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unification-alg

# unification-alg - CISC 404/604 Unication and Resolution Let...

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CISC 404/604 Unification and Resolution Let L be a set of literals that we wish to unify. Let sub [ ]. While | L sub | 6 = 1 Scan left to right till a disagreement is found If neither term (at place of disagreement) is a variable then return(”not unifiable”) else Let x be the ”variable” term and let the other term be t If x occurs in t then return(”not unifiable”) else sub sub · [ x | t ] return sub We will now apply this algorithm from the example from Uwe Schoening’s book that was discussed in class. L = { P ( f ( z, g ( a, y )) , h ( z )) , P ( f ( f ( u, v ) , w ) , h ( f ( a, b ))) } sub [ z | f ( u, v )] L sub = { P ( f ( f ( u, v ) , g ( a, y )) , h ( f ( u, v ))) , P ( f ( f ( u, v ) , w ) , h ( f ( a, b ))) } sub [ z | f ( u, v )] · [ w | g ( a, y )] L sub = { P ( f ( f ( u, v ) , g ( a, y )) , h ( f ( u, v ))) , P ( f ( f ( u, v ) , g ( a, y )) , h ( f ( a, b ))) } sub [ z | f ( u, v )] · [ w | g ( a, y )] · [ u | a ] L sub = { P ( f ( f ( a, v ) , g ( a, y )) , h ( f ( a, v ))) , P ( f ( f ( a, v ) , g ( a, y )) , h ( f ( a, b ))) } sub [ z | f ( u, v )] · [ w | g ( a, y )] · [ u | a ] · [ v | b ] L sub = { P ( f ( f ( a, b ) , g ( a, y )) , h ( f ( a, b ))) } The unifying substitution can also be rewritten as [ z | f ( a, b ) , w | g ( a, y ) , u | a, v | b ]

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A clause R is obtained by resolving clauses C 1 and C 2 if 1. Let σ 1 and σ 2 be substitutions such that the clauses C 1 σ 1 and C 2 σ 2 have no variables in common, 2. Let L 1 , . . . , L n ∈ C 1 σ 1 ( n 1) and L 0 1 , . . . , L
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unification-alg - CISC 404/604 Unication and Resolution Let...

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