Axiomatizing GSOS with termination

We discuss a combination of GSOS-type structural operational semantics with explicit termination, that we call the tagh-format (tagh being short for termination and GSOS hybrid). The tagh-format distinguishes between transition and termination rules, but, besides active and negative premises as in GSOS, also allows for what we call terminating and passive arguments. We extend the result of Aceto, Bloom and Vaandrager on the automatic generation of sound and complete axiomatizations for GSOS to the setting of tagh-transition systems. The construction of the equational theory is based upon the notion of a smooth and distinctive operation, which have been generalized from GSOS to tagh. We prove the soundness of the synthesized laws and show their completeness modulo bisimulation. The examples provided indicate a significant, though yet not ideal, improvement over the axiomatization techniques known so far.

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