Many “semiring-like” structures are used in Soft Constraint Satisfaction Problems (SCSPs). We review a few properties of semirings that are useful for dealing with soft constraints, highlighting the differences between alternative proposals in the literature.
We then extend the semiring structure by adding the notion of division as a weak inverse operation of product. In particular, division is needed to apply constraint relaxation when the product operation of the semiring is not idempotent. The division operator is introduced via residuation and it is also able to deal with partial orders, generalizing the approach given for Valued CSPs.
IOS Press, Inc.
6751 Tepper Drive
Clifton, VA 20124
Tel.: +1 703 830 6300
Fax: +1 703 830 2300 firstname.lastname@example.org
(Corporate matters and books only) IOS Press c/o Accucoms US, Inc.
For North America Sales and Customer Service
West Point Commons
Lansdale PA 19446
Tel.: +1 866 855 8967
Fax: +1 215 660 5042 email@example.com