Completeness and cut-elimination theorems for trilattice logics

Abstract: A sequent calculus for Odintsov’s Hilbert-style axiomatization of a logic related to the trilattice of generalized truth values is introduced. The completeness theorem w.r.t. a simple semantics for is proved using Maehara’s decomposition method that simultaneously derives the cut-elimination theorem for . A first-order extension of and its semantics are also introduced. The completeness and cut-elimination theorems for are proved using Schütte’s method. [Copyright &y& Elsevier]