Logical Semantics for CafeOBJ

This paper presents the semantics of CafeOBJ system and language. CafeOBJ is a succesor of the famous algebraic specification and programming language OBJ but adding several new primitive paradigms to the traditional OBJ language, such as rewriting logic, and behavioural concurrent specification. We do not address here the detalied mathematical aspects of CafeOBJ semantics (which sometimes could be rather sophisticated), but rather survey this semantics. However all concepts and facts are fully backed by solid mathematical concepts and results, and we give pointers to mathematical works backing our claims. We provide in the appendices very brief surveys of several key structures; we hope this will make this paper more self contained. Some familiarity with the OBJ tradition (including some key mathematical concepts) is of course necessary for understanding the semantics of CafeOBJ.