Completeness and cut-elimination theorems for trilattice logics

作者：Kamide Norihiro^*; Wansing Heinrich

来源：Annals of Pure and Applied Logic, 2011, 162(10): 816-835.

DOI：10.1016/j.apal.2011.03.001

• Trilattice logics
• Trilattice SIXTEEN3
• Sequent systems
• Co-ordinate valuations semantics
• Maehara's method
• Schutte's method

A sequent calculus L-16 for Odintsov's Hilbert-style axiomatization L-B of a logic related to the trilattice SIXTEEN3 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 LIB. 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 Schutte's method.

• 出版日期2011-10