Sentence examples for it logically implies from inspiring English sources

It logically implies both extensionality and the conversion schemata ("If u is a member of the set of all and only Fs, then u is an F", and "If u is an F, and the set of all and only Fs exists, then u is a member of it"), but does not guarantee the existence of any sets not even that of the empty set.

When a replication succeeds, it logically implies that every step in the replication "worked".

When a replication fails, it logically implies that at least one or more of the steps in the replication failed including the possibility that the experimental hypothesis is false but we do not know which step(s) failed.

Thus a sentence is valid in the general semantics iff it is logically implied (in first-order logic) by the set of comprehension axioms.

That such a reinterpretation strategy guarantees relative consistency can be seen via the following reasoning: If the set AX were inconsistent, then it would logically imply a contradiction.

But that seems crazy: it seems, quite to the contrary, that the claim that a given particular has mass 5 kg logically implies that it does not have mass 7 kg.

We also consider a stronger version of redundancy elimination: a clause C is strongly condensed iff it does not contain any proper subset C′ such that C logically implies C′.

Yes, we have won promotion to the top division every so often; but the fact of promotion logically implies an earlier relegation.

The implication problem is the most important one in dependency theory, and is the problem of determining if a set of dependencies logically implies another dependency.

The idea of saving or delivering from some dire situation logically implies that humankind, as a whole or in part, is in such a situation.

They refuse to admit that their argument logically implies that every expenditure of tax revenues that is alleged to violate the Establishment Clause is subject to suit under Flast.