# Translating an English sentence to first-order language

Suppose we have the predicate I(x,y), which means that x has influenced y. And we have C, which is the set of all composers.

If I translate the following sentence:

All composers are influenced by Bach.

to first-order logic I believe I will get:

∀x(C(x) → I(Bach,x))

Say now I need to translate the following sentence and I can re-use all my predicates etc.:

All russian composers are influenced by Bach.

What would be a good way of writing this senctence to first-order logic? Should I define an entire new set R, being the set of all Russian composers? That doesn't seem efficient, but I can't figure out what else to do.

• Yes; "for all $x$, if $x$ is a Composer and Russian, then Bach Influenced $x$". – Mauro ALLEGRANZA Sep 16 '17 at 19:45

A more analytic, thus "better" way than simply defining a set of Russian composers ad hoc is to break this set down into a set of Russians $R$ and a set of composers $C$, and then picking those individuals that satisfy both predicates; thus:
$\forall x (R(x) \land C(x) \to I(Bach, x))$
(Note that this procedure does not work without exceptions - an "alleged murderer" is not meaningfully someone who is $Murderer(x) \land Alleged(x)$. But it's good enough for most cases you'll have to deal with.)