Common Instance

Definition

A common instance of Term $A,B$ if there exists Substitutions $S_1,S_2$ s.t $C=S_1(A)=S_2(B)$

Example

• $A=\text{parent}(bob,X)$
• $B=\text{parent}(Y,sue)$
• $S_1=\{X/sue\}$
• $S_2=\{Y/bob\}$
• $S_1(A)=S_2(B)=\text{parent}(bob,sue)=C$