Jaroslav Peregrin, What is the Logic of Inference?

Abstract.

The topic of this paper is the question whether there is a logic which
could be justly called the logic of inference. It may seem that at least since Prawitz,
Dummett and others demonstrated the proof-theoretical prominency of intuitionistic logic,
the forthcoming answer is that it is this logic that is the obvious choice for the accolade.
Though there is little doubt that this choice is correct (provided that inference is construed
as inherently single-conclusion and complying with the Gentzenian structural rules), I do
not think that the usual justification of it is satisfactory. Therefore, I will first try to
clarify what exactly is meant by the question, and then sketch a conceptual framework in
which it can be reasonably handled. I will introduce the concept of ‘inferentially native’
logical operators (those which explicate inferential properties) and I will show that the
axiomatization of these operators leads to the axiomatic system of intuitionistic logic.
Finally, I will discuss what modifications of this answer enter the picture when more
general notions of inference are considered.