Subpullbacks and Po-flatness Properties of S-posets

In (Golchin A. and Rezaei P., Subpullbacks and flatness properties of S-posets. Comm. Algebra. 37: 1995-2007 (2009)) study was initiated of flatness properties of right S-posets A_S over a pomonoid S that can be described by surjectivity of ? corresponding to certain (sub)pullback diagrams and new properties such as ?(PWP)?_w and ?(WP)?_w were discovered. In this article first of all we describe po-flatness properties of S-posets over pomonoids by po-surjectivity of ? corresponding to certain subpullback diagrams. Then we introduce three new Conditions (P_sw), ?(WP)?_sw and ?(PWP)?_sw and investigate the relation between them and Conditions (P), (P_w), (WP), ?(WP)?_w, (PWP) and ?(PWP)?_w. Also we describe these properties by po-surjectivity of ? corresponding to certain subpullback diagrams and describe Conditions (P_w), ?(WP)?_w and ?(PWP)?_w by weak po-surjectivity of ? corresponding to certain subpullback diagrams.