DYNAMIC CONSEQUENCE AND PUBLIC ANNOUNCEMENT

In van Benthem (2008), van Benthem proposes a dynamic consequence relation defined as psi(1),...,psi(n) vertical bar=(d) psi iff vertical bar=(pa) [psi(1)]...[psi(n)]psi where the latter denotes consequence in public announcement logic, a dynamic epistemic logic. In this paper we investigate the structural properties of a conditional dynamic consequence relation | d extending van Benthem's proposal. It takes into account a set of background conditions inspired by Makinson (2003) wherein Makinson calls this reasoning ` modulo' a se. In the presence of common knowledge, conditional dynamic consequence is definable from (unconditional) dynamic consequence. An open question is whether dynamic consequence is compact. We further investigate a dynamic consequence relation for soft instead of hard announcements. Surprisingly, it shares many properties with (hard) dynamic consequence. Dynamic consequence relations provide a novel perspective on reasoning about protocols in multi- agent systems.