Completeness properties of transitive binary relational sets

Completeness of logics with the transitive closure modality and related logics

We give a sufficient condition for Kripke completeness of modal logics enriched with the transitive closure modality. More precisely, we show that if a logic admits what we call definable filtration (ADF), then such an expansion of the logic is complete; in addition, has the finite model property, and again ADF. This argument can be iterated, and as an application we obtain the finite model property for PDL-like expansions of logics that ADF.

关系代数完备性的 cylindric 代数方法

Completeness of Relational Algebra via Cylindric Algebra

本文通过 cylindric 代数方法重新证明了关系代数对一阶逻辑允许公式完备性，并提出一种生成等价关系表达式的新算法，为处理不完整或模糊信息的扩展提供基础。

Completeness results for many-valued \Lukasiewicz modal systems and relational semantics

The paper is dedicated to the problem of adding a modality to the \Lukasiewicz many-valued logics in the purpose of obtaining completeness results for Kripke semantics. We define a class of modal many-valued logics and their corresponding Kripke models and modal many-valued algebras. Completeness results are considered through the construction of a canonical model. Completeness is obtained for modal finitely-valued logics but also for a modal many-valued system with an infinitary deduction rule. We introduce two classes of frames for the finitely-valued logics and show that they define two dis…

带交集与常量的Lambek演算的关系模型

Relational Models for the Lambek Calculus with Intersection and Constants

本文研究了带交集与常量的Lambek演算的关系语义，证明禁止空前件限制下强完备性失效，但为常量非标准解释证明了弱完备性，并扩展至迭代除法及无积片段。

作为关系模型的偏序集乘积

Poset Products as Relational Models

本研究提出基于偏序集乘积的关系语义学，给出其对各类子结构逻辑的可靠性与完备性充分条件，统一并推广两种已有语义，复现相关结果并拓展至无穷多种子结构逻辑。

大多数性质对于传递时态逻辑是不可判定的

Most Properties are Undecidable for Transitive Tense Logics

本文通过从Minsky机器的不可判定问题归约，证明了传递时态逻辑格NExt(K4t)中大多数性质（如Kripke完全性、有限模型性质和可判定性）是不可判定的。