Structural operational semantics for modern process languages (like p-calculi) involves features such as variable binding and substitution. These are not found in basic .rst-order calculi (like Milner’s Pure CCS). In [3, 4], I have shown that, if we are careful, we can understand the semantics of the more elaborate modern calculi as follows: .rst, move from the category of sets to a di.erent category, such as a presheaf category; secondly, reinterpret the old results for .rst-order calculi in these di.erent categories. Recent work in coalgebraic modal logic (e.g. [1, 2]) has also shown that this approach is helpful. 
Selected references 
[1] 	M. M. Bonsangue and A. Kurz. Pi-calculus in logical form. In Proc. LICS’07, pp. 303–312. 2007. 
[2] 	B. Klin. Coalgebraic modal logic beyond sets. In Proc. MFPS’07. ENTCS vol. 173, pp. 177–201. 2007. 
[3] 	S. Staton. General structural operational semantics through categorical logic. In Proc. LICS’08), pp. 166–177. 2008. 
[4] 	S. Staton. Substitution in Structural Operational Semantics and value-passing process calculi. In Proc. 2nd International Workshop on Theory and Applications of Abstraction, Substitution and Naming (TAASN 2009).