Lattice logic, bilattice logic, and paraconsistent quantum logic are investigated based on monosequent systems. Paraconsistent quantum logic is an extension of lattice logic, and bilattice logic is an extension of paraconsistent quantum logic. Monosequent system is a sequent calculus based on the restricted sequent that contains exactly one formula in both the antecedent and succedent. It is known that a completeness theorem with respect to a lattice-valued semantics holds for a monosequent system for lattice logic. A completeness theorem with respect to a lattice-valued semantics is proved for paraconsistent quantum logic, and a completeness theorem with respect to a bilattice-valued semantics is proved for bilattice logic. Some syntactical properties, including cut-elimination and duality, are also investigated for the monosequent systems for these logics.

基于单序系统研究了格逻辑，双方逻辑和超一致量子逻辑。超一致的量子逻辑是晶格逻辑的扩展，而双态逻辑是超一致的量子逻辑的扩展。Monosequent系统是基于受限序列的序列演算，该序列在先行和后继中仅包含一个公式。众所周知，关于晶格值语义的完整性定理对于晶格逻辑的单序系统成立。证明了超相容的量子逻辑关于格值语义的完备性定理，证明了关于双值逻辑关于双值值语义的完备性定理。一些句法属性，包括删节和对偶，