Abstract
This work furnishes mathematical apparatus for theoretical foundations of multisets as used in Algebraic, Modal and Temporal Logics. It establishes a sufficiently generalized concept of mappings on multisets, thus resolving a long-standing obstacle in the structural study of multiset processing. It has been shown that the mapping defined herein is applicable to a vast array of already defined rewriting problems within the domain of Theoretical Computer Science. Specifically, this paper unifies and generalizes the works of Parikh in Dassow (2000), Hickman (1980), Khomenko (2003) and Nazmul et al. (2013).