Sentence examples for valid formula from inspiring English sources

We accept also, of course, that (ii) for every calculus $C$ sound with respect to model-theoretic validity there is a model-theoretically valid formula that is not derivable in $C$.

From all this it doesn't follow that (iii) there is a model-theoretically valid formula $F$ such that for every calculus $C$ sound for model-theoretic validity $F$ is not derivable in C. From (iii) and (i) it follows of course that there are model-theoretically valid formulae that are not obtainable by a priori or analytic reasoning.

Any valid formula can fail at a world.

In classical logic and in positive free logic any substitution instance of a valid formula (or form of inference) is itself a valid formula (or form of inference).

In the semantics for relevant logics, not every world makes true every valid formula.

But it seems silly to say that every valid formula ought to be the case.

Thanks to the notion of 'valid formula' just given, we can claim that Zsyntax is constructed from two basic kinds of valid formulae: These represent reactions, and their validity depends only on empirical information acquired in the laboratory.

The axiomatic system \(\mathbf{K}_{t}\) is sound and complete for validity in TL, in the sense that it can derive all valid formulae of TL and only them.

The same definitions are then still possible, but the list of valid formulas is different; e.g., ∼∼p ⊃ p, which was previously valid, now has the value 1/2 when p has the value 1/2.

Hence valid formulas may have invalid substitution instances.

Property (3) is proved from the still valid formulas (2.14)–(2.14).