0
$\begingroup$

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?

$\endgroup$
2
  • 1
    $\begingroup$ 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. $\endgroup$
    – Community Bot
    Aug 28, 2021 at 17:42
  • $\begingroup$ I added a sentence. Did that help? Addend is to addition as what is to substitution? $\endgroup$ Aug 28, 2021 at 18:24

2 Answers 2

4
$\begingroup$

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.)

$\endgroup$
0
$\begingroup$

$F$ 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.

$\endgroup$
1
  • $\begingroup$ I predict you will find no dictionary agreeing with your claim for "substituent". Substituent is jargon specific to chemistry. $\endgroup$ Aug 30, 2021 at 12:06

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .