Mapping tile logic into rewriting logic

extends to concurrent systems with state changes the body of theory developed within the algebraic semantics approach. It is both a foundational tool and the kernel language of several implementation e orts (Cafe, ELAN, Maude). extends (unconditional) rewriting logic since it takes into account state changes with side e ects and synchronization. It is especially useful for de ning compositional models of computation of reactive systems, coordination languages, mobile calculi, and causal and located concurrent systems. In this paper, the two logics are de ned and compared using a recently developed algebraic speci cation methodology, . Given a theory , the rewriting logic of is the free monoidal -category, and the tile logic of is the free monoidal category, both generated by . An extended version of monoidal 2-categories, called , is also de ned, able to include in an appropriate sense the structure of monoidal double categories. We show that 2VH-categories correspond to an extended version of rewriting logic, which is able to embed tile logic, and which can be implemented in the basic version of rewriting logic using suitable . These strategies can be signi cantly simpler when the theory is . A uniform theory is provided in the paper for CCS, and it is conjectured that uniform theories exist for most process algebras.