Where is an interpretation and and represent formulas, the definition of an argument, given in , may then be stated as a pair , where is the set of premises and is the conclusion. The definition of an argument's validity, i.e. its property that , can then be stated as its absence of a counterexample, where a counterexample is defined as a case in which the argument's premises are all true but the conclusion is not true. As will be seen in , this is the same as to say that the conclusion is a semantic consequence of the premises.
Where is an interpretation and and represent formulas, the definition of an argument, given in , may then be stated as a pair , where is the set of premises and is the conclusion. The definition of an argument's validity, i.e its property that , can then be stated as its absence of a counterexample, where a counterexample is defined as a case in which the argument's premises are all true but the conclusion is not true. As will be seen in , this is the same as to say that the conclusion is a semantic consequence of the premises