Nicolai, Carlo Cut elimination for systems of transparent truth with restricted initial sequents. (English) Zbl 1529.03270 Notre Dame J. Formal Logic 62, No. 4, 619-642 (2021). Summary: The paper studies a cluster of systems for fully disquotational truth based on the restriction of initial sequents. Unlike well-known alternative approaches, such systems display both a simple and intuitive model theory and remarkable proof-theoretic properties. We start by showing that, due to a strong form of invertibility of the truth rules, cut is eliminable in the systems via a standard strategy supplemented by a suitable measure of the number of applications of truth rules to formulas in derivations. Next, we notice that cut remains eliminable when suitable arithmetical axioms are added to the system. Finally, we establish a direct link between cut-free derivability in infinitary formulations of the systems considered and fixed-point semantics. Noticeably, unlike what happens with other background logics, such links are established without imposing any restriction to the premises of the truth rules. Cited in 1 Document MSC: 03F05 Cut-elimination and normal-form theorems 03A05 Philosophical and critical aspects of logic and foundations Keywords:cut elimination; formal theories of truth; substructural logic × Cite Format Result Cite Review PDF Full Text: DOI arXiv References: [1] Beall, J. C., Spandrels of Truth, Oxford University Press, Oxford, 2009. [2] Burgess, J. 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