Embedding constraint relationships into C-semirings

These notes provide technical details that are required to embed constraint relationships into the c-semiring framework presented in terms of category theory. It contains all steps required to map a dag to a partial order (Section 1), construct the free meet monoid from this partial order (Section 3) as well as the free c-semiring (Section 4). A constraint solving algorithm based on branch-and-bound search is presented in §34 for c-semirings and in §36 for meet monoids. A concrete instantiation for constraint relationships along with an example soft constraint problem concludes the report in Section 7