Polyadic soft constraints

We propose a formalism for manipulating soft constraints based on polyadic algebras. The choice of such algebras in place of classical cylindric ones simplifies the structure of the partial order of preference values by removing diagonals, a family of constants used for modelling parameter passing and variable substitution, whose presence require completeness. Removing diagonals also allows for an easy representation of preference/cost functions in terms of polynomials, thus streamlining their manipulation on languages based on (stores of) constraints. Besides presenting the main features of the new formalism, the paper investigates how the operators of polyadic algebras interact with the residuated monoid structure that is used for representing the set of preference values.