Semirings for Soft Constraint Solving and Programming Constraint satisfaction and constraint programming have shown to be very simple but powerful ideas with applications in various areas. Still in the last ten years the simple notion of constraints has shown some deficiencies concerning both theory and practice typically in the way over constrained problems and preferences are treated. For this reason the notion of soft constraints has been introduced with semiring based soft constraints and valued constraints being the two main general frameworks. This book includes formal definitions and properties of semiring based soft constraints as well as their use within constraint logic programming and concurrent constraint programming. Moreover the author shows how to adapt existing notions and techniques such as abstraction and interchangeability to the soft constraint framework and it is demonstrated how soft constraints can be used in some application areas such as security. Overall this book is a great starting point for anyone interested in understanding the basics of semiring based soft constraints