# Artificial Intelligence1.docx - Part 1 a Find all answer...

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Part 1 a. Find all answer sets of the following program: ? ? ? , ? ?
b. Find all answer sets of the following program: ? not ? not ? not ? ? not ? ? ? ? r
It is evident that the set S has the sets {p, q} Exercise 2 : Description Logic Representation a. ∃? . ? ∃? . B Examples This is Sub summed by r. (A u B) Hence we have A= ( r.A) u ( r.B) u ¬( r.(A u B)) A r.A r.B is subsumed by A r.B A ¬A is by B b. ∃? . ( ? ? ) ∆ = {b, c, d}; r = {(b, c); (b, d)}; A = {c}; and B = {d}. c. ∃? . ? ∃? . ? ∃? . ( ? ? ) Examples we have ( r.A) I = {2, 4} and so (B u r.A) I = {4}. Thus (B u r.A) I = {4} {3, 4} = ( r.A) I A r.(B u C) is subsumed by A r.B A r.B is subsumed by A r.B Exercise 3: Tableau Reasoning
a. ∃? . ? ∃? . B The Negataion form form for l form ∃? . ? ∃? . B is C 0 = ( r.A) u ( r.B) b. ∃? . ( ? ? ) The Negation form is ¬ r.(¬A t ¬B) c. ∃? . ? ∃? . ? ∃? . ( ? ? ) Negation form is r.AUB r. ¬B= ∃?.(AUB) Use the tableau algorithm to decide whether the formula you created in (a) is satisfiable