Quantitative logic has been the subject of an increasing interest since a seminal paper by Chauvin et al. in 2004, which presented the first Analytic Combinatorics approach of the subject. Since then, the understanding of random Boolean trees has been deeply widened, even if the question of Shannon effect remains open for the majority of the models. We focus in this paper on the original case of Catalan And/Or trees and propose a new specification of those objects that implies easier ways to describe large families of trees. Equipped with this specification, we prove that the model of Catalan And/Or binary trees do not exhibit Shannon effect, i.e. there exists a family of functions with small complexities, that have a positive probability.