Dynamic Consequence and Public announcement

In [25] van Benthem proposes a dynamic consequence relation defined as ψ1, . . . , ψn |= φ iff |= [ψ1]...[ψn]φ, 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 |=Γ extending van Benthem’s proposal. It takes into account a set of background conditions Γ, inspired by [18] wherein Makinson calls this reasoning ‘modulo’ a set Γ. 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.