Abstract
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.
Research partially supported by the MIUR PRIN 2017FTXR7S “IT-MaTTerS”.
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- 1.
“Weaker alternative” here means that diagonals allow for axiomatising substitutions at the expenses of working with complete partial orders: see e.g. [11, Definition 11].
- 2.
The operator is called projection in the soft framework, and \(\exists _X c\) is denoted \(c\Downarrow _{V\setminus X}\).
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Bonchi, F., Bussi, L., Gadducci, F., Santini, F. (2019). Polyadic Soft Constraints. In: Alvim, M., Chatzikokolakis, K., Olarte, C., Valencia, F. (eds) The Art of Modelling Computational Systems: A Journey from Logic and Concurrency to Security and Privacy. Lecture Notes in Computer Science(), vol 11760. Springer, Cham. https://doi.org/10.1007/978-3-030-31175-9_14
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