Completeness and cut-elimination theorems for trilattice logics

A sequent calculus L 16 for Odintsov’s Hilbert-style axiomatization L B of a logic related to the trilattice S I X T E E N 3 of generalized truth values is introduced. The completeness theorem w.r.t. a simple semantics for L 16 is proved using Maehara’s decomposition method that simultaneously derives the cut-elimination theorem for L 16 . A first-order extension F 16 of L 16 and its semantics are also introduced. The completeness and cut-elimination theorems for F 16 are proved using Schütte’s method.