i have a question about most general unifier in logic. i'll begin by saying that in the class we were only given a summary in a few words, without any example, and they just moved on to the next topic and left us wondering on how to solve it, so i am trying based on what i've learnt from reading here:

i need to find the MGU, if it exists, for every pair of atomic propositions.

1)$Q(one, two, two)$ , $Q(x,y,z)$

2)$R(x,F(A,B)$ , $R(F(y,y),x)$

my attempt:

1)not exist because Two is written twice and we can't use substitution so that it will have two different meanings.

2)$R(F(x,B), F(A,B)), R(F(y,y),F(x,B))$

is it correct? would really appreciate your assistance and correction with this. thank you very much

  • $\begingroup$ See this post for the def of unifier. $\endgroup$ – Mauro ALLEGRANZA Apr 18 at 7:36
  • $\begingroup$ The subst : $x \leftarrow \text {one}, y \leftarrow \text {two}, z \leftarrow \text {two}$ will work. $\endgroup$ – Mauro ALLEGRANZA Apr 18 at 7:37
  • $\begingroup$ and for the second? meanwhile i am trying to find also explanations on youtube and worked examples to learn how to apply the theory correctly $\endgroup$ – hps13 Apr 18 at 7:58
  • $\begingroup$ Similar; see the def in the linked post. A subst is an operation of replacing terms in place of variables. Thus, start with $A$ and $B$ in place of $y$. $\endgroup$ – Mauro ALLEGRANZA Apr 18 at 8:13
  • $\begingroup$ @MauroALLEGRANZA the second should be $/theta = [F(y,y)/x, a/x,b/x]$ ? $\endgroup$ – hps13 Apr 22 at 11:55

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