Proof systems with sequents of the form
U ⊢ Φ for
proving validity of a propositional
modal μ-calculus formula Φ over a set U of
states in a given model 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 et al. which, in the case
of least fixed-point formulae, are applicable to singleton U sets only.