I have stressed the sociocosmic character of the Polynesian society of Wallis in a long term study of the life cycle rituals and the specific way the components of the person are ritually elaborated and transformed all life long. The Wallisian sociocosmic world displays an extensive, complex and intricate system of relationships. In such a relation-based conception of the world, humans and things are defined by the particular settings of the relations that constitute them and give existence to them. Plants (yams and kava for example), animals (pigs) and other kinds of wealth (such as mats, barkcloth and money) are used for meaningful relationships to be perceived, lived, evaluated but also established and modified. Thus, they enter complex, interconnected circulation and semiotic systems. I will show that these systems work as processors of the relationships framed by every day and ceremonial circulations and by the ritual culminating moments, when efficiency of action and dynamics of social renewal are stemming from the World-beyond. In such a world, based on a complex economy of relationships, the fundamental principle of the society - which is the backdrop of its deep and essential logics and values - appears to be the ritual system, more precisely the system of meaningful circulations that make these relationships personally perceivable and socially existing. This paper wishes to enlarge the path towards the comparison between Polynesia and Melanesia and offer an opportunity to look more closely at some of their important common social and cognitive features.