In this paper we develop what we can describe as a “dual two-sided” cut-free sequent calculus system for the non-classical logics of truth lp, k 3, stt and a non-reflexive logic ts which is, arguably, more elegant than the three-sided sequent calculus developed by Ripley (The Review of Symbolic Logic 5:354–378, 2012) for the same logics. Its elegance stems from how it employs more or less the standard sequent calculus rules for the various connectives and truth, and the fact that it offers a rather neat connection between derivable sequents and validity in comparison to the calculus developed by Ripley (The Review of Symbolic Logic 5:354–378, 2012).
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Fjellstad, A. Non-classical Elegance for Sequent Calculus Enthusiasts. Stud Logica 105, 93–119 (2017). https://doi.org/10.1007/s11225-016-9683-y