Transition system specifications with negative premises

In this article the general approach to Plotkin-style operational semantics of Groote and Vaandrager (1989) is extended to transition system specifications (TSSs) with rules that may contain negative premises. Two problems arise: firstly the rules may be inconsistent, and secondly it is not obvious how a TSS determines a transition relation. We present a general method, based on the stratification technique in logic programming, to prove consistency of a set of rules and we show how a specific transition relation can be associated with a TSS in a natural way. Then a special format for the rules, the ntyft/ntyxt format, is defined. It is shown that for this format three important theorems hold. The first theorem says that bisimulation is a congruence if all operators are defined using this format. The second theorem states that, under certain restrictions, a TSS in ntyft format can be added conservatively to a TSS in pure ntyft/ntyxt format. Finally, it is shown that the trace congruence for image-finite processes induced by the pure ntyft/ntyxt format is precisely bisimulation equivalence.