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Andreas Fjellstad | Herzberger’s Limit Rule with Labelled Sequent Calculus | Studia Logica

Herzberger’s Limit Rule with Labelled Sequent Calculus

Andreas Fjellstad

ABSTRACT

Inspired by recent work on proof theory for modal logic, this paper develops a cut-free labelled sequent calculus obtained by imitating Herzberger’s limit rule for revision sequences as a clause in a possible world semantics. With the help of two completeness theorems, one between the labelled sequent calculus and the corresponding possible world semantics, and one between the axiomatic theory of truth PosFS and a neighbourhood semantics, together with the proof of the equivalence between the two semantics, we show that the theory of truth obtained with the labelled sequent calculus based on Herzberger’s limit rule is equivalent to PosFS.

KEYWORDS: Revision theory of truth, Labelled sequent calculus, Herzberger Possible world semantics, Neighbourhood semantics