Studia Logica ( IF 0.6 ) Pub Date : 2021-03-25 , DOI: 10.1007/s11225-021-09942-5 Minghui Ma , Qian Chen
A finitely alternative normal tense logic \(T_{n,m}\) is a normal tense logic characterized by frames in which every point has at most n future alternatives and m past alternatives. The structure of the lattice \(\Lambda (T_{1,1})\) is described. There are \(\aleph _0\) logics in \(\Lambda (T_{1,1})\) without the finite model property (FMP), and only one pretabular logic in \(\Lambda (T_{1,1})\). There are \(2^{\aleph _0}\) logics in \(\Lambda (T_{1,1})\) which are not finitely axiomatizable. For \(nm\ge 2\), there are \(2^{\aleph _0}\) logics in \(\Lambda (T_{n,m})\) without the FMP, and infinitely many pretabular extensions of \(T_{n,m}\).
中文翻译:
有限替代正态时态逻辑格
有限替代的正态时态逻辑\(T_ {n,m} \)是一个特征为帧的正态时态逻辑,其中每个点最多具有n个将来的替代项和m个过去的替代项。描述了晶格\(\ Lambda(T_ {1,1})\)的结构。\(\ Lambda(T_ {1,1})\)中有\(\ aleph _0 \)逻辑没有有限模型属性(FMP),\(\ Lambda(T_ {1,1 })\)。\(\ Lambda(T_ {1,1})\)中有\(2 ^ {\ aleph _0} \)个逻辑,这些逻辑不是可无限地公理化的。对于\(nm \ ge 2 \),存在\(2 ^ {\ aleph _0} \)逻辑\(\ Lambda(T_ {n,m})\)不带FMP,并且无数个表格前扩展名\(T_ {n,m} \)。