ABSTRACT
An important question is how far our logical calculi capture the logically valid arguments in natural language, in particular how does the relation of inference generated by the calculus reconstruct the pre-theoretical relation of following-from or some of its relevant parts. We call any “reasonable” projection of the formal language on a natural one its (acceptable) interpretation. We call an argument scheme in the formal language valid if all its interpretations are correct arguments; and we call a calculus sound if it captures only valid argument schemes whereas we call it complete if it captures all the valid schemes. All these concepts concern the relationship of the formal language to the natural one. Therefore, to distinguish them from parallel concepts concerning its relationship to a formal semantic, we call them material and supply them with the index “M”: interpretation M, valid M, sound M, complete M. Logical calculi can also be investigated as mathematical objects in their own right; important mathematical properties a calculus can have are, for example, decidability or deductive completeness.
