Agradecimentos: We thank the suggestions of the two anonymous referees, which helped us to improve the overall quality of this paper. We also thank Martin Figallo for drawing our attention to Tarski algebras, and to Rodolfo Ertola for improving our intuitions on implicative lattices. The first author acknowledges financial support from the National Council for Scientific and Technological Development (CNPq), Brazil, under research grant 306530/2019-8. The second author was initially supported by a doctoral scholarship from the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES) - Finance Code 001 (Brazil), and lateron by a postdoctoral fellowship by NSF-BSF, grant number 2020704 Ver menos