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# Lect7 - Unifier A unifier(also substitution binding list is...

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A unifier (also substitution , binding list* ) is a set of pairings of variables with terms: {v 1 = e 1 , v 2 = e 2 , v 3 = e 3 , … v n = e n } such that each variable is paired at most once • a variable’s pairing term may not contain the variable directly or indirectly Unifier {x = Socrates} * Do not confuse with bound / free variables!!! 1

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Most General Unifier MGU The MGU imposes the fewest constraints, specifying the weakest conditions for matching MGU is unique order is not important variable names are not important (alphabetic variants) Applying the MGU to an expression yields a most general unification instance . Variable substitutions are always interpreted with the unifier applied 2
What is the MGU? M(Ann,x,Bob) M(Ann,x,Bob) M(Ann,x,Bob) M(y,x,Chuck) M(Ann,x,Bob) M(y,x,Father-of(Chuck)) P(w,w,Fred) P(x,y,y) Q(r,r) Q(x,F(x)) Q(r,r) Q(x,F(y)) R(G(x,Bob),y,y) R(z,G(Fred,w),z) 3

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Negation and Quantifiers   x P(x)   x P(x)   x P(x)   x P(x) x P(x)   y Q(y)   x y [P(x) Q(y)] x y [P(x) Q(y)]   y x [P(x) Q(y)] (also , also all ’s) BUT x y P(x,y) is NOT the same as y x P(x,y) 4
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Lect7 - Unifier A unifier(also substitution binding list is...

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