A note on negative tagging for least fixed-point formulae

We consider proof systems with sequents of the form U for proving validity of a propositional modal calculus formula over a set U of states in a given model Such proof systems usually handle xed point formulae through unfolding thus allowing such formulae to reappear in a proof Tagging is a technique originated by Winskel for annotating xed 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 investi gate 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 xed point formulae are unfolded In this paper we generalise results of earlier work by Andersen Stir ling and Winskel which in the case of least xed point formulae are applicable to singleton U sets only