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School of Industrial and Information Engineering Knowledge Engineering 2014–15 Test 5 – 1st February 2016 Part I 1 5 pt. Let: K be a SROIQ knowledge base; C be a class and a be an individual of K; and R be a reasoning procedure that is sound and complete for SROIQ. 1. Is it possible that in the attempt to prove K ⊢R C(a) the reasoning process does not terminate? 2. Is it possible that both K ⊢R C(a) and K ⊢R ¬C(a) terminate with a positive answer? 3. Is it possible that both K ⊢R C(a) and K ⊢R ¬C(a) terminate with a negative answer? Justify your answers. 1. No, because provability is decidable in SROIQ. 2. No, assuming that K is a consistent knowledge bases. Under such assumption it cannot be the case that both C(a) and ¬C(a) are provable from K. 3. Yes, because the axioms of K may be insufficient to establish either C(a) or ¬C(a). 2 15 pt. Requirements: 1. (Only) a town may have a local airport. Every flight has exactly one departure and exactly one arrival airport. 2. Airport x is directly linked to airport y if there is a flight that departs from x and arrives at y. 3. If airport x is directly linked to airport y, then y is directly linked to x. 4. Town u is connected to town v if there is a finite sequence of direct links, starting from a local airport of v and arriving at a local airport of u. (Warning: do not confuse direct links between airports with connections between towns!) 5. Town t001 has airport a001 as its only local airport. Town t002 has airport a002 as one of its local airports (it may have more). There is at least one flight departing from a001 and arriving at a002. DL queries: 6. To which towns is town t001 connected? 7. May a town that has no local airport be connected to some town? Scoring: 3 points for item 4; 2 points each for all other items.…