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Conversion to CNF

Conversion to CNF. Everyone who loves all animals is loved by someone x [y Animal(y)  Love(x,y)]  y Love(y,x) x ¬[ y Animal(y)  Love(x,y)]  y Love(y,x) x y ¬[ Animal(y)  Love(x,y)]  y Love(y,x) x y[ ¬ Animal(y)  ¬ Love(x,y)]  y Love(y,x)

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Conversion to CNF

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  1. Conversion to CNF • Everyone who loves all animals is loved by someone • x [y Animal(y)  Love(x,y)]  y Love(y,x) • x ¬[y Animal(y)  Love(x,y)]  y Love(y,x) • x y ¬[Animal(y)  Love(x,y)]  y Love(y,x)x y[¬Animal(y) ¬Love(x,y)] y Love(y,x) • x y ¬Animal(y) ¬Love(x,y)  z Love(z,x) • x ¬Animal(C1) ¬Love(x,C1)  Love(C2,x) • ¬Animal(C1) ¬Love(x,C1)  Love(C2,x) ECE457 Applied Artificial Intelligence R. Khoury (2007) Page 1

  2. Conversion to CNF • There is a book which everyone buys only if there is a class that requires it • x Book(x)  {[y Buy(y,x)]  [y Class(y)  Requires(y,x)]} • x Book(x)  {[y Buy(y,x)]  [y Class(y)  Requires(y,x)]}  {[y Class(y)  Requires(y,x)] [y Buy(y,x)]} • x Book(x)  {¬[y Buy(y,x)]  [y Class(y)  Requires(y,x)]}  {¬[y Class(y)  Requires(y,x)]  [y Buy(y,x)]} • x Book(x)  {[y ¬Buy(y,x)]  [y Class(y)  Requires(y,x)]}  {[y ¬Class(y) ¬Requires(y,x)]  [y Buy(y,x)]} • x Book(x)  {y ¬Buy(y,x)  [z Class(z)  Requires(z,x)]}  {[z ¬Class(z) ¬Requires(z,x)]  y Buy(y,x)} • Book(C1)  {¬Buy(C2,C1)  [Class(C3)  Requires(C3,C1)]}  {[z ¬Class(z) ¬Requires(z,C1)]  y Buy(y,C1)} • Book(C1)  {¬Buy(C2,C1)  [Class(C3)  Requires(C3,C1)]}  {¬Class(z) ¬Requires(z,C1)  Buy(y,C1)} • Book(C1)  [¬Buy(C2,C1)  Class(C3)]  [¬Buy(C2,C1)  Requires(C3,C1)]  [¬Class(z) ¬Requires(z,C1)  Buy(y,C1)] ECE457 Applied Artificial Intelligence R. Khoury (2007) Page 2

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