Transition System Specifications with Negative Premises (Extended Abstract)

In thLs article the general approach to Plotkin style operational semantics of [7] is extended to Transrtion System Specifications (TSS's) with rules that may contain negative premises. Two problems arise: firstly the rules may be inconsistent, and secondly it is not obvious how such rules determine a transttion relation. We present a general method, based on the stratiflcatPon technique of logic programm~ng, to show consistency of a set of rules. Then we show how a specific transition relation can be associated with each consistent TSS in a very natural way. A special format for the rules, the pure ntytt/ntyxt-format, is defined. For this format three important theorems hold: firstly, bis~mulation is a congruence if all operators are defined using this format, secondly under certain natural restrictions a TSS in ntylt-tormat can be added conservatively to a TSS in pure ntyft/ntyxt-format and finally, the trace congruence for image finite processes induced by our format is precisely bistmulation equivalence.

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