A note on negative tagging for least fixed-point formulae
We consider proof systems with sequents of the formU |- F for proving validity of a propositional 
modal mu-calculus formula F over a set U of 
states in a given model. Such proof systems usually handle 
fixed-point formulae through unfolding, thus allowing such formulae 
to reappear in a proof. Tagging is a technique originated by Winskel 
for annotating fixed-point formulae with information 
about the proof states at which these are unfolded. This information 
is used later in the proof to avoid unnecessary unfolding, without 
having to investigate the history of the proof. Depending on whether 
tags are used for acceptance or for rejection of a branch in the proof 
tree, we refer to ``positive'' or ``negative'' tagging, respectively. 
In their simplest form, tags consist of the sets U at which 
fixed-point formulae are unfolded. In this paper, we generalise results 
of earlier work by Andersen, Stirling and Winskel which, in the case 
of least fixed-point formulae, are applicable to singleton U sets only.