Sentence examples for valid sentence from inspiring English sources

Completeness means that every valid sentence of the calculus is a theorem.

It is easy to show that the propositional calculus is complete in the sense that every valid sentence in it i.e., every tautology, or sentence true in all possible worlds (in all interpretations)—is a theorem, as may be seen in the following example.

For example, a valid sentence is "bin blue at Z three please".

In particular, Kripke notes that when the quantifiers of a valid sentence of pure quantificational logic are suitably rewritten as substitutional quantifiers, we obtain a valid sentence in the language of pure substitutional quantificational logic.

The sentence κ ↔ λ is a valid sentence if the continuum hypothesis is true, and only then.

For example, the spectrum of a valid sentence is the class of all non-zero cardinal numbers.

The conclusion, in fact, asserts more than consistency, for it holds that only valid sentences are provable.

Since all valid sentences, and only these, are theorems, each sentence can be tested mechanically by putting true and false for each letter in the sentence.

The consistency of the propositional calculus (its freedom from contradiction) is more or less obvious, because it can easily be checked that all its axioms are valid i.e., true in all possible worlds and that the rules of inference carry from valid sentences to valid sentences.

This theorem states that the axioms and rules of inference of basic ("first-order") logic are complete, that is, that they are sufficient to prove all logically valid sentences within the logic.

Let V¹ be the set of valid sentences of first-order logic and let V² be the set of valid sentences of second-order logic.