Herzberger’s Limit Rule with Labelled Sequent Calculus
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.
KeywordsRevision theory of truth Labelled sequent calculus Herzberger Possible world semantics Neighbourhood semantics
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For discussions and comments on the material that resulted in this paper, I would like to thank Casper Storm Hansen, Fausto Barbero, Jan von Plato, Maria Hämeen-Anttila, Marianna Girlando, Ole Hjortland, Sara Negri and Tuukka Tanninen. I would also like to thank the anonymous referees for their many helpful suggestions. The research for this paper was supported by a FRIPRO Mobility Fellowship for the project Expressing Validity by Revision: Logical and Philosophical Aspects from the Research Council of Norway (project no 262837/F10, co-funded by the European Union’s Seventh Framework Programme for research, technological development and demonstration under Marie Curie grant agreement no 608695).
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