Exploiting Algebraic Laws to Improve Mechanized Axiomatizations

In the field of structural operational semantics (SOS), there have been several proposals both for syntactic rule formats guaranteeing the validity of algebraic laws, and for algorithms for automatically generating ground-complete axiomatizations. However, there has been no synergy between these two types of results. This paper takes the first steps in marrying these two areas of research in the meta-theory of SOS and shows that taking algebraic laws into account in the mechanical generation of axiomatizations results in simpler axiomatizations. The proposed theory is applied to a paradigmatic example from the literature, showing that, in this case, the generated axiomatization coincides with a classic hand-crafted one.