Theoretical Computer Science
Natural 3-valued logic—characterization and proof theory
Journal of Symbolic Logic
The method of hypersequents in the proof theory of propositional non-classical logics
Logic: from foundations to applications
Proof Theory of Fuzzy Logics: Urquhart's C and Related Logics
MFCS '98 Proceedings of the 23rd International Symposium on Mathematical Foundations of Computer Science
On the Undecidability of some Sub-Classical First-Order Logics
Proceedings of the 19th Conference on Foundations of Software Technology and Theoretical Computer Science
Uninorm logic with the n-potency axiom
Fuzzy Sets and Systems
Involutive uninorm logic with the n-potency axiom
Fuzzy Sets and Systems
Logics for residuated pseudo-uninorms and their residua
Fuzzy Sets and Systems
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The aim of this work is to perform a proof-theoretical investigation of some propositional logics underlying either finite-valued Gödel logic or finite-valued Lukasiewicz logic. We define cut-free hyper-sequent calculi for logics obtained by adding either the n-contraction law or the n-weak law of excluded middle to affine intuitionistic linear logic with the linearity axiom (A → B) ∨ (B → A). We also develop cut-free calculi for the classical counterparts of these logics. Moreover we define a hypersequent calculus for Ł3 ∩ Ł4 in which the cut-elimination theorem holds. This calculus allows to define an alternative axiomatization of Ł4 making no use of the Łukasiewicz axiom.