Modal Semirings and Applications (Trends in Logic, 72)

The book serves as a systematic exposition of modal semirings.Next to motivating the definitions, developing the basic calculus and discussing the most interesting examples of modal semirings, it presents a wide variety of applications.On the side of program semantics, Hoare Logic, the theory of general and partial correctness, demonic semantics and various temporal logics such as PDL, LTL andCTL* are treated.The book is situated in the general area of formal methods.Among the many approaches there, it concentrates on a strongly calculational style using algebra as its main ingredient.This field is often called emph{algebraic logic}. Its aim is to compact series of small steps of general logical inference into larger (in)equational steps.Moreover, it attempts to replace tedious model-theoretic argumentation, in particular, element-wise argumentation, by more abstract and compact reasoning.The structure of the book is as follows: Part I presents the basic theory.Part II contains applica