1.2.5 Validities
Concepts of validity, valid formula and valid argument.
Later in this course we are going to make extensive use of logical inference, and by making use of the semantic concepts just introduced we can explain what we mean by this. This will be done in two separate steps. First we'll establish what valid formulae (or more simply, validities) are, then we'll give a definition of valid arguments (or valid inferences).
Valid Formulae.
A valid formula is a formula that is satisfied in all models (of the appropriate vocabulary) given any variable assignment. That is, if 
is a valid formula, it is impossible to find a situation and a context in which would not be satisfied. We indicate that a formula is valid by writing 
.
For example:
In any model, given any variable assignment, one (and indeed, only one) of the two disjuncts must be true, and hence the whole formula will be satisfied too.
Valid Sentences.
Note that for sentences the definition of validity can be rephrased as follows, without reference to assignments: A valid sentence is a sentence that is true in all models (of the appropriate vocabulary). That is, it is impossible to falsify a valid sentence. For example:
Exercise 1.5 shows that the validity of arbitrary formulae is equivalent to the validity of certain sentences.