This topic refers to the course Meaning explanations and dialogues (Klev). Here is a description and a bibliography for addressing it.
P. Martin-Löf, "Truth of a proposition, evidence of a judgement, validity of a proof", in Synthese 73, 1987, pp. 407-420 [especially the first three pages]
G. Sundholm, "A plea for logical atavism", in Logica Yearbook 2000 [available online at https://hdl.handle.net/1887/10422]