# Is there a name for the arguments of the substitution operation?

In logic, there is the substitution operation which takes two logical formulae and substitutes one into the other. For example, substituting R→S and T→S for P and Q in the expression P&Q, we obtain:

(R → S) & (T → S).

The substitution of t for x in the formula F is written [t/x]F. Taking another example, let t be 1, x be x, and F be ∃x.s(x)=0, then [t/x]F yields the formula s(1)=0.

The arguments to the addition operation are called addends or summands. What do we call the arguments to the substitution operation? What do we call t, x, and F above?

• Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking.
– Community Bot
Aug 28, 2021 at 17:42
• I added a sentence. Did that help? Addend is to addition as what is to substitution? Aug 28, 2021 at 18:24

In your example, $$R-S$$ is a substituend and $$T-S$$ is a substituend. They are substituends. (You can find this definition in most English language dictionaries.) There does not appear to be a term for the thing that is to be replaced. Most constructions I find either explicitly use the replaced symbol or its symbol class to refer to it. For instance, "... being a substituend of free first-order variables ..." (from N.B. Cocchiarella Two Views of the Logic of Plurals and a Reduction of One to the Other, 2015.)

$$F$$ is called a substituting before $$x$$ is replaced by $$t$$;

$$t$$ is called a substituend which is to replace $$x$$;

$$x$$ is called a substituand or substituent which is to be replaced by $$t$$;

and $$[t/x]F$$ is called a substitution instance or substitution or substituted after $$x$$ is replaced by $$t$$.

Here, both substituting and substituted are used to be nouns.

• I predict you will find no dictionary agreeing with your claim for "substituent". Substituent is jargon specific to chemistry. Aug 30, 2021 at 12:06