This topic refers to the course Dialogical logic, old and new (McConaughey). Here is a description and a bibliography for addressing it.
M. Marion and H. Rücker, "Aristotle on universal quantification: a study from the point of view of game semantics", in History and philosophy of logic, 37(3), 2016, pp. 201-229 [this paper argues in favor of a dialogical interpretation of Aristotle's "dictum de omni et de nullo", a very short passage in which Aristotle provides the meaning explanation of universal quantification]
M. Crubellier, "The programme of Aristotelian analytics", Revista de humanidades de Valparaiîso 10, 2017, pp. 29-59 [this is a paper in history of philosophy, with few references to modern logic. It argues that Aristotle's syllogisms were intended as a backward movement from conclusion to premises, not, as is usually understood, in a forward movement of inferences, from premises to conclusion]
M. Crubellier, M. Marion, Z. McConaughey, S. Rahman, "Dialectic, the dictum de omni and echtesis", History and philosophy of logic, 4(3), 2019, pp. 207-233 [this paper is rather technical on both the historical side (critical survey of the interpretations of Aristotle's echtesis) and the logical side (first formalization of ecthesis using the dialogical variant "immanent reasoning"). However, it argues in favor of an instatiated use of quantification in Aristotle's syllogistic, were content was right beneath the formal surface]