One can mechanically determine whether any given finite sequence of sentences is a proof. Although logical calculuses can be objects of study in their own right, it is their application to the construction and criticism of arguments that gives calculuses their original point. An argument in English is valid just in case it is not possible for all the premisses to be true and the conclusion false. Valid arguments can be grouped according to their shapes or form. For example, it is easy to see that the following arguments share their form, despite their different content or subject-matter.
Logical calculuses differ according as they concentrate on different kinds of valid argument forms.
Arguments in English are often hard to make out. Better to translate English arguments into a logical calculus which is brief and unambiguous and then determine whether the translation is a proof or can be made into a proof by inserting extra steps. To guarantee that the existence of a proof entails that the original English argument is valid the rules of inference must be truth-preserving. A semantics for the calculus explicates, using the notion of an interpretation, the idea of a possible situation in which sentences are true or false. An argument of the calculus is defined to be valid just in case in any interpretation in which all the premisses are true, the conclusion is also true.