本文在《Modal Logic over Lattices》的基础工作之上,进一步探索了模态逻辑与格理论之间的关系。在之前的研究中,使用带二元模态词<sup>,<inf>的多元混合逻辑通过标准克里普克语义讨论格结构。本文将讨论如何使用模态逻辑...本文在《Modal Logic over Lattices》的基础工作之上,进一步探索了模态逻辑与格理论之间的关系。在之前的研究中,使用带二元模态词<sup>,<inf>的多元混合逻辑通过标准克里普克语义讨论格结构。本文将讨论如何使用模态逻辑刻画下半格结构。为了刻画下半格,本文使用了带有一元模态词P和二元模态词<inf>的多元混合逻辑语言并给出了半格上的多元混合逻辑的完整公理化。在已有的相关结果中,格的定义主要基于偏序关系。在本文的后半部分,提出了一种更符合代数视角的格的替代定义,并给出了相应的模态公理化结果。展开更多
Weakly aggregative modal logics (WAML) are a series of natural weakenings o the minimal modal logic K.The natural semantics for them are based on Kripke frames with an N+1-ary relation,where □φ is true at a world if...Weakly aggregative modal logics (WAML) are a series of natural weakenings o the minimal modal logic K.The natural semantics for them are based on Kripke frames with an N+1-ary relation,where □φ is true at a world iff all of its successor N-tuples has at leas one world making φ true.We study the notion of saturated models and ultrafilter extension fo this relational semantics of WAML.The Goldblatt-Thomason theorem for WAML is proved as an application.展开更多
基金supported by the National Social Science Fund of China(No.19ZDA041)。
文摘本文在《Modal Logic over Lattices》的基础工作之上,进一步探索了模态逻辑与格理论之间的关系。在之前的研究中,使用带二元模态词<sup>,<inf>的多元混合逻辑通过标准克里普克语义讨论格结构。本文将讨论如何使用模态逻辑刻画下半格结构。为了刻画下半格,本文使用了带有一元模态词P和二元模态词<inf>的多元混合逻辑语言并给出了半格上的多元混合逻辑的完整公理化。在已有的相关结果中,格的定义主要基于偏序关系。在本文的后半部分,提出了一种更符合代数视角的格的替代定义,并给出了相应的模态公理化结果。
基金supported by Tsinghua University Initiative Scientific Research Programsupported by Taishan Young Scholars Program of the Government of Shandong Province,China(No.tsqn201909151)+1 种基金Shandong Provincial Natural Science Foundation,China(No.ZR2023QF021)Support Plan on Science and Technology for Youth Innovation of Universities in Shandong Province(No.2021KJ086)。
文摘Weakly aggregative modal logics (WAML) are a series of natural weakenings o the minimal modal logic K.The natural semantics for them are based on Kripke frames with an N+1-ary relation,where □φ is true at a world iff all of its successor N-tuples has at leas one world making φ true.We study the notion of saturated models and ultrafilter extension fo this relational semantics of WAML.The Goldblatt-Thomason theorem for WAML is proved as an application.
