A kinship relation can be represented in several different notations. Puck basically uses two of them : the *standard* and the *positional* notations.

The conventional notation of kinship relations uses capital letters for indicating the type of 8 basic kinship relations. These letters are mostly abbreviations of the corresponding English kinship term. They contain information on the gender of Alter and of the direction of the basic kinship relation (ascendance, descent, marriage, as well as siblingship). The following table shows its logic :

These basic kinship relations are composed into more complex ones by the simple juxtaposition of letters according to their position in the kinship chain, starting from ego (as in English, but contrary, for example, to French, where kinship terms have to be composed starting with alter!). The gender of Ego must be indicated by additional signs such as ♂ [male Ego] or ♀ [female Ego] placed before the initial letter. The resulting combination of letters can be read as a direct abbreviation of an English kinship term: MBD (mother’s brother’s daughter, a matrilateral cross-cousin), ZH (sister’s husband, a brother in-law), FWS(father’s wife’s son, a step-brother) are examples of this.

Half-sibling relations are distinguished from full sibling relations by using explicit combination of ascendance and descendance letters instead of sibling letters: for instance, FS (father’s son, paternal half-brother). In addition to genealogical relations, relative age can be indicated by minor letters e (elder) and y (younger) placed before the kinship letter concerned: for instance, FeB (father’s elder brother), MyZ (mother’s younger sister). Standard kinship notation is highly intuitive and easy to read (at least for anglophones). However, it expresses the ethnocentric viewpoint of English kinship terminology and, by using simple abbreviations, tells us little or nothing about the structure of the kinship relation. It is therefore certainly not the best tool for analytical purposes.

In the positional notation, developed by Laurent Barry (Barry, 2004), a kinship relation is represented by a sequence of letters indicating gender (by abbreviations of the french terms H - homme - for male, and et F - femme - for female) and two diacritical signs :

- The point or full stop “.” which indicates marriage ;
- The parentheses () surround an apical position, that is, the position of an individual which is not descendant of any of its neighbors. If both neighbors are spouses, the parentheses may be dropped.

Relations of ascendance and descent are indicated by simple juxtaposition, where direction changes after every pair of parentheses and every marriage dot. By convention, the starting direction is ascendance.

By replacing gender letters with the variable X, more comprehensive classes of kinship relations can be represented in positional notation. For instance, X(H)X denotes paternal half- siblings, XX(X)F direct aunts, X(F)FH uterine nephews.

Note that the translation of kinship relations from standard notation (without using ♀ and ♂ signs for the gender of ego) into positional notation always implies the variable letter X in the first position.

Positional notation can be used not only to represent abstract kinship relations, but also concrete kinship chains. In this case, gender letters are replaced by identity numbers of the individuals in the respective positions.

The major advantages of positional notation are :

- The clear representation of the kinship relations structural properties, which remain unchanged by symmetry transformations HF( )HF becomes FH( )FH, but MBD becomes FZS ;
- The integration of the sex of ego and not only of alter ;
- The applicability not only as a notation but as a classification tool (by use of gender variables) ;
- The homogeneity of notations of kinship chains (with individual numbers), kinship relations (with gender letters) and kinship relation classes (with gender variables).

The following table shows some examples of kinship relations translation from positional to standard notation :