Erratum to Compositionality of Projection Inheritance W.M.P. van der Aalst and K.M. van Hee and R.A. van der Toorn Eindhoven University of Technology, Faculty ofTechnology and Management, Department of Information and Technology, P.O.Box 513, NL-5600 MB, Eindhoven, The Netherlands. w.m.p.v.d.aalst@tm.tue.nl Theorem 40 (Compositionality of Projection Inheritance) is one of the central theorems in the paper “Component-Based Software Architectures: A Framework Based on In- heritance of Behavior” (cf. [1], pages 157–158). This theorem states that, given certain requirements, a component can be replaced by another component which is subclass without changing the overall behavior of the system. This is indeed the case. However, Theorem 40 also states that the resulting system is sound (i.e., proper termination, ab- sence of deadlocks, etc.). Note that a strong notion of soundness is used. This notion of soundness does not allow for dead transitions (transitions which can never be ac- tivated). Unfortunately, the requirements of Theorem 40 do not imply the absence of dead transitions in the newly added component. A counter example for the theorem as it is formulated in [1] is shown in the figure below: N B a b c d e f h g N A N C a b c d e f g h g f N A dead The C-net composed of and is a sound C-net in the spirit of Theorem 40. More- over, both and correspond to sound C-nets and is a subclass of under projection inheritance [2]. (In fact and are branching bisimilar.) If is re-