Authors
Carlo Nicolai
King's College London
Abstract
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 premisses of the truth rules.
Keywords Truth  Substructural logic  Proof-Theory
Categories (categorize this paper)
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

Our Archive
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

No references found.

Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles

Indexed Systems of Sequents and Cut-Elimination.Grigori Mints - 1997 - Journal of Philosophical Logic 26 (6):671-696.
Reference and Truth.Lavinia Picollo - 2020 - Journal of Philosophical Logic 49 (3):439-474.
Noncontractive Classical Logic.Lucas Rosenblatt - 2019 - Notre Dame Journal of Formal Logic 60 (4):559-585.
Proof Theory for Admissible Rules.Rosalie Iemhoff & George Metcalfe - 2009 - Annals of Pure and Applied Logic 159 (1-2):171-186.
On the Explanatory Power of Truth in Logic.Gila Sher - 2018 - Philosophical Issues 28 (1):348-373.
Deep Sequent Systems for Modal Logic.Kai Brünnler - 2009 - Archive for Mathematical Logic 48 (6):551-577.
A Note on Typed Truth and Consistency Assertions.Carlo Nicolai - 2016 - Journal of Philosophical Logic 45 (1):89-119.

Analytics

Added to PP index
2020-06-14

Total views
63 ( #145,981 of 2,326,758 )

Recent downloads (6 months)
63 ( #8,922 of 2,326,758 )

How can I increase my downloads?

Downloads

My notes