A real-time semantics for norms with deadlines

Norms have been proposed as a way to regulate multi-agent systems. In order to operationalize norms, several computational frameworks have been proposed for programming norm-governed agent organizations. It has been argued that in such systems it is essential that norms, in particular those giving rise to achievement obligations, have deadlines. In this paper we propose a novel semantic framework that takes into account and formalizes real-time aspects of such norms with deadlines. The framework introduced provides a semantics for norms with real-time deadlines that is a conservative extension of more traditional transition systems semantics that has been used for specifying multi-agent systems. Our framework thus provides a natural extension for formalizing multi-agent systems with norms that have real-time deadlines. We address several important aspects of semantics of norms with deadlines such as deadline termination and, in particular, investigate the issue of deadline shifting that arises naturally in a real-time setting as a result of interactions between norms. A new normative model is presented for handling such interactions. We present several formal results showing that our semantics corresponds with basic intuitions that any operational semantics for norms with (real-time) deadlines should satisfy, and that it is well-defined.