deleted constructor inheritance

Default, copy, and move constructors are not inherited, nor can inheriting a constructor implicitly declare a copy or move constructor for the derived class. Also, an inheriting constructor declaration will essentially just "skip over" a base class constructor if there's already a constructor with the same signature in the derived class.

For each non-template constructor in the candidate set of inherited constructors other than a constructor having no parameters or a copy/move constructor having a single parameter, a constructor is implicitly declared with the same constructor characteristics unless there is a user-declared constructor with the same signature in the complete class where the using-declaration appears or the constructor would be a default, copy, or move constructor for that class.

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Also, an inherited constructor is deleted if the corresponding base class constructor is deleted.

A constructor so declared has the same access as the corresponding constructor in X. It is deleted if the corresponding constructor in X is deleted (8.4). An inheriting constructor shall not be explicitly instantiated (14.7.2) or explicitly specialized (14.7.3).

([class.inhctor]/4)

Foo constructor is deleted, so you can't define a constructor of class Bar that uses deleted Foo constructor. It doesn't make sense to talk about inheritance there, because you can never create an object of class Bar that uses deleted Foo constructor.

Are deleted constructors inherited at all?

No. They are deleted, there is nothing to inherit from.

If so, Bar() and Foo() have the same signature, does this make the code invalid?

Default constructor can't be inherited.

You could argue that Foo(const Foo& a_Foo) and Bar(const Bar& a_Bar) have different signatures. How do copy constructors behave under constructor inheritance?

Copy constructors can't be inherited as well.