The ability to form institutional relations is universal across our species. A culturally socialized individual could intuitively recognize the logic of the structural relationship between positions and roles, duties and capabilities for every complex social phenomenon. Institutional thinking that lies at the core of human orientation in the social world implies unity of generative operations for calculation of logical structure underlying any social relationship. From this point of view, it makes sense to talk about the system that covers a maximum range of situations with minimum rules: minimum basic generative operations to derive the logical structure of a wide range of institutionalized relationships. One of such basic generative operations is binary operation merge that recursively combines components in one structure. This article offers, as a heuristic model, alternative binary operations that generate the logical structure of institutionalized relationships universally: symmetric-pair and asymmetric-pair compositions of atomic elements. The proposed heuristic approach is based on a compositional comparison of possible structures that can be generated by simple binary operations on a finite set of elements. Simple binary operations, asymmetry and pair, allow deriving the logical structure of social relations universally such that the entire inference process can be described by a small set of procedures. Social relationship logic is intuitively recognized by the culturally socialized individual as a conclusion regarding deontic power and normative characters of relationship (rights, obligations, requirements) that based on the relational positions of structural elements (social categories, statuses, nomenclatures).