♥❝♦♥tr❛rá ❡ss❛ ✐♥❢♦r♠❛çã♦❄ ❙❡rá q✉❡ s❡❣✉✐♥❞♦ ♣♦r ❤✐♣❡r❧✐❣❛çõ❡s ❡♥tr❡ ♣á❣✐♥❛s✱ ❡❧❡ ❝♦♥s❡❣✉✐rá ❡♥❝♦♥tr❛r ♦s ❞❛❞♦s q✉❡ ♣r❡❝✐s❛❄ ❊ss❛s ❡ ♦✉tr❛s ♣❡r❣✉♥t❛s ❢♦r❛♠ ❜❛s❡ ♣❛r❛ ❛ ❝♦♥str✉çã♦ ❞❡ ✉♠❛ ❡①t❡♥sã♦ ❞❛ ❲❡❜ q✉❡ s❡r✈❡ ♣❛r❛ ❢❛❝✐❧✐t❛r q✉❡ ❝♦♠♣✉t❛❞♦r❡s ♣♦ss❛♠ ❛tr✐❜✉✐r ✉♠ s✐❣♥✐✜❝❛❞♦ ✭s❡♥t✐❞♦✮ ❛♦s ❝♦♥t❡ú❞♦s ♣✉❜❧✐❝❛❞♦s ♥❛ ■♥t❡r♥❡t ❞❡ ♠♦❞♦ q✉❡ s❡❥❛ ♣❡r❝❡♣tí✈❡❧ t❛♥t♦ ♣❡❧♦ ❤✉♠❛♥♦ ❝♦♠♦ ♣❡❧♦ ❝♦♠♣✉t❛❞♦r✿ ❛ ❲❡❜ ❙❡♠â♥t✐❝❛✳
❖ ♦❜❥❡t✐✈♦ ♣r✐♥❝✐♣❛❧ ❞❛ ❲❡❜ ❙❡♠â♥t✐❝❛ ♥ã♦ é✱ ❛♣❡♥❛s tr❡✐♥❛r ❛s ♠áq✉✐♥❛s ♣❛r❛ q✉❡ s❡ ❝♦♠♣♦rt❡♠ ❝♦♠♦ ♣❡ss♦❛s✱ ♠❛s s✐♠ ❞❡s❡♥✈♦❧✈❡r t❡❝♥♦❧♦❣✐❛s ❡ ❧✐♥❣✉❛❣❡♥s q✉❡ t♦r♥❡♠ ❛ ✐♥❢♦r♠❛çã♦ ❧❡❣í✈❡❧ ♣❛r❛ ❛s ♠áq✉✐♥❛s✳ ❆ ✜♥❛❧✐❞❛❞❡ ♣❛ss❛ ♣❡❧♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❡ ✉♠ ♠♦❞❡❧♦ t❡❝♥♦❧ó❣✐❝♦ q✉❡ ♣❡r♠✐t❛ ❛ ♣❛rt✐❧❤❛ ❣❧♦❜❛❧ ❞❡ ❝♦♥❤❡❝✐♠❡♥t♦ ❛ss✐st✐❞♦ ♣♦r ♠áq✉✐♥❛s ✭❲✸❈ ✷✵✵✶✮✳ ❆ ✐♥t❡❣r❛çã♦ ❞❛s ❧✐♥❣✉❛❣❡♥s ♦✉ t❡❝♥♦❧♦❣✐❛s ❡❳t❡♥s✐❜❧❡ ▼❛r❦✉♣ ▲❛♥❣✉❛❣❡ ✭❳▼▲✮✱ ❘❡s♦✉r❝❡ ❉❡s❝r✐♣t✐♦♥ ❋r❛♠❡✇♦r❦ ✭❘❉❋✮✱ ❛rq✉✐t❡t✉r❛s ❞❡ ♠❡t❛✲❞❛❞♦s✱ ♦♥t♦❧♦✲ ❣✐❛s✱ ❛❣❡♥t❡s ❝♦♠♣✉t❛❝✐♦♥❛✐s✱ ❡♥tr❡ ♦✉tr❛s✱ ❢❛✈♦r❡❝❡ ♦ ❛♣❛r❡❝✐♠❡♥t♦ ❞❡ s❡r✈✐ç♦s ❲❡❜ q✉❡ ❣❛r❛♥t❛♠ ❛ ✐♥t❡r♦♣❡r❛❜✐❧✐❞❛❞❡ ❡ ❝♦♦♣❡r❛çã♦✳
❊♠ ✷✵✵✶✱ ✭❇❊❘◆❊❘❙✲▲❊❊❀ ❍❊◆❉▲❊❘❀ ▲❆❙❙■▲❆✱ ✷✵✵✶✮ ❞❡✜♥✐✉ ♦ ❝♦♥❝❡✐t♦ ❞❡ ❲❡❜
❙❡♠â♥t✐❝❛ ❜❡♠ ❝♦♠♦ ✉♠❛ ♣♦ssí✈❡❧ ❛rq✉✐t❡t✉r❛ ♣❛r❛ ❛♣❧✐❝❛çõ❡s s♦❜ ♦ ♠❡s♠♦ ❝♦♥t❡①t♦✳ ❆ ❛rq✉✐t❡t✉r❛ ♣❛ss♦✉ ♣♦r ✈ár✐❛s ♠♦❞✐✜❝❛çõ❡s ❡ ❛ s✉❛ ❝♦♥✜❣✉r❛çã♦ ❛t✉❛❧ é ✐❧✉str❛❞❛ ♥❛ ✜❣✉r❛ ❛❜❛✐①♦✿
✶✶
❋✐❣✉r❛ ✶✿ ❲❡❜ ❙❡♠â♥t✐❝❛ ✲ ❘❡♣r❡s❡♥t❛çã♦ ❡♠ ❈❛♠❛❞❛s
s✉r❣❡ ❛❣♦r❛ é q✉❛❧ ▲ó❣✐❝❛ s❡rá ✉t✐❧✐③❛❞❛✳ ❯♠❛ ♦♣çã♦ s❡r✐❛ tr❛❜❛❧❤❛r♠♦s ❝♦♠ ❛ ▲ó❣✐❝❛ ❞❡ Pr✐♠❡✐r❛ ❖r❞❡♠ ✭❋❖▲✮✳ ❊❧❛ ♣♦ss✉✐ ❝♦♠♦ ❣r❛♥❞❡ ✈❛♥t❛❣❡♠ s❡r ✉♠❛ ❧ó❣✐❝❛ ❜❡♠ ♠❛❞✉r❛ ❡ r♦❜✉st❛✳ ❖ ♣r♦❜❧❡♠❛ ♣r✐♥❝✐♣❛❧ é q✉❡✱ ♣❛r❛ ✉t✐❧✐③á✲❧❛ ♥❛ ❲❡❜ ❙❡♠â♥t✐❝❛✱ ❡st❛ ♣r❡❝✐s❛ s❡r ❞❡❝✐❞í✈❡❧✳ ■st♦ ♥❡♠ s❡♠♣r❡ ❛❝♦♥t❡❝❡✳
❖✉tr♦ ❛s♣❡❝t♦ ✐♠♣♦rt❛♥t❡ é q✉❡ ❣r❛♥❞❡ ♣❛rt❡ ❞❛s ✐♥❢♦r♠❛çõ❡s ❞❛ ❲❡❜ ❙❡♠â♥t✐❝❛ sã♦ ❡①♣r❡ss❛s ✉t✐❧✐③❛♥❞♦ s✐st❡♠❛s ❤✐❡rárq✉✐❝♦s ❞❡ s✐♠♣❧❡s r❡♣r❡s❡♥t❛çã♦✳ ▲♦❣♦✱ ♥ã♦ s❡ ♠♦str❛ ♥❡❝❡ssár✐♦ t❛♥t❛ ❡①♣r❡ss✐✈✐❞❛❞❡ q✉❛♥t♦ ❛ ❋❖▲ ♦❢❡r❡❝❡✳ ❙❡♥❞♦ ❛ss✐♠✱ ♣❛rt✐r❡♠♦s ♣❛r❛ ♦✉tr❛ ♦♣çã♦✳ ❯♠❛ ❧ó❣✐❝❛ q✉❡ t❡♠ s✐❞♦ ❜❛st❛♥t❡ ✉t✐❧✐③❛❞❛ é ❛ ▲ó❣✐❝❛ ❞❡ ❉❡s❝r✐çã♦ ✭❉▲✮ ✭❇❆❆❉❊❘ ❡t ❛❧✳✱ ✷✵✵✸✮✳ ❋♦❝❛r❡♠♦s ♥♦ss❛ ♣❡sq✉✐s❛ ♥❡ss❛ ❧ó❣✐❝❛✳
❊♥tr❡t❛♥t♦✱ ♣♦r q✉❡ ♥ã♦ ✉t✐❧✐③❛♠♦s Pr♦❣r❛♠❛çã♦ ❡♠ ▲ó❣✐❝❛ ✭P▲✮ ❛♦ ✐♥✈és ❞❛ ▲ó❣✐❝❛ ❞❡ ❉❡s❝r✐çã♦❄ ❙❡❣✉♥❞♦ ✭❆◆❚❖◆■❖❯❀ ❍❆❘▼❊▲❊◆✱ ✷✵✵✹✮✱ é ✐♥t❡r❡ss❛♥t❡ ♥♦t❛r♠♦s
q✉❡ ❉▲ ❡ P▲ sã♦ ♦rt♦❣♦♥❛✐s ♥♦ s❡♥t✐❞♦ ❞❡ q✉❡ ♥❡♥❤✉♠❛ ❞❡❧❛s é s✉❜❝♦♥❥✉♥t♦ ❞❛ ♦✉tr❛✳ ❊♠ ♦✉tr❛s ♣❛❧❛✈r❛s✱ ❡①✐st❡♠ ✐♥❢♦r♠❛çõ❡s q✉❡ ❛ ❉▲ ♥ã♦ ❝♦♥s❡❣✉❡ ❡①♣r❡ss❛r ❡ q✉❡ ❛ P▲ ❢❛❝✐❧♠❡♥t❡ ❡①♣r❡ss❛✳ ❖ ✐♥✈❡rs♦ t❛♠❜é♠ ❛❝♦♥t❡❝❡✳
❈♦♠♦ ❡①❡♠♣❧♦✱
❊①❡♠♣❧♦ ✶✳✶✳ ✭❉❡✜♥✐♥❞♦ ❛ r❡❧❛çã♦ ❚✐♦ ❡♠ ❉▲ ❡ P▲✮
◆♦t❡ q✉❡ é ✐♠♣♦ssí✈❡❧ ❡①♣r❡ss❛r♠♦s ❛ r❡❧❛çã♦ ❚✐♦✭❳✱❨✮ ❡♠ ❉▲✳ ❉❡s❝r❡✈❡♠♦✲❧❛ ❛ s❡❣✉✐r ❡♠ ❋❖▲✿
∀X, Y.∃Z.✭■r♠ã♦❉❡(X, Z) ∧F ilhoDe(Z, Y) →T io(X, Y))
❊ss❛ r❡❧❛çã♦ é ❢❛❝✐❧♠❡♥t❡ ❡①♣r❡ss❛ ❡♠ P▲✿
■r♠ã♦❉❡(X, Z), F ilhoDe(Z, Y) →T io(X, Y)
✳
✶✷
❼ ♥❡❣❛çã♦✴❝♦♠♣❧❡♠❡♥t♦ ❞❡ ❝❧❛ss❡s
❼ ✐♥❢♦r♠❛çã♦ ❞✐s❥✉♥t✐✈❛
❼ q✉❛♥t✐✜❝❛çã♦ ❡①✐st❡♥❝✐❛❧
❼ q✉❛♥t✐✜❝❛çã♦ ✉♥✐✈❡rs❛❧ ❡①♣❧✐❝✐t❛♠❡♥t❡
❈♦♥❝❧✉✐♠♦s✱ ❛ss✐♠✱ q✉❡ ❛ ❡s❝♦❧❤❛ ❡♥tr❡ P▲ ❡ ❉▲ é ❢❡✐t❛ ❞❡ ❛❝♦r❞♦ ❝♦♠ ♦ q✉❡ s❡ q✉❡r r❡♣r❡s❡♥t❛r✳
❖✉tr❛ ❝❛♠❛❞❛ ✐♠♣♦rt❛♥t❡ ❞❛ ❲❡❜ ❙❡♠â♥t✐❝❛ é ❛ ❝❛♠❛❞❛ ❞❡ ❘❡❣r❛s✳ ❊st❛ ❝❛♠❛❞❛ ♠♦str❛✲s❡ ❞❡ ❡①tr❡♠❛ ✐♠♣♦rtâ♥❝✐❛ ❛♦ ✐♥❢❡r✐r♠♦s ♥♦✈❛s ✐♥❢♦r♠❛çõ❡s ❛ ♣❛rt✐r ❞♦ ❝♦♥❤❡❝✐✲ ♠❡♥t♦ ❥á ❡①✐st❡♥t❡✳ ❆ ▲ó❣✐❝❛ t❡♠ ♠✉✐t♦ ❛ ❝♦♥tr✐❜✉✐r ♣❛r❛ ♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❛ ❲❡❜ ❙❡♠â♥t✐❝❛ ♥❡ss❡ ❛s♣❡❝t♦✱ ✉♠❛ ✈❡③ q✉❡ ❥á ❢♦r❛♠ ❞❡s❡♥✈♦❧✈✐❞♦s ❞✐✈❡rs♦s tr❛❜❛❧❤♦s t❛♥t♦ ♥❛ ár❡❛ ❞❡ r❛❝✐♦❝✐♥❛❞♦r❡s q✉❡ ✉t✐❧✐③❛♠ Pr♦❣r❛♠❛çã♦ ❡♠ ▲ó❣✐❝❛ ❝♦♠♦ ♣❡❧❛ ár❡❛ ✈♦❧t❛❞❛ ♣❛r❛ ♦ r❛❝✐♦❝í♥✐♦ ♥ã♦✲♠♦♥♦tô♥✐❝♦ ✭●■◆❙❇❊❘●✱ ✶✾✽✼❛✮✳
P♦r q✉❡ ♣r❡❝✐s❛♠♦s ✐♥tr♦❞✉③✐r ♦ r❛❝✐♦❝í♥✐♦ ♥ã♦✲♠♦♥♦tô♥✐❝♦ ❡♠ ♥♦ss❛ ♣❡sq✉✐s❛❄ ❆s ❧ó❣✐❝❛s ♠♦♥♦tô♥✐❝❛s✱ ♣♦r ❡①❡♠♣❧♦ ❛ ❋❖▲✱ sã♦ ♣❡r❢❡✐t❛s ♣❛r❛ ♠♦❞❡❧❛r s✐t✉❛çã♦ ✐❞❡❛✐s ♥❛s q✉❛✐s ♦ ❝♦♥❤❡❝✐♠❡♥t♦ ♦❜t✐❞♦ é ♣r❡❝✐s♦ ❡ ❝♦♠♣❧❡t♦ ♦ s✉✜❝✐❡♥t❡ ♣❛r❛ ❡❢❡t✉❛r♠♦s ✐♥❢❡rê♥❝✐❛s ❝✉❥❛s ❝♦♥❝❧✉sõ❡s t❡♠ ♦ st❛t✉s ❞❡ ❝❡rt❡③❛✳ ❊♠ s✐t✉❛çõ❡s r❡❛✐s ✭♥♦ ♥♦ss♦ ❝❛s♦✱ ❛s ❡①♣r❡ss❛s ♥❛ ❲❡❜✮✱ ♥❛s q✉❛✐s ♦ ❝♦♥❤❡❝✐♠❡♥t♦ é ✐♥❝♦♠♣❧❡t♦ ❡ ✐♠♣r❡❝✐s♦✱ ❛ ❋❖▲ q✉❡ é ♠♦♥♦tô♥✐❝❛✱ ♥ã♦ é s✉✜❝✐❡♥t❡✳ ❆s ❧ó❣✐❝❛s ♥ã♦✲♠♦♥♦tô♥✐❝❛s sã♦ ♣❡r❢❡✐t❛s ♣❛r❛ r❡♣r❡s❡♥t❛çã♦ ❡ r❛❝✐♦❝í♥✐♦ ❡♠ ❜❛s❡s ❞❡ ❝♦♥❤❡❝✐♠❡♥t♦ ♣❛r❝✐❛✐s✳
❆s ▲ó❣✐❝❛s ◆ã♦✲♠♦♥♦tô♥✐❝❛s sã♦ s✐st❡♠❛s ❧ó❣✐❝♦s ♥♦s q✉❛✐s ❛ ♣r♦♣r✐❡❞❛❞❡ ❞❛ ♠♦♥♦t♦♥✐❝✐❞❛❞❡ ❢❛❧❤❛✳ ❊ss❛ ♣r♦♣r✐❡❞❛❞❡ ❣❛r❛♥t❡ q✉❡✱ s❡ ❛ ❝♦♥❝❧✉sã♦ é ✐♥❢❡r✐❞❛ ❛ ♣❛rt✐r ❞❡ ❛❧❣✉♠❛s ♣r❡♠✐ss❛s✱ ♥❡♥❤✉♠❛ ♣r❡♠✐ss❛ ❛❞✐❝✐♦♥❛❧ ✐♥✈❛❧✐❞❛rá ❛ ❝♦♥❝❧✉sã♦✳ ❊♥tr❡t❛♥t♦✱ ❡♠ s✐t✉❛çõ❡s r❡❛✐s✱ é ❝♦♠✉♠ ❝♦♥❝❧✉✐r♠♦s ✐♥❢♦r♠❛çõ❡s ❛ ♣❛rt✐r ❞❡ ♥♦ss❛s ❡①♣❡r✐ê♥❝✐❛s ❡♠ ❢❛t♦s q✉❡ ❛❝❤❛♠♦s s❡r❡♠ ❝♦st✉♠❡✐r♦s✱ ♦s q✉❛✐s ♣♦❞❡♠ s❡r r❡❢✉tá✈❡✐s ❡♠ ❢❛❝❡ ❞❡ ♥♦✈❛s ✐♥❢♦r♠❛çõ❡s✳ ❙ã♦ ❞✐✈❡rs❛s ❛s ár❡❛s ❞❡ ❛♣❧✐❝❛çã♦ ❞♦ r❛❝✐♦❝í♥✐♦ ♥ã♦✲♠♦♥♦tô♥✐❝♦✱ ❞❡♥tr❡ ❡❧❛s ✭▼❆❘❚■◆❙✱ ✶✾✾✼✮✱ ✭❇❆❙❙■▲■❆❉❊❙❀ ❆◆❚❖◆■❖❯❀ ❱▲❆❍❆❱❆❙✱ ✷✵✵✻✮✿
❘❛❝✐♦❝í♥✐♦ s♦❜r❡ ❛çõ❡s r❡♣r❡s❡♥t❛çã♦ ❞❡ s✐t✉❛çõ❡s ♦♥❞❡ ✉♠❛ ❛çã♦ ♣♦❞❡ ❢❛❧❤❛r✳ ❈♦♠♦ ❡①❡♠♣❧♦✱ q✉❛♥❞♦ ❞❛♠♦s ❛ ♣❛rt✐❞❛ ❡♠ ✉♠ ❝❛rr♦✱ ❡❧❡ ❢✉♥❝✐♦♥❛rá✱ ❛ ♠❡♥♦s q✉❡ ♥ã♦ t❡♥❤❛ ❝♦♠❜✉stí✈❡❧✱ ❛ ❜❛t❡r✐❛ ❞❡s❝❛rr❡❣♦✉ ♦✉ t❡♥❤❛ ❛❧❣✉♠ ♦✉tr♦ ♣r♦❜❧❡♠❛ ♠❡❝â♥✐❝♦❀
❘❡❣r❛s ❝♦♠ ❡①❝❡çã♦ ❊ss❛ ár❡❛ tr❛❜❛❧❤❛ ❜✉s❝❛♥❞♦ s♦❧✉çõ❡s ♣❛r❛ ❝♦♥✢✐t♦s ❡♥tr❡ r❡❣r❛s✳ ❈♦♠♦ ❡①❡♠♣❧♦✱ ❝✐t❛r❡♠♦s ♥♦✈❛♠❡♥t❡ ♦ ❝❛s♦ ❞♦s ♣✐♥❣✉✐♥s ♥ã♦ ✈♦❛r❡♠ s❡r ✉♠❛ ❡①✲ ❝❡çã♦ ❛♦ ❝❛s♦ ❣❡r❛❧ ❞♦s ♣áss❛r♦s ✈♦❛r❡♠❀
✶✸
■♥❢♦r♠❛çã♦ ♥❡❣❛t✐✈❛ ❡①♣r❡ss❛r ✐♥❢♦r♠❛çõ❡s ♥❡❣❛t✐✈❛s s❡♠♣r❡ ❢♦✐ ❛ss✉♥t♦ ❞❡ ♠✉✐t♦s ❡s✲ t✉❞♦s ❞❡✈✐❞♦ ❛♦ s❡✉ ❛❧t♦ ❝✉st♦ ❞❡ ❡①♣r❡ss✐✈✐❞❛❞❡✳ ❉✐✈❡rs❛s ❢♦r♠❛s ❢♦r❛♠ ❞❡s❡♥✈♦❧✈✐✲ ❞❛s ❜✉s❝❛♥❞♦ ❛♣r♦①✐♠❛çõ❡s✳ ❈✐t❛♠♦s ❝♦♠♦ ✉♠ ❡①❡♠♣❧♦ ❞❡st❡s tr❛❜❛❧❤♦s ❛ ♥❡❣❛çã♦ ♣♦r ❢❛❧❤❛❀
❉✐❛❣♥óst✐❝♦ ❊ss❛ ár❡❛ ♣♦ss✉✐ ❝♦♠♦ ♦❜❥❡t✐✈♦ ♣r✐♥❝✐♣❛❧ ❛❝❤❛r ✉♠ ❝♦♥❥✉♥t♦ ♠✐♥✐♠❛❧ ❞❡ ♣♦ssí✈❡✐s ❝❛✉s❛s q✉❡ ♣♦❞❡♠ ❡①♣❧✐❝❛r ♦ ♠❛❧ ❢✉♥❝✐♦♥❛♠❡♥t♦ ❞♦ ♦❜❥❡t♦ ❡♠ q✉❡stã♦❀
❉❡✜♥✐çõ❡s ✐♥❞✉t✐✈❛s ❞❡✜♥✐çõ❡s r❡❝✉rs✐✈❛s ♣♦❞❡♠ s❡r ✈✐st❛s ❝♦♠♦ ❣❡♥❡r❛❧✐③❛çõ❡s ❞❡ ❞❡✜♥✐çõ❡s ❝❛s♦ ❛ ❝❛s♦✳ ❉❡♥tr❡ ❛s ❞❡✜♥✐çõ❡s ❝❛s♦ ❛ ❝❛s♦ s❡♠♣r❡ t❡♠♦s ✉♠❛ ❝❤❛♠❛❞❛ ❝❧á✉s✉❧❛ ❞❡ ❢❡❝❤❛♠❡♥t♦ q✉❡ ♣❡r♠✐t❡✱ ❞❡♥tr❡ ♦✉tr❛s ❝♦✐s❛s✱ ♣r♦✈❛s ❞❡ r❡s✉❧t❛❞♦s ♥❡✲ ❣❛t✐✈♦s❀
❋✉sã♦ ❞❡ ❝♦♥❤❡❝✐♠❡♥t♦ ❙ã♦ ✈ár✐♦s ♦s ♣r♦❜❧❡♠❛s ❡♥❝♦♥tr❛❞♦s q✉❛♥❞♦ ✈✐s❛♠♦s ❛ ❢✉sã♦ ❞❡ tr❛❜❛❧❤♦s ❞❡ ❛✉t♦r❡s ❞✐❢❡r❡♥t❡s✳ ❈♦♥tr❛❞✐çã♦ é ✉♠ ❞♦s ♣r♦❜❧❡♠❛s q✉❡ ♦❝♦rr❡♠ ♠❛✐s ❢r❡q✉❡♥t❡♠❡♥t❡✳ ❖ ✉s♦ ❞❡ r❡❣r❛s ❞❡ ♣r✐♦r✐❞❛❞❡ ♣♦❞❡ s❡r ✉♠❛ ♣♦ssí✈❡❧ s♦❧✉çã♦ ♣❛r❛ ♦ ❝❛s♦✳
❉❡♥tr❡ ❛s ❢♦r♠❛❧✐③❛çõ❡s ❞♦ r❛❝✐♦❝í♥✐♦ ♥ã♦✲♠♦♥♦tô♥✐❝♦✱ ❝✐t❛♠♦s ❛s ♣r✐♥❝✐♣❛✐s ▲ó❣✐✲ ❝❛s✿ ❉❡❢❡❛s✐❜❧❡✭❇❆❙❙■▲■❆❉❊❙❀ ❆◆❚❖◆■❖❯❀ ❱▲❆❍❆❱❆❙✱ ✷✵✵✻✮✱ ❈✐r❝✉♥s❝r✐çã♦ ✭▼❈❈❆❘❚❍❨✱
✶✾✽✵✮✱ ❆✉t♦✲❡♣✐stê♠✐❝❛ ✭●■◆❙❇❊❘●✱ ✶✾✽✼❛✮ ❡ ❉❡❢❛✉❧t ❞❡ ❘❡✐t❡r ✭❘✱ ✶✾✽✼✮✳ ❉❡❝✐❞✐♠♦s ✉t✐✲
❧✐③❛r ❛ ❧ó❣✐❝❛ ❉❡❢❛✉❧t ❞❡ ❘❡✐t❡r✳ ❊ss❛ ❡s❝♦❧❤❛ ❢♦✐ ❢❡✐t❛ ❞❡✈✐❞♦ ❛♦ ❢❛t♦ ❞❡ t❡r♠♦s ❝♦♠♦ ♦❜❥❡t✐✈♦ ❡①♣r❡ss❛r ❛s ✐♥❢♦r♠❛çõ❡s ✐♥❝♦♠♣❧❡t❛s ❝♦♠♦ r❡❣r❛s ❡♠ q✉❡ ❞❡s❝r❡✈❡♠♦s ♦s ❝❛s♦s ❣❡r❛✐s ♦✉ ♠❛✐s ❢r❡q✉❡♥t❡s ❞❛s ✐♥❢♦r♠❛çõ❡s ❥✉♥t❛♠❡♥t❡ ❝♦♠ s✉❛s ❡①❝❡çõ❡s✳
✶✳✷ ❖❜❥❡t✐✈♦s ❞❛ ❉✐ss❡rt❛çã♦
❖ ♦❜❥❡t✐✈♦ ❞❡ ♥♦ss❛ ♣❡sq✉✐s❛ é ✐♥✈❡st✐❣❛r✱ ❛♣r❡s❡♥t❛r ❡ ❞❡s❡♥✈♦❧✈❡r ✉♠ s✐st❡♠❛ ❞❡ r❡♣r❡s❡♥t❛çã♦ ❞❡ ❝♦♥❤❡❝✐♠❡♥t♦ ♥ã♦✲♠♦♥♦tô♥✐❝♦ q✉❡ s❡❥❛ ❛♣❧✐❝á✈❡❧ ❛ ❲❡❜ ❡ q✉❡ s✉❛s ✐♥❢❡rê♥❝✐❛s s❡❥❛♠ ❞❡❝✐❞í✈❡✐s✳
❆♦ ✉t✐❧✐③❛r♠♦s ❛ ▲ó❣✐❝❛ ❉❡❢❛✉❧t✱ ♥♦s ❞❡♣❛r❛♠♦s ❝♦♠ ✉♠❛ ❧ó❣✐❝❛ ✐♥❞❡❝✐❞í✈❡❧✳ ❋❖▲✱ q✉❡ é ❛ ♣❛rt❡ ♠♦♥♦tô♥✐❝❛ ❞❛ ▲ó❣✐❝❛ ❉❡❢❛✉❧t t❛♠❜é♠ ♥ã♦ é ❞❡❝✐❞í✈❡❧✱ s❡♥❞♦ s♦♠❡♥t❡ s❡♠✐✲❞❡❝✐❞í✈❡❧✳ ■ss♦ ♦❝♦rr❡ ♣❡❧♦ ❢❛t♦ ❞❡ q✉❡ ♦ ❝♦♥❥✉♥t♦ ❞❡ s❡✉s t❡♦r❡♠❛s é r❡❝✉rs✐✈❛♠❡♥t❡ ❡♥✉♠❡rá✈❡❧✳ ❏á ♣❛r❛ ❛ ▲ó❣✐❝❛ ❉❡❢❛✉❧t✱ s❡✉ ❝♦♥❥✉♥t♦ ❞❡ t❡♦r❡♠❛s ♥ã♦ é ♥❡♠ r❡❝✉rs✐✈❛♠❡♥t❡ ❡♥✉♠❡rá✈❡❧✳
❯♠❛ ♣♦ssí✈❡❧ s♦❧✉çã♦ ♣❛r❛ ♦❜t❡r♠♦s ✉♠❛ ❧ó❣✐❝❛ ♥ã♦✲♠♦♥♦tô♥✐❝❛ ❞❡❝✐❞í✈❡❧ é r❡s✲ tr✐♥❣✐r♠♦s s✉❛s ♣❛rt❡s ♠♦♥♦tô♥✐❝❛ ❡ ♥ã♦✲♠♦♥♦tô♥✐❝❛✳
❘❡str✐♥❣✐♠♦s ❛ ♣❛rt❡ ♠♦♥♦tô♥✐❝❛ ❛♦ ✉t✐❧✐③❛r♠♦s ❛❣♦r❛ ❛ ❉▲ ALC✱ ❛❜♦r❞❛❞❛ ♥♦ ❝❛♣ít✉❧♦ ✷✳ ALC ♣♦❞❡ s❡r ❞❡s❝r✐t❛ ❝♦♠♦ ✉♠ ❢r❛❣♠❡♥t♦ ❞❡ ❋❖▲ ❝♦♠ s♦♠❡♥t❡ r❡❧❛çõ❡s ✉♥ár✐❛s ❡ ❜✐♥ár✐❛s ❛❝r❡s❝✐❞❛ ❞❛ ♥♦çã♦ ❞❡ ❝♦♠♣❧❡♠❡♥t♦ ❞❡ ❝♦♥❝❡✐t♦s ❛r❜✐trár✐♦s✳ ❈♦♠♦
ALC ♣♦❞❡ s❡r tr❛❞✉③✐❞❛ ♣❛r❛L2✱ ♦ ❢r❛❣♠❡♥t♦ r❡❧❛❝✐♦♥❛❧ ❞❡ ❋❖▲ ❛❝r❡s❝✐❞❛ ❞❡ ❝♦♥st❛♥t❡s
✶✹
✜♥✐t♦ ❡✱ ❛ss✐♠✱ ♦ ♣r♦❜❧❡♠❛ ❞❡ s❛t✐s❢❛t✐❜✐❧✐❞❛❞❡ é ❞❡❝✐❞í✈❡❧ ❡♠N T IM E(2O(n))✱ ❝♦♠♦ ❧✐♠✐t❡ s✉♣❡r✐♦r ✭❇Ö❘●❊❘❀ ●❘➘❉❊▲❀ ●❯❘❊❱■❈❍✱ ✶✾✾✼✮✳
❯♠❛ ✈❡③ q✉❡ ❛ ♣❛rt❡ ♠♦♥♦tô♥✐❝❛ ❛❣♦r❛ é ❞❡❝✐❞í✈❡❧✱ ❞❡✈❡♠♦s ❧✐♠✐t❛r ❛ ▲ó❣✐❝❛ ❉❡❢❛✉❧t ❞❡ ❢♦r♠❛ q✉❡ ❡❧❛ ♣r❡s❡r✈❡ ❛ ❞❡❝✐❞✐❜✐❧✐❞❛❞❡ ♣❛r❛ ♦ r❛❝✐♦❝í♥✐♦ ♥ã♦✲♠♦♥♦tô♥✐❝♦✳ ■ss♦ é ❣❛r❛♥t✐❞♦ ♣❡❧❛ ✐♠♣♦s✐çã♦ ❞❡ ✉♠❛ ♦r❞❡♠ s♦❜r❡ ❛ ❛♣❧✐❝❛çã♦ ❞❛s r❡❣r❛s ❞❡❢❛✉❧t✱ ❛♣r❡s❡♥t❛❞❛s ♥♦ ❝❛♣ít✉❧♦ ✸✱ q✉❡ r❡s♣❡✐t❛♠ ♦ ♣r✐♥❝í♣✐♦ ❞❛s ✏❡①❝❡çõ❡s ♣r✐♠❡✐r♦✑ ✭P❊◗❯❊◆❖✱ ✶✾✾✹✮✱ ❧❡✈❛♥❞♦
t❛♠❜é♠ ❡♠ ❝♦♥t❛ ♦ ❝♦♥❤❡❝✐♠❡♥t♦ r❡♣r❡s❡♥t❛❞♦ ♣❡❧❛ ❧ó❣✐❝❛ALC✳ ❊ss❡ ♣r✐♥❝í♣✐♦ é ❛ ❝❤❛✈❡ ♣❛r❛ r❡s♦❧✈❡r ♦ ♣r♦❜❧❡♠❛ ❞❡ ❡①t❡♥sõ❡s ❛♥ô♠❛❧❛s ❝♦♠♦ ♦ ✐♥tr♦❞✉③✐❞♦ ♣❡❧♦ ✏❨❛❧❡ ❙❤♦♦t✐♥❣ Pr♦❜❧❡♠✑ ✭●■◆❙❇❊❘●✱ ✶✾✽✼❜✮ q✉❡ s❡rá ❛♣r❡s❡♥t❛❞♦ ♥♦ ❝❛♣ít✉❧♦ ✸✳
✶✳✸ ❖r❣❛♥✐③❛çã♦ ❞❛ ❉✐ss❡rt❛çã♦
◆♦ ❝❛♣ít✉❧♦ ✷✱ ❢❛r❡♠♦s ✉♠ ❡st✉❞♦ s♦❜r❡ ❛s ▲ó❣✐❝❛s ❞❡ ❉❡s❝r✐çã♦ ✭❉▲✮✱ ✉♠❛ ❢❛♠í❧✐❛ ❞❡ ❧ó❣✐❝❛s q✉❡ s❡r✈✐rã♦ ❞❡ ❜❛s❡ ♣❛r❛ ❛ ❝❛♠❛❞❛ ❞❡ r❡❣r❛s ♣r❡✈✐❛♠❡♥t❡ ♠❡♥❝✐♦♥❛❞❛✳ Pr✐♠❡✐r❛♠❡♥t❡✱ s❡rá ❛❜♦r❞❛❞❛ ❛ ❧ó❣✐❝❛ AL✱ ♣♦r s❡r ❛ ❉▲ ♠❛✐s s✐♠♣❧❡s✳ ❊♠ s❡❣✉✐❞❛✱ ♦ ❝❛♣ít✉❧♦ ❛❜♦r❞❛rá ♦ s✐st❡♠❛ ❞❡ r❡♣r❡s❡♥t❛çã♦ ❞❡ ❝♦♥❤❡❝✐♠❡♥t♦✱ ❛ s✐♥t❛①❡ ❡ s❡♠â♥t✐❝❛ ❞❛s ❉▲✳ P♦r ✜♠✱ s❡rá ❛♣r❡s❡♥t❛❞♦ ❞♦✐s ❛❧❣♦r✐t♠♦s ❞❡ t❛❜❧❡❛✉① q✉❡ ♥♦s ♣❡r♠✐t❡♠ r❛❝✐♦❝✐♥❛r s♦❜r❡ ❛s ✐♥❢♦r♠❛çõ❡s ❞❡s❝r✐t❛s ❡♠ ALC✱ ❛ ❉▲ ♠❛✐s s✐♠♣❧❡s ❛❝r❡s❝✐❞❛ ❞❛ ♥♦çã♦ ❞❡ ❝♦♠✲ ♣❧❡♠❡♥t♦ ❞❡ ❝♦♥❝❡✐t♦s ❛r❜✐trár✐♦s✳ ❖ ♣r✐♠❡✐r♦ ❛❧❣♦r✐t♠♦✱ ❛♣r❡s❡♥t❛❞♦ ❡♠ ✭❇❆❆❉❊❘ ❡t ❛❧✳✱ ✷✵✵✸✮✱ é ♦ ♠❛✐s s✐♠♣❧❡s ❡ s♦♠❡♥t❡ r❛❝✐♦❝✐♥❛ s♦❜r❡ ❛①✐♦♠❛s ❞❡ ✐❣✉❛❧❞❛❞❡✳ ❊❧❡ ♣♦ss✉✐
❝♦♠♣❧❡①✐❞❛❞❡ P❙P❆❈❊✲❝♦♠♣❧❡t❡✳ ❏á ♦ s❡❣✉♥❞♦✱ ❢♦✐ ❞❡s❡♥✈♦❧✈✐❞♦ ❡♠ ✭❉❖◆■◆■❀ ▼❆❙❙❆❈❈■✱
✷✵✵✵✮✳ ❊❧❡ ♣❡r♠✐t❡ ❛①✐♦♠❛s ❣❡r❛✐s ❡ ♣♦ss✉✐ ❝♦♠♣❧❡①✐❞❛❞❡ ❡①♣♦♥❡♥❝✐❛❧ s✐♠♣❧❡s✱ ♦✉ s❡❥❛✱ ❊❳P❚■▼❊✳
❖ ❝❛♣ít✉❧♦ ✸ ❛❜♦r❞❛rá ♦ ❡st✉❞♦ ❞❛ s✐♥t❛①❡ ❡ s❡♠â♥t✐❝❛ ❞❛ ▲ó❣✐❝❛ ❉❡❢❛✉❧t ❞❡ ❘❡✐t❡r✱ ❜❡♠ ❝♦♠♦ ❛ ♥♦çã♦ ❞❡ ❡①t❡♥sõ❡s ♣♦ssí✈❡✐s ♣❛r❛ ❡ss❛ ❧ó❣✐❝❛✳ ❆❧❣✉♥s ♣r♦❜❧❡♠❛s ♣♦❞❡♠ ♦❝♦rr❡r às ❡①t❡♥sõ❡s ❡①✐st❡♥t❡s ❡ ❡st❡s t❛♠❜é♠ sã♦ ❛❜♦r❞❛❞♦s✳ ❊♠ s❡❣✉✐❞❛✱ é ❛♣r❡s❡♥t❛❞♦ ♦ ❛❧❣♦r✐t♠♦ ❞❡ ❝♦♥str✉çã♦ ❞❡ ❡①t❡♥sõ❡s ♣❛r❛ ▲ó❣✐❝❛ ❉❡❢❛✉❧t ♣r♦♣♦st♦ ♣♦r ❊t❤❡r✐♥❣t♦♥ ❡ s❡✉s ♣r♦❜❧❡♠❛s ✭❊❚❍❊❘■◆●❚❖◆✱ ✶✾✽✽✮✳
❏á ♥♦ ❝❛♣ít✉❧♦ ✹✱ ❛♣r❡s❡♥t❛♠♦s ✉♠❛ ♣r♦♣♦st❛ ❞❡ ▲ó❣✐❝❛ ❞❡ ❉❡s❝r✐çã♦ ❉❡❢❛✉❧t ✭❉❉▲✮✳ ❆ ❉❉▲ é ❝♦♠♣♦st❛ ❛ ♣❛rt✐r ❞❛ ▲ó❣✐❝❛ ❞❡ ❉❡s❝r✐çã♦ ❛❝r❡s❝✐❞❛ ❞❡ r❡❣r❛s ❞❡❢❛✉❧t✳ ❆✐♥❞❛✱ ❞❡s❡♥✈♦❧✈❡r❡♠♦s ❛❧❣♦r✐t♠♦s ❥✉♥t❛♠❡♥t❡ ❝♦♠ ♦ ❝á❧❝✉❧♦ ❞❡ s✉❛s ❝♦♠♣❧❡①✐❞❛❞❡s ❝♦♠✲ ♣✉t❛❝✐♦♥❛✐s q✉❡ ♥♦s ♣❡r♠✐t✐rã♦ ❝♦♥str✉✐r ❞❡ ❢♦r♠❛ ❞❡❝✐❞í✈❡❧ ✉♠❛ ❡①t❡♥sã♦ ♣❛r❛ ❛ ❉❉▲ ❡ q✉❡ ❡✈✐t❛rá t♦❞♦s ♦s ♣r♦❜❧❡♠❛s ❡♥❝♦♥tr❛❞♦s ♥♦ ❛❧❣♦r✐t♠♦ ❞❡ ❝♦♥str✉çã♦ ❞❡ ❡①t❡♥sõ❡s ❛♣r❡s❡♥t❛❞♦ ♥♦ ❝❛♣ít✉❧♦ ✸✳
✷ ▲Ó●■❈❆❙ ❉❊ ❉❊❙❈❘■➬➹❖
◆❡st❡ ❝❛♣ít✉❧♦✱ ❛♣r❡s❡♥t❛r❡♠♦s ✉♠❛ ❢❛♠í❧✐❛ ❞❡ ❧ó❣✐❝❛s ❝♦♥❤❡❝✐❞❛ ❝♦♠♦ ▲ó❣✐❝❛ ❞❡ ❉❡s❝r✐çã♦ ✭❉▲✮✳ P❛r❛ s✐♠♣❧✐✜❝❛r✱ ✉s❛r❡♠♦s ✐♥❞✐st✐♥t❛♠❡♥t❡ ♦ t❡r♠♦ ✏▲ó❣✐❝❛ ❞❡ ❉❡s❝r✐çã♦✑ ♣❛r❛ ❞❡s✐❣♥❛r t❛♥t♦ ✉♠❛ ❢❛♠í❧✐❛ ❞❡ ▲ó❣✐❝❛s ❞❡ ❉❡s❝r✐çã♦ ❝♦♠♦ ✉♠❛ ▲ó❣✐❝❛ ❞❡ ❉❡s❝r✐çã♦ ♣❛rt✐❝✉❧❛r✳ ■♥✐❝✐❛r❡♠♦s ✐♥tr♦❞✉③✐♥❞♦ ❛ ▲ó❣✐❝❛ ❞❡ ❉❡s❝r✐çã♦ ♠❛✐s s✐♠♣❧❡s✱ ❛ ❧ó❣✐❝❛ AL✱ ❡ ❞❡♣♦✐s ❛♣r❡s❡♥t❛r❡♠♦s ❛❧❣✉♠❛s ❞❡ s✉❛s ❡①t❡♥sõ❡s✳ ❆❜♦r❞❛r❡♠♦s ❞❡t❛❧❤❡s s♦❜r❡ ♦ s✐st❡♠❛ ❞❡ r❡♣r❡s❡♥t❛çã♦ ❞❡ ❝♦♥❤❡❝✐♠❡♥t♦✱ ❛ s✐♥t❛①❡ ❡ s❡♠â♥t✐❝❛ ❞❡st❛s ❧ó❣✐❝❛s✳ ❋✐♥❛❧✐③❛r❡♠♦s ❡st❡ ❝❛♣ít✉❧♦ ❛♣r❡s❡♥t❛♥❞♦ ❞♦✐s ❛❧❣♦r✐t♠♦s ❞❡ t❛❜❧❡❛✉① q✉❡ ♥♦s ♣❡r♠✐t❡♠ r❛❝✐♦❝✐♥❛r s♦❜r❡ ❛s ✐♥❢♦r♠❛çõ❡s ❞❡s❝r✐t❛s ❡♠ ALC✱ ♦✉ s❡❥❛✱ ✉♠ ❡①❡♠♣❧♦ ❞❡ ❡①t❡♥sã♦ ❞❡ AL✳ ❖ ♣r✐♠❡✐r♦✱ ♠❛✐s s✐♠♣❧❡s✱ s♦♠❡♥t❡ ♣❡r♠✐t❡ ✉♠ t✐♣♦ r❡str✐t♦ ❞❡ ❛①✐♦♠❛s✳ ❖ s❡❣✉♥❞♦ ❥á ❛❜♦r❞❛ ♦ ❝❛s♦ ♠❛✐s ❣❡r❛❧✳
❯t✐❧✐③❛♠♦s ✭❇❆❆❉❊❘ ❡t ❛❧✳✱ ✷✵✵✸✮ ❝♦♠♦ ❢♦♥t❡ ❞❡ r❡❢❡rê♥❝✐❛ ♣r✐♥❝✐♣❛❧ ♣❛r❛ ❡st❡
❝❛♣ít✉❧♦✳ ❉❡✜♥✐çõ❡s✱ ❧❡♠❛s✱ t❡♦r❡♠❛s ❡ ♦✉tr❛s ✐♥❢♦r♠❛çõ❡s ❛q✉✐ ❛♣r❡s❡♥t❛❞❛s ❡ ♥ã♦ r❡❢❡✲ r❡♥❝✐❛❞❛s s✉♣õ❡♠✲s❡ r❡t✐r❛❞❛s ❞❡ss❛ ❢♦♥t❡✳ ❆s ✐♥❢♦r♠❛çõ❡s ♦❜t✐❞❛s ❞❡ ♦✉tr❛s ❢♦♥t❡s s❡rã♦ ❡①♣❧✐❝✐t❛♠❡♥t❡ r❡❢❡r❡♥❝✐❛❞❛s✳
❆ ❉▲ s✉r❣✐✉ ❛ ♣❛rt✐r ❞❛s ❘❡❞❡s ❙❡♠â♥t✐❝❛s ✭❙❖❲❆✱ ✶✾✾✷✮✳ ❆s ❘❡❞❡s ❙❡♠â♥t✐❝❛s
sã♦ ❡str✉t✉r❛s ❢♦r♠❛❞❛s ❛ ♣❛rt✐r ❞♦s ❡❧❡♠❡♥t♦s✿✭✶✮ ♦s ♥ós✱ q✉❡ r❡♣r❡s❡♥t❛♠ ❝♦♥❝❡✐t♦s✱ ❝♦♥❥✉♥t♦s ♦✉ ❝❧❛ss❡s ❞❡ ♦❜❥❡t♦s ✐♥❞✐✈✐❞✉❛✐s✱ ❡ ✭✷✮ ❛r❝♦s✱ q✉❡ r❡♣r❡s❡♥t❛♠✱ ♥❛ ♠❛✐♦r✐❛ ❞❛s ✈❡③❡s✱ ✉♠❛ r❡❧❛çã♦ ❡♥tr❡ ♦s ♥ós ❝✉❥♦ s❡♥t✐❞♦ é ❞❡ ✏❡stá ❝♦♥t✐❞♦✑✳
❆ ❉▲ ❢♦✐ ❞❡s❡♥✈♦❧✈✐❞❛ ♣❛r❛ s♦❧✉❝✐♦♥❛r ❛❧❣✉♠❛s ❞❡s✈❛♥t❛❣❡♥s ❞❛s ❘❡❞❡s ❙❡♠â♥✲ t✐❝❛s✱ ♣r✐♥❝✐♣❛❧♠❡♥t❡ ❛ ♣♦✉❝❛ ❢♦r♠❛❧✐③❛çã♦ ❞❡ s✉❛ ❧✐♥❣✉❛❣❡♠✳ ❊❧❛ ♣♦ss✉✐ ❝♦♠♦ ❝❛r❛❝✲ t❡ríst✐❝❛ ♣r✐♥❝✐♣❛❧ ❛ ♣r❡s❡r✈❛çã♦ ❞❛s ✈❛♥t❛❣❡♥s ❞❛s ❘❡❞❡s ❙❡♠â♥t✐❝❛s✱ t❛✐s ❝♦♠♦ s✐♠♣❧✐❝✐✲ ❞❛❞❡ ❡ ❡✜❝✐ê♥❝✐❛ ❞♦s ♠❡❝❛♥✐s♠♦s ❞❡ ✐♥❢❡rê♥❝✐❛s✱ ❢❛❝✐❧✐❞❛❞❡ ♥♦ r❛❝✐♦❝í♥✐♦ s♦❜r❡ ❤❡r❛♥ç❛ ❡ tr❛♥s♣❛rê♥❝✐❛ ❞❛s ✐♥❢♦r♠❛çõ❡s ❛♣r❡s❡♥t❛❞❛s✳ ❖✉tr❛s ❝❛r❛❝t❡ríst✐❝❛s ❞❡ ❜❛st❛♥t❡ ❞❡st❛q✉❡ sã♦ q✉❡ ❛s ▲ó❣✐❝❛s ❞❡ ❉❡s❝r✐çã♦ sã♦ ❞❡❝✐❞í✈❡✐s✳
◆❛ s❡çã♦ ❛ s❡❣✉✐r✱ ✐♥✐❝✐❛r❡♠♦s ♥♦ss♦ ❡st✉❞♦ s♦❜r❡ ❛ ❉▲✳
✷✳✶ ❚❜♦① ❡ ❆❜♦①
✶✻
❋✐❣✉r❛ ✷✿ ❙✐st❡♠❛ ❞❡ ❈♦♥❤❡❝✐♠❡♥t♦ ▲ó❣✐❝❛ ❞❡ ❉❡s❝r✐çã♦
✭❆ss❡rt✐♦♥❛❧ ❇♦①✮✳
❖ ❚❜♦① ✐♥tr♦❞✉③ ❛ t❡r♠✐♥♦❧♦❣✐❛✱ ♦✉ s❡❥❛✱ ❞❡✜♥❡ ♦s ❝♦♥❝❡✐t♦s ❡ ♣❛♣é✐s ❛ss✐♠ ❝♦♠♦ ❡st❛❜❡❧❡❝❡ r❡❧❛çõ❡s ❞❡ ✐♥❝❧✉sã♦ ❡♥tr❡ ❡❧❡s✳ ❖s ❝♦♥❝❡✐t♦s ❡ ♣❛♣é✐s✱ ♥❛ ❧✐♥❣✉❛❣❡♠ ❞❛ ▲ó❣✐❝❛ ❞❡ Pr✐♠❡✐r❛ ❖r❞❡♠ ✭❋❖▲✮✱ sã♦ ❞❡♥♦♠✐♥❛❞♦s ❞❡ r❡❧❛çõ❡s ✉♥ár✐❛s ❡ ❜✐♥ár✐❛s✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✳ ◆♦ ❝❛s♦ ❞♦ ❆❜♦①✱ ❡❧❡ ❝♦♥té♠ ❛ss❡rçõ❡s s♦❜r❡ ♦s ✐♥❞✐✈í❞✉♦s✳ ❆♣r❡s❡♥t❛r❡♠♦s ❛ s❡❣✉✐r ❛❧❣✉♥s ❡①❡♠♣❧♦s ❞❡ ❚❜♦① ❡ ❆❜♦①✿
❊①❡♠♣❧♦ ✷✳✶✳ ✭❚❜♦①✮
M ae≡P essoa⊓ ∃temF ilho.P essoa ✭✷✳✶✮ M ulher⊑P essoa ✭✷✳✷✮
❊♠ ✭✷✳✶✮✱ t❡♠♦s ✉♠ ❚❜♦① q✉❡ ❞❡s❝r❡✈❡ ❛ r❡❧❛çã♦ ❢❛♠✐❧✐❛r ▼ã❡ ❞❛ s❡❣✉✐♥t❡ ❢♦r♠❛✿ ▼ã❡ é ✉♠❛ ♣❡ss♦❛ q✉❡ t❡♠ ✜❧❤♦ ♦ q✉❛❧ t❛♠❜é♠ é ✉♠❛ ♣❡ss♦❛✳ ❯t✐❧✐③❛♠♦s ♦s ❝♦♥❝❡✐t♦s ▼ã❡ ❡ P❡ss♦❛ ❡ ♦ ♣❛♣❡❧ t❡♠❋✐❧❤♦✳
◆♦t❡ q✉❡✱ ❛tr❛✈és ❞❛ ❡s♣❡❝✐✜❝❛çã♦ ❞❡ ❝❛r❛❝t❡ríst✐❝❛s ❞❡t❡r♠✐♥❛♥t❡s ❞❡✜♥✐♠♦s ♥♦✈♦s ❝♦♥❝❡✐t♦s ❡①✐st❡♥t❡s ♥❛ ♥♦ss❛ r❡❛❧✐❞❛❞❡✳ ■♥❢❡❧✐③♠❡♥t❡✱ ♥❡♠ s❡♠♣r❡ é ♣♦ssí✈❡❧ ❞❡✜♥✐r ❝♦♥❝❡✐t♦s ❞❡ ❢♦r♠❛ ❝♦♠♣❧❡t❛ ❛tr❛✈és ❞❛ ❉▲ ✉♠❛ ✈❡③ q✉❡ ♥❡♠ s❡♠♣r❡ ❝♦♥s❡❣✉✐♠♦s ❞❡s❝r❡✲ ✈❡r t♦❞❛s ❛s ❝❛r❛❝t❡ríst✐❝❛s ❞❡ ❝❡rt♦s ❡❧❡♠❡♥t♦s ❞❛ r❡❛❧✐❞❛❞❡✳ ❆♦ ❡s❝♦❧❤❡r♠♦s ❛s ❝❛r❛❝t❡✲ ríst✐❝❛s ♣r✐♥❝✐♣❛✐s✱ ❝♦♥s❡❣✉✐♠♦s ✉♠❛ ❞❡s❝r✐çã♦ ❜❡♠ ♣ró①✐♠❛ ❞❛ r❡❛❧✐❞❛❞❡✳
❖ s❡❣✉♥❞♦ ❚❜♦① ✭✷✳✷✮ ❞❡s❝r❡✈❡ ♦ ❢❛t♦ ❞❡ s❡r ▼✉❧❤❡r ✐♠♣❧✐❝❛ s❡r ✉♠❛ P❡ss♦❛✳ ❙ã♦ ✉t✐❧✐③❛❞♦s ♦s ❝♦♥❝❡✐t♦s ▼✉❧❤❡r ❡ P❡ss♦❛✳
❊①❡♠♣❧♦ ✷✳✷✳ ✭❆❜♦①✮
✶✼
❊♠ ✭✷✳✸✮✱ t❡♠♦s ♦ ❆❜♦① q✉❡ tr❛♥s♠✐t❡ ❛ ✐♥❢♦r♠❛çã♦ q✉❡ P❊❉❘❖ é P❛✐✳ ❏á ❡♠ ✭✷✳✹✮✱ ♦ ❆❜♦① ❞❡s❝r❡✈❡ q✉❡ P❊❉❘❖ t❡♠ ✉♠ ✜❧❤♦ q✉❡ s❡ ❝❤❛♠❛ ❍❊◆❘■◗❯❊✳
P❛r❛ ❝♦♠♣❧❡t❛r ♦ s✐st❡♠❛✱ ❛ ❉▲ ♣♦ss✉✐ t❛r❡❢❛s ❞❡ r❛❝✐♦❝í♥✐♦ ♦✉ ✐♥❢❡rê♥❝✐❛s✳ ❊ss❛s t❛r❡❢❛s sã♦ ✉s❛❞❛s ♣❛r❛ ✐♥❢❡r✐r ♦ ❝♦♥❤❡❝✐♠❡♥t♦ q✉❡ s❡ ❡♥❝♦♥tr❛ ✐♠♣❧í❝✐t♦ ♥❛ ❑❇✳ ❯♠ ❡①❡♠♣❧♦ ❞❡ss❛s t❛r❡❢❛s é ❛ s✉❜s✉♥çã♦✳ ❊❧❛ ♥♦s ❧❡✈❛ ❛ ✉♠❛ ❤✐❡r❛rq✉✐③❛çã♦ ❞♦s ❝♦♥❝❡✐t♦s ✐♥tr♦❞✉③✐❞♦s ♣❡❧♦s ❚❜♦① ❡ ❆❜♦①✳
❈♦♠♦ ❡①❡♠♣❧♦✱ ❛♥❛❧✐s❡♠♦s ♦ ❚❜♦① M ulher⊑P essoa✳ ❉❡❧❡ ♣♦❞❡♠♦s ✐♥❢❡r✐r q✉❡
♦ ❝♦♥❝❡✐t♦M ulheré ♠❛✐s ❡s♣❡❝✐❛❧✐③❛❞♦ q✉❡ ♦ ❝♦♥❝❡✐t♦ P essoa✳ ❆♥❛❧♦❣❛♠❡♥t❡✱ ✐♥❢❡r✐♠♦s
q✉❡ ♦ ❝♦♥❝❡✐t♦P essoa é ♠❛✐s ❣❡♥❡r❛❧✐③❛❞♦ q✉❡ ♦ ❝♦♥❝❡✐t♦ M ulher✳
❆ ✜❣✉r❛ ✷ r❡s✉♠❡ ❛s ❡str✉t✉r❛s ❞♦ s✐st❡♠❛ ❞❡ r❡♣r❡s❡♥t❛çã♦ ❞❡ ❝♦♥❤❡❝✐♠❡♥t♦ ❞❡ ❉▲✳
◆❛ ♣ró①✐♠❛ s❡çã♦✱ ❛♣r❡s❡♥t❛r❡♠♦s ❛❧❣✉♠❛s ❞❡✜♥✐çõ❡s ✐♠♣♦rt❛♥t❡s ❞❛ ❧✐♥❣✉❛❣❡♠ ♣❛❞rã♦ ❜ás✐❝❛ ❞❛ ▲ó❣✐❝❛ ❞❡ ❉❡s❝r✐çã♦ r❡❢❡r✐❞❛ ♣❡❧❛ ❧✐t❡r❛t✉r❛ ❝♦♠♦ ❆ttr✐❜✉t✐✈❡ ▲❛♥❣✉❛❣❡ ✭AL✮ ✭❇❆❆❉❊❘ ❡t ❛❧✳✱ ✷✵✵✸✮✳
✷✳✷ ❉❡✜♥✐çã♦ ❞❛ ❙✐♥t❛①❡ ❡ ❞❛ ❙❡♠â♥t✐❝❛ ❞❡
AL
❆ ▲ó❣✐❝❛ ❞❡ ❉❡s❝r✐çã♦ é✱ ♥❛ ✈❡r❞❛❞❡✱ ✉♠❛ ❢❛♠í❧✐❛ ❞❡ ▲ó❣✐❝❛s ❞❡ ❉❡s❝r✐çã♦ ❞❡ ❝❛r❛❝t❡ríst✐❝❛s ✈❛r✐❛❞❛s✳ ■r❡♠♦s ❛❜♦r❞❛r ♥❡st❡ tr❛❜❛❧❤♦ ❛ ❧ó❣✐❝❛ q✉❡ é ❜ás✐❝❛ ♣❛r❛ t♦❞❛s ❛s ♦✉tr❛s ❞❛ ❢❛♠í❧✐❛✿ ❛ AL✳
❆♣r❡s❡♥t❛r❡♠♦s ♥❛s ♣ró①✐♠❛s s❡çõ❡s ❞❡✜♥✐çõ❡s ❛ r❡s♣❡✐t♦ ❞❡ s✉❛ s✐♥t❛①❡ ❡ s❡♠â♥✲ t✐❝❛✳
✷✳✷✳✶ ❙✐♥t❛①❡
❆ ❞❡✜♥✐çã♦ s❡❣✉✐♥t❡ ❞❡✜♥❡ ❛ ♥♦çã♦ ❞❡ ❝♦♥❝❡✐t♦s ❞❡ ♠❛♥❡✐r❛ ♣r❡❝✐s❛✿ ❉❡✜♥✐çã♦ ✷✳✸✳ ✭AL✲❝♦♥❝❡✐t♦✮
❆ ❧✐♥❣✉❛❣❡♠ ❞♦sAL✲❝♦♥❝❡✐t♦s ✭♦✉ s♦♠❡♥t❡ ❝♦♥❝❡✐t♦s✮ é ♦ ♠❡♥♦r ❝♦♥❥✉♥t♦ ❞❡✜♥✐❞♦ ✐♥❞✉t✐✈❛♠❡♥t❡ ❝♦♠♦ s❡❣✉❡✿
❼ ⊺ ✭❈♦♥❝❡✐t♦ ❯♥✐✈❡rs❛❧✮ é ✉♠ AL✲❝♦♥❝❡✐t♦❀
❼ ✭❈♦♥❝❡✐t♦ ❇♦tt♦♠✮ é ✉♠ AL✲❝♦♥❝❡✐t♦❀
❼ s❡ ❈ é ✉♠ ❝♦♥❝❡✐t♦ ❛tô♠✐❝♦ ✭♣r❡❞✐❝❛❞♦ ✉♥ár✐♦✮✱ ❈ é ✉♠ AL✲❝♦♥❝❡✐t♦❀
❼ s❡ ❈ é ✉♠ AL✲❝♦♥❝❡✐t♦ ❛tô♠✐❝♦✱ ¬C é ✉♠ AL✲❝♦♥❝❡✐t♦
✶✽
✕ C⊓D ✭■♥t❡rs❡çã♦✮
✕ ∃R.⊺ ✭◗✉❛♥t✐✜❝❛çã♦ ❊①✐st❡♥❝✐❛❧ ▲✐♠✐t❛❞❛✮
✕ ∀R.C ✭❘❡str✐çã♦ ❞❡ ❱❛❧♦r✮
❖❜s❡r✈❛çõ❡s✿
❼ ❯t✐❧✐③❛r❡♠♦s ❛s ❧❡tr❛s C, D ♣❛r❛ ♥♦s r❡❢❡r✐r ❛ ❝♦♥❝❡✐t♦s ❡ R, S ♣❛r❛ ♣❛♣❡❧❀
❼ ❖ ❝♦♥❝❡✐t♦ ✉♥✐✈❡rs❛❧ ⊺ só ♣♦❞❡ s❡r ✉s❛❞♦ ❝♦♠ ♦ q✉❛♥t✐✜❝❛❞♦r ❡①✐st❡♥❝✐❛❧ ❧✐♠✐t❛❞♦
✭∃R.⊺✮❀
❼ ❆ ♥❡❣❛çã♦ só ♣♦❞❡ s❡r ❛♣❧✐❝❛❞❛ ❛ ❝♦♥❝❡✐t♦s ❛tô♠✐❝♦s✳
❆ ❧✐♥❣✉❛❣❡♠ AL✲❝♦♥❝❡✐t♦ s❡ ♠♦str❛ ❝♦♠♦ ❜❛s❡ ♣❛r❛ ❞❡✜♥✐r♠♦s ♦s ❛①✐♦♠❛s t❡r✲ ♠✐♥♦❧ó❣✐❝♦s✳
❉❡✜♥✐çã♦ ✷✳✹✳ ✭❆①✐♦♠❛s ❚❡r♠✐♥♦❧ó❣✐❝♦s✮
❆ s❡❣✉✐r✱ ❞❡✜♥✐r❡♠♦s ♦s ❛①✐♦♠❛s t❡r♠✐♥♦❧ó❣✐❝♦s✳ ❊①✐st❡♠ ❞♦✐s t✐♣♦s✿
❼ ❆①✐♦♠❛s ❞❡ ✐♥❝❧✉sã♦✿ C⊑D✱ ❝♦♠ ❈ ❡ ❉ s❡♥❞♦ AL✲❝♦♥❝❡✐t♦s❀
❼ ❆①✐♦♠❛s ❞❡ ✐❣✉❛❧❞❛❞❡✿ C≡D✱ ❝♦♠ ❈ ❡ ❉ s❡♥❞♦ AL✲❝♦♥❝❡✐t♦s✳
❆♣ós ❡st❛s ❞❡✜♥✐çõ❡s✱ ♣♦❞❡♠♦s ✜♥❛❧♠❡♥t❡ ❞❡✜♥✐r ♦s ❚❜♦①✿
❉❡✜♥✐çã♦ ✷✳✺✳ ✭❚❜♦①✮
❯♠ ❚❜♦① é ✉♠ ❝♦♥❥✉♥t♦ ✜♥✐t♦ ❞❡ ❛①✐♦♠❛s t❡r♠✐♥♦❧ó❣✐❝♦s✳
❈♦♥t✐♥✉❛r❡♠♦s ❛s ❞❡✜♥✐çõ❡s ❛❣♦r❛ ♣❛r❛ ♦s ❆❜♦①✳ ❊st❡s ♣♦❞❡♠ s❡r ❞❡ ❞♦✐s t✐♣♦s✿
❉❡✜♥✐çã♦ ✷✳✻✳ ✭❆ss❡rçã♦ ❞❡ ❈♦♥❝❡✐t♦s✮
✏a✑ é ❝❤❛♠❛❞♦ ❞❡ ✐♥stâ♥❝✐❛ ❞❡ C✱ ♦♥❞❡ C é ✉♠ ❝♦♥❝❡✐t♦ ❡ ✏a✑ ✉♠ ✐♥❞✐✈í❞✉♦✳
❘❡♣r❡s❡♥t❛✲s❡ ❡ss❡ ❢❛t♦ ❞❛ s❡❣✉✐♥t❡ ❢♦r♠❛✿ C(a) ♦✉ a∶C✳
❉❡✜♥✐çã♦ ✷✳✼✳ ✭❆ss❡rçã♦ ❞❡ ♣❛♣é✐s✮
R(a, b) é ❝❤❛♠❛❞♦ ❞❡ ✐♥stâ♥❝✐❛ ❞❡ ❘✱ ♦♥❞❡ ❘ é ✉♠ ♣❛♣❡❧ ❡ ❛ ❡ ❜ sã♦ ✐♥❞✐✈í❞✉♦s✳
❘❡♣r❡s❡♥t❛✲s❡ ❡st❡ ❢❛t♦ ❞❛ s❡❣✉✐♥t❡ ❢♦r♠❛✿ R(a, b) ♦✉ ⟨a, b⟩∶R✳
❆♣ós ❡ss❛s ❞❡✜♥✐çõ❡s✱ ♣♦❞❡♠♦s ❞❡✜♥✐r ♦s ❆❜♦①✿
❉❡✜♥✐çã♦ ✷✳✽✳ ✭❆❜♦①✮
✶✾
❆ ❞❡✜♥✐çã♦ ❛ s❡r ❛♣r❡s❡♥t❛❞❛ ❛ s❡❣✉✐r é s♦❜r❡ ❛ ❜❛s❡ ❞❡ ❝♦♥❤❡❝✐♠❡♥t♦ ✭❑❇✮ ❞❡
AL✳ ❈♦♥❢♦r♠❡ ♠❡♥❝✐♦♥❛❞♦ ❛♥t❡r✐♦r♠❡♥t❡ ✭✈❡❥❛ ✜❣✉r❛ ✷✮✱ t❡♠♦s q✉❡ s✉❛ ❑❇ é ❢♦r♠❛❞♦ ♣❡❧♦s ❚❜♦① ❡ ❆❜♦①✳ ❆ss✐♠✱
❉❡✜♥✐çã♦ ✷✳✾✳ ✭ALKB✮
❯♠❛ ❜❛s❡ ❞❡ ❝♦♥❤❡❝✐♠❡♥t♦ ❞❡ AL ✭ALKB✮ é ❞❡✜♥✐❞❛ ❞❛ s❡❣✉✐♥t❡ ❢♦r♠❛✿
ALKB=⟨T,A⟩✱ ♦♥❞❡ T ❡ A sã♦ ♦s ❚❜♦① ❡ ❆❜♦①✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✳
✷✳✷✳✷ ❙ê♠❛♥t✐❝❛
P❛ss❛♥❞♦ ❛❣♦r❛ ♣❛r❛ ❛ ♣❛rt❡ s❡♠â♥t✐❝❛ ❞❛ ❧✐♥❣✉❛❣❡♠ AL✱ ❝♦♠❡ç❛♠♦s ❝♦♠ ❛ ❞❡✜♥✐çã♦ ❞❛ s❡♠â♥t✐❝❛ ❞❛ ❧✐♥❣✉❛❣❡♠ ❞❡AL✲❝♦♥❝❡✐t♦✿
❉❡✜♥✐çã♦ ✷✳✶✵✳ ✭❙❡♠â♥t✐❝❛ ❞❡ AL✲❝♦♥❝❡✐t♦s✮
❉❛❞❛ ✉♠❛ ✐♥t❡r♣r❡t❛çã♦ I =⟨∆I, .I⟩ ♦♥❞❡ ∆I r❡♣r❡s❡♥t❛ ♦ ❞♦♠í♥✐♦ ❞❛ ✐♥t❡r♣r❡✲ t❛çã♦ ❡.I✱ ✉♠❛ ❢✉♥çã♦ q✉❡ ♠❛♣❡✐❛ ❝❛❞❛ ❝♦♥❝❡✐t♦ ❈ ❛♦ ❝♦♥❥✉♥t♦ CI ⊆∆I ❡ ♣❛r❛ t♦❞♦ ♣❛♣❡❧
R✱ RI ⊆∆I×∆I✱ t❡♠♦s✿
⊺I = ∆I
I = ∅I
(¬C)I = ∆I∖CI
(C⊓D)I = CI∩DI
(∀R.C)I = {a∈∆I∣∀b(a, b)∈RI →b∈CI}
(∃R.⊺)I = {a∈∆I∣∃b(a, b)∈RI}
❆ ♥♦çã♦ ❞❡ s❛t✐s❢❛çã♦ ♣❛r❛ ♦s ❛①✐♦♠❛s t❡r♠✐♥♦❧ó❣✐❝♦s ❡ ♣❛r❛ ♦s ❚❜♦① s❡❣✉❡ ❛❜❛✐①♦✿
❉❡✜♥✐çã♦ ✷✳✶✶✳ ✭❙❛t✐s❢❛çã♦ ❞♦s ❛①✐♦♠❛s t❡r♠✐♥♦❧ó❣✐❝♦s✮
❖s ❛①✐♦♠❛s t❡r♠✐♥♦❧ó❣✐❝♦s sã♦ s❛t✐s❢❡✐t♦s ♣♦r ✉♠❛ ✐♥t❡r♣r❡t❛çã♦ I✱ ♦✉ s❡❥❛✱
❼ I ⊧C⊑D s❡ ❡ s♦♠❡♥t❡ s❡ CI ⊆DI❀ ❼ I ⊧C≡D s❡ ❡ s♦♠❡♥t❡ s❡ CI =DI❀ ❉❡✜♥✐çã♦ ✷✳✶✷✳ ✭❙❛t✐s❢❛çã♦ ♣❛r❛ ♦s ❚❜♦①✮
❯♠ ❚❜♦① é s❛t✐s❢❡✐t♦ ♣♦r ✉♠❛ ✐♥t❡r♣r❡t❛çã♦ I✱ ♦✉ s❡❥❛✱ I ⊧ T s❡ ❡ s♦♠❡♥t❡ s❡ ♣❛r❛ t♦❞♦C ⊑D ❡ C≡D ❡♠ T✱ I ⊧C⊑D ❡ I ⊧C≡D✳
◗✉❛♥❞♦ ✉♠❛ ✐♥t❡r♣r❡t❛çã♦ I s❛t✐s❢❛③ ✉♠ ❚❜♦① T✱ I é ❝❤❛♠❛❞❛ ❞❡ ♠♦❞❡❧♦ ❞❡ T✳
✷✵
❆ss✐♠✱ ✜♥❛❧✐③❛♠♦s ❛s ❞❡✜♥✐çõ❡s ♣❛r❛ ♦s ❚❜♦①✳ ❆❣♦r❛✱ ❛❜♦r❞❛r❡♠♦s ❛s ❞❡✜♥✐çõ❡s s❡♠â♥t✐❝❛s ♣❛r❛ ♦s ❆❜♦①✿
❆s ❞❡✜♥✐çõ❡s s❡❣✉✐♥t❡s sã♦ r❡❢❡r❡♥t❡s à ♥♦çã♦ ❞❡ s❛t✐s❢❛çã♦ ❞♦s ❆❜♦①✿
❉❡✜♥✐çã♦ ✷✳✶✸✳ ✭❙❛t✐s❢❛çã♦ ❞❡ ✉♠❛ ❛ss❡rçã♦ ❞❡ ❝♦♥❝❡✐t♦✮
❯♠❛ ❛ss❡rçã♦ ❞❡ ❝♦♥❝❡✐t♦ C(a) é s❛t✐s❢❡✐t❛ ♣♦r ✉♠❛ ✐♥t❡r♣r❡t❛çã♦ I✱ ♦✉ s❡❥❛✱
I ⊧C(a) s❡ ❡ s♦♠❡♥t❡ s❡ aI ∈CI✳
❉❡✜♥✐çã♦ ✷✳✶✹✳ ✭❙❛t✐s❢❛çã♦ ❞❡ ✉♠❛ ❛ss❡rçã♦ ❞❡ ♣❛♣❡❧✮
❯♠❛ ❛ss❡rçã♦ ❞❡ ♣❛♣❡❧ R(a, b) é s❛t✐s❢❡✐t❛ ♣♦r ✉♠❛ ✐♥t❡r♣r❡t❛çã♦ I✱ ♦✉ s❡❥❛✱
I ⊧R(a, b) s❡ ❡ s♦♠❡♥t❡ s❡ ⟨aI, bI⟩ ∈RI✳ ❉❡✜♥✐çã♦ ✷✳✶✺✳ ✭❙❛t✐s❢❛çã♦ ❞❡ ✉♠ ❆❜♦①✮
❯♠ ❆❜♦① é s❛t✐s❢❡✐t♦ ♣♦r ✉♠❛ ✐♥t❡r♣r❡t❛çã♦ I✱ ♦✉ s❡❥❛✱ I ⊧ A s❡ ❡ s♦♠❡♥t❡ s❡ ♣❛r❛ t♦❞❛ ❛ss❡rçã♦ ❞❛ ❢♦r♠❛ α=C(a) ♦✉ α=R(a, b) ❡♠ A✱ I ⊧α✳
❆ ❞❡✜♥✐çã♦ ❛ s❡❣✉✐r r❡❢❡r❡✲s❡ à ♥♦çã♦ ❞❡ s❛t✐s❢❛çã♦ ♣❛r❛ ❛ ❜❛s❡ ❞❡ ❝♦♥❤❡❝✐♠❡♥t♦
ALKB = ⟨T,A⟩ ❛ q✉❛❧ só ♦❝♦rr❡ q✉❛♥❞♦ ALKB s❛t✐s❢❛③ t❛♥t♦ ♦ ❚❜♦① ❝♦♠♦ ♦ ❆❜♦①✳
❆ss✐♠✱
❉❡✜♥✐çã♦ ✷✳✶✻✳ ✭❙❛t✐s❢❛çã♦ ❞❡ ✉♠ ALKB✮
❯♠❛ ❜❛s❡ ❞❡ ❝♦♥❤❡❝✐♠❡♥t♦ ALKB=⟨T,A⟩ é s❛t✐s❢❡✐t❛ ♣♦r ✉♠❛ ✐♥t❡r♣r❡t❛çã♦I✱
♦✉ s❡❥❛✱I ⊧ ALKB s❡ ❡ s♦♠❡♥t❡ s❡ I ⊧ T ❡ I ⊧ A
✷✳✸ ❊①t❡♥sõ❡s ❞❛ ▲✐♥❣✉❛❣❡♠
AL
❆ ❧✐♥❣✉❛❣❡♠ AL é ✉♠❛ ❧✐♥❣✉❛❣❡♠ ✉t✐❧✐③❛❞❛ ♣♦r ♦✉tr❛s ▲ó❣✐❝❛s ❞❡ ❉❡s❝r✐çã♦ ❝♦♠♦ ❧✐♥❣✉❛❣❡♠ ❜❛s❡ ♥❛ q✉❛❧ sã♦ ❛❝r❡s❝❡♥t❛❞❛s ♥♦✈❛s ❢✉♥❝✐♦♥❛❧✐❞❛❞❡s✳ ◆❛ t❛❜❡❧❛ ✶✱ t❡♠♦s ❛❧❣✉♥s ❡①❡♠♣❧♦s ❞❡ss❛s ❧✐♥❣✉❛❣❡♥s✳
P❡❧❛ t❛❜❡❧❛✱ ♣♦❞❡♠♦s ❢♦r♠❛r ❞✐✈❡rs❛s ❧✐♥❣✉❛❣❡♥s ❞❡ ❛❝♦r❞♦ ❝♦♠ ❛ ❢✉♥❝✐♦♥❛❧✐❞❛❞❡ q✉❡ ❞❡s❡❥❛♠♦s ❛❞✐❝✐♦♥❛r✳
❉❡♥♦♠✐♥❛♠♦s ❡ss❛ ♥♦✈❛ ❧✐♥❣✉❛❣❡♠ ❞❡ ALx1x2. . . xn(y1, . . . , ym)✱ ♦♥❞❡ x1, . . . , xn
sã♦ ♦s sí♠❜♦❧♦s ❞❛ t❛❜❡❧❛ ❛❝✐♠❛ q✉❡ r❡♣r❡s❡♥t❛♠ ❛s ♥♦✈❛s ❢✉♥❝✐♦♥❛❧✐❞❛❞❡s ❛♣❧✐❝❛❞❛s ❛♦s ❝♦♥❝❡✐t♦s ❛❝r❡s❝✐❞❛s ❡ y1, . . . , ym ♦s sí♠❜♦❧♦s q✉❡ r❡♣r❡s❡♥t❛♠ ❛s ♥♦✈❛s ❢✉♥❝✐♦♥❛❧✐❞❛❞❡s
❛♣❧✐❝❛❞❛s ❛♦s ♣❛♣é✐s✳
❆❧❣✉♥s ❡①❡♠♣❧♦s ❞❡ ❧✐♥❣✉❛❣❡♥s ❉▲ ❡st❡♥❞✐❞❛s ♠❛✐s ❝♦♥❤❡❝✐❞❛s sã♦✿ ❛ALC✱ALC(∪)✱
ALCN ❡ALCQIO ♦✉SHOIQ✱ ❝♦♠♦ é ♠❛✐s ❝♦♥❤❡❝✐❞❛✳ ❖✉tr❛ ❉▲ ❞❡ ❜❛st❛♥t❡ ❞❡st❛q✉❡
q✉❡ ♥ã♦ s❡❣✉❡ ❛ r❡❣r❛ ❞❡ ❡s❝r✐t❛ ❝✐t❛❞❛ ❛❝✐♠❛ é ❛ SHOIN✳ ❊st❛ ❉▲ é s✉♣♦rt❛❞❛ ♣❡❧♦
❡❞✐t♦r ❞❡ ♦♥t♦❧♦❣✐❛s ❡ r❛❝✐♦❝✐♥❛❞♦r Pr♦t❡❣é✭P❘❖❚é●é✱ ✮ ❛t✉❛❧♠❡♥t❡ ❜❛st❛♥t❡ ✉t✐❧✐③❛❞♦ ♣❡❧❛
✷✶
❆❞✐❝✐♦♥❛♥❞♦ ❛ ❉▲ ❙í♠❜♦❧♦ ❙✐♥t❛①❡ ❙❡♠â♥t✐❝❛
◆❡❣❛çã♦ ❞❡ ❝♦♥❝❡✐t♦s C ¬C ∆I∖CI
❯♥✐ã♦ ❞❡ ❈♦♥❝❡✐t♦s U C⊔D CI∪DI
◗✉❛♥t✐✜❝❛çã♦ ❊①✐st❡♥❝✐❛❧ ●❡r❛❧ E ∃R.C {a∈∆I∣∃b.(a, b) ∈RI∧b∈CI}
❘❡str✐çã♦ ◆✉♠ér✐❝❛ ❙✉♣❡r✐♦r N ≥n.R {a∈∆I∣∣{
b∣(a, b) ∈RI}∣ ≥n}
❘❡str✐çã♦ ◆✉♠ér✐❝❛ ■♥❢❡r✐♦r N ≤n.R {a∈∆I∣ ∣{b∣(a, b) ∈RI}∣ ≤n}
❘❡str✐çã♦ ◆✉♠ér✐❝❛ ◗✉❛❧✐✜❝❛❞❛ ❙✉♣❡r✐♦r Q ≥nR.C {a∈∆I∣ ∣{b∣(a, b) ∈RI∧b∈CI}∣ ≥n}
❘❡str✐çã♦ ◆✉♠ér✐❝❛ ◗✉❛❧✐✜❝❛❞❛ ■♥❢❡r✐♦r Q ≤nR.C {a∈∆I∣ ∣{b∣(a, b) ∈RI∧b∈CI}∣ ≤n}
❋✉♥çõ❡s F ≤1.R {a∈∆I∣∀b, c(a, b) ∈RI∧(a, c) ∈RI→b=c}
◆♦♠✐♥❛✐s O {a1, . . . , an} {a1, . . . , an}I={aI1, . . . , aIn}
■♥t❡rs❡çã♦ ❞❡ P❛♣é✐s (∩) R∩S RI∩SI
❯♥✐ã♦ ❞❡ P❛♣é✐s ✭∪✮ R∪S RI∪SI
❈♦♠♣❧❡♠❡♥t♦ ❞❡ P❛♣é✐s (¬) ¬R ∆I×∆I/RI
■♥✈❡rs♦ ❞❡ P❛♣é✐s I R− {(b, a)∈∆I×∆I∣(a, b)∈RI}
❈♦♠♣♦s✐çã♦ ❞❡ P❛♣é✐s (○) R○S {(a, c)∈∆I×∆I∣∃b.(a, b)∈RI∧(b, c)∈SI}
❚r❛♥s✐t✐✈✐❞❛❞❡ ❞❡ P❛♣é✐s S R+ ⋃i≥1(RI)
i
❍✐❡r❛rq✉✐❛ ❞❡ P❛♣é✐s H R⊆S {a∈∆I∣∀b(a, b)∈RI→ (a, b)∈SI}
❚❛❜❡❧❛ ✶✿ ❊①❡♠♣❧♦s ❞❡ ▲ó❣✐❝❛s ❞❡ ❉❡s❝r✐çã♦ ❡ s✉❛s ♥♦✈❛s ❢✉♥❝✐♦♥❛❧✐❞❛❞❡s
✷✳✹
AL
❝♦♠♦ ✉♠ ❢r❛❣♠❡♥t♦ ❞❡ ❋❖▲
P❛r❛ ✜♥s ❝♦♠♣❛r❛t✐✈♦s✱ ❛♣r❡s❡♥t❛r❡♠♦s ❛ t❛❜❡❧❛ ✷ ❞❡ ❝♦rr❡s♣♦♥❞ê♥❝✐❛ ❡♥tr❡ ❛s ❢ór♠✉❧❛s ❡s❝r✐t❛s ❡♠ ❉▲ ✭❡ ❛❧❣✉♠❛s ❞❡ s✉❛s ❡①t❡♥sõ❡s✮ ❡ ❛s ❡s❝r✐t❛s ❡♠ ❋❖▲✳
❖ ❢♦❝♦ ♣r✐♥❝✐♣❛❧ ❞❛ t❛❜❡❧❛ ✷ é ♥♦s ♠♦str❛r q✉❡ t✉❞♦ ❡①♣r❡ss♦ ❡♠ ❉▲ ♣♦❞❡ s❡r ❡①♣r❡ss♦ ❡♠ ❋❖▲✳
❆ ❉▲ ✈❡♠ s❡♥❞♦ ❛♠♣❧❛♠❡♥t❡ ✉t✐❧✐③❛❞❛ ♣❡❧♦s ♣r♦✜ss✐♦♥❛✐s ❞❛s ár❡❛s ❞❡ ❜❛♥❝♦ ❞❡ ❞❛❞♦s✱ ♠♦❞❡❧❛❣❡♠ ❡ ❡♥❣❡♥❤❛r✐❛ ❞❡ s♦❢t✇❛r❡ ♣❛r❛ ❞❡s❝r✐çã♦ ❞❡ ♦♥t♦❧♦❣✐❛s ❞❛ ✇❡❜✳ ❉✐❛♥t❡ ❞❡st❡ ❣r❛♥❞❡ ✉s♦✱ ❤á ✉♠❛ ❣r❛♥❞❡ ♥❡❝❡ss✐❞❛❞❡ ❞❡ ✐♥✈❡st✐❣❛çã♦ s♦❜r❡ ❛s ♣r♦♣r✐❡❞❛❞❡s ❞❡st❡ ❢r❛❣♠❡♥t♦ ♣❛rt✐❝✉❧❛r ❞❛ ❋❖▲✳ P♦r ❡①❡♠♣❧♦✱ ♦ ♣r♦❜❧❡♠❛ ❞❡ s❛❜❡r s❡ ✉♠❛ ❢ór♠✉❧❛α é ✉♠
t❡♦r❡♠❛ ❡♠ ❋❖▲ é s❡♠✐✲❞❡❝✐❞í✈❡❧ ❡♥q✉❛♥t♦ q✉❡ ♦ ♠❡s♠♦ ♣r♦❜❧❡♠❛ ❡♠ ❉▲ é ❞❡❝✐❞✐✈❡❧✳
✷✳✺ ❚❛r❡❢❛s ❞❡ ❘❛❝✐♦❝í♥✐♦ ♦✉ ■♥❢❡rê♥❝✐❛s
✷✷
❉▲ ❋❖▲
C C(x) R R(x, y) a∶C C(a)
⟨a, b⟩ ∶R R(a, b)
¬C ¬C(x)
C1⊓C2 C1(x)∧C2(x)
∃R.C ∃y(R(x, y)∧C(y))
∀R.C ∀y(R(x, y) →C(y)) C1⊔C2 C1(x)∨C2(x)
≥nR ∃y1, . . . , yn⋀1≤i≤n(R(x, yi))∧⋀1≤i<n,i<j≤nyi≠yj
≤nR ∀y1, . . . , yn+1⋀1≤i≤n+1(R(x, yi)) → (⋁1≤i<n+1,i<j≤n+1yi=yj) ≥nR.C ∃y1, . . . , yn⋀1≤i≤n(R(x, yi)∧C(yi))∧⋀1≤i<n,i<j≤nyi≠yj
≤nR.C ∀y1, . . . , yn+1⋀1≤i≤n+1(R(x, yi)∧C(yi)) → (⋁1≤i<n+1,i<j≤n+1yi =yj) ≤1R ∀x, y(R(x, y)∧R(x, z)) →y=z
{a1,⋯, an} x=a1∨ ⋯ ∨x=an
R1∩R2 R1(x)∧R2(x)
R1∪R2 R1(x)∨R2(x)
¬R ¬R(x, y) R− ∀x, yR(y, x)
R○S ∃y(R(x, y)∧S(y, z) →T(x, z)) R+ ∀x, y, z(R(x, y)∧R(y, z)) →R(x, z)
R⊆S ∀x.R(x) →S(x) C⊑D ∀x.C(x) →D(x)
C≡D ∀x.((C(x) →D(x))∧(D(x) →C(x)))
❚❛❜❡❧❛ ✷✿ ❈♦rr❡s♣♦♥❞ê♥❝✐❛ ❡♥tr❡ ❛❧❣✉♠❛s ❢ór♠✉❧❛s ❞❡ ❉▲ ❡ ❋❖▲
❆♥t❡s ❞❡ ❞❡✜♥✐r♠♦s ❢♦r♠❛❧♠❡♥t❡ t❛✐s t❛r❡❢❛s✱ ✈❡❥❛♠♦s ✉♠ ❡①❡♠♣❧♦ q✉❡ ♥♦s ♠♦str❛rá ❛ ♦❜t❡♥çã♦ ❞❡ ❝♦♥❤❡❝✐♠❡♥t♦ ❛✐♥❞❛ ✐♠♣❧✐❝✐t♦ ♥❛ ❜❛s❡ ❞❡ ❝♦♥❤❡❝✐♠❡♥t♦ ❡♠ q✉❡stã♦✿
❊①❡♠♣❧♦ ✷✳✶✼✳ ✭❚❜♦① ❡ ❆❜♦① ❞❡ ❘❡❧❛çõ❡s ❋❛♠✐❧✐❛r❡s✮
✷✸
✭✷✳✷✵✮✳
M ulher ≡ P essoa⊓SexoF eminino ✭✷✳✺✮ Homem ≡ P essoa⊓SexoM asculino ✭✷✳✻✮ M ae ≡ M ulher⊓ ∃temF ilho.P essoa ✭✷✳✼✮
M amae ≡ M ae ✭✷✳✽✮
P ai ≡ Homem⊓ ∃temF ilho.P essoa ✭✷✳✾✮ P apai ≡ P ai ✭✷✳✶✵✮ P ais ≡ P ai⊔M ae ✭✷✳✶✶✮ Avo ≡ M ae⊓ ∃temF ilho.P ais ✭✷✳✶✷✮ M aeComM uitosF ilhos ≡ M ae⊓ ≥3temF ilho ✭✷✳✶✸✮ M aeSemF ilhas ≡ M ae⊓ ∀temF ilho.¬M ulher ✭✷✳✶✹✮ Esposa ≡ M ulher⊓ ∃temM arido.Homem ✭✷✳✶✺✮
M aeSemF ilhas(M ARIA) ✭✷✳✶✻✮ P ai(P EDRO) ✭✷✳✶✼✮ temF ilho(M ARIA, P EDRO) ✭✷✳✶✽✮ temF ilho(M ARIA, P AU LO) ✭✷✳✶✾✮ temF ilho(P EDRO, HEN RIQU E) ✭✷✳✷✵✮
❆ ♣❛rt✐r ❞❡ss❡ ❚❜♦① ✭✷✳✺✮✲✭✷✳✶✺✮ ❡ ❆❜♦① ✭✷✳✶✻✮ ✲ ✭✷✳✷✵✮✱ ❝♦♥s❡❣✉✐♠♦s ✐♥❢❡r✐r q✉❡ ▼❆❘■❆ é ✉♠❛ ❛✈ó✿ ❆♥❛❧✐s❛♥❞♦ ✭✷✳✶✻✮ ❡ ✭✷✳✶✹✮ ❞❡❞✉③✐♠♦s q✉❡ ▼❆❘■❆ é ♠ã❡✳ ❆♣❧✐❝❛♥❞♦ ✭✷✳✶✼✮ ❡ ✭✷✳✶✶✮ t❡♠♦s q✉❡ P❊❉❘❖ ♣❡rt❡♥❝❡ ❛ ❝❧❛ss❡ ❞♦s ♣❛✐s✳ ❈♦♠♦ ▼❆❘■❆ t❡♠ ✜❧❤♦ P❊❉❘❖ ✭✷✳✶✽✮ ❡ P❊❉❘❖ t❡♠ ✜❧❤♦ ❍❊◆❘■◗❯❊ ✭✷✳✷✵✮✱ ❞❡❞✉③✐♠♦s ✜♥❛❧♠❡♥t❡ q✉❡ ▼❆❘■❆ é ❛✈ó ✭✷✳✶✷✮✳
◆❛s s❡çõ❡s s❡❣✉✐♥t❡s✱ ❛♣r❡s❡♥t❛r❡♠♦s ❛s ♣r✐♥❝✐♣❛✐s t❛r❡❢❛s ❞❡ r❛❝✐♦❝í♥✐♦✳ ❉✐✈✐❞✐r❡✲ ♠♦s ❛ ❛♣r❡s❡♥t❛çã♦ ❡♠ ❞✉❛s ♣❛rt❡s✳ Pr✐♠❡✐r❛♠❡♥t❡✱ ❛♣r❡s❡♥t❛r❡♠♦s ❛s ♣r✐♥❝✐♣❛✐s t❛r❡❢❛s ❞❡ r❛❝✐♦❝í♥✐♦ ♣❛r❛ ❝♦♥❝❡✐t♦s ❡ ❚❜♦①✳ ▲♦❣♦ ❛♣ós✱ ♠♦str❛r❡♠♦s ❛s ♣r✐♥❝✐♣❛✐s t❛r❡❢❛s ❞❡ r❛❝✐♦❝í♥✐♦ ♣❛r❛ ❆❜♦①✳
✷✳✺✳✶ ❚❛r❡❢❛s ❞❡ ❘❛❝✐♦❝í♥✐♦ ♣❛r❛ ❚❜♦①
❊①✐st❡♠ ❞✐✈❡rs♦s t✐♣♦s ❞❡ r❛❝✐♦❝í♥✐♦s ♦✉ ✐♥❢❡rê♥❝✐❛s r❡❢❡r❡♥t❡s ❛♦s ❝♦♥❝❡✐t♦s ❡ ❚❜♦①✳ ❋♦❝❛r❡♠♦s ♥♦ss❛ ❛t❡♥çã♦ ♥❛s q✉❛tr♦ ♣r✐♥❝✐♣❛✐s✳
❉❡✜♥✐çã♦ ✷✳✶✽✳ ✭❙❛t✐s❢❛çã♦ ❞❡ ✉♠ ❝♦♥❝❡✐t♦ ❝♦♠ r❡s♣❡✐t♦ ❛ ✉♠ ❚❜♦①✮
❯♠ ❝♦♥❝❡✐t♦ ❈ é s❛t✐s❢❛tí✈❡❧ ❝♦♠ r❡s♣❡✐t♦ ❛♦ ❚❜♦① T s❡ ❡①✐st❡ ✉♠ ♠♦❞❡❧♦ I ❞❡ T
t❛❧ q✉❡ CI ≠ ∅✳
