Bruno Teheux
We study two notions of definability for classes of relational structures based on modal extensions of Łukasiewicz finitely valued-logics. The main results of the paper are the equivalent of the Goldblatt - Thomason theorem for these notions of definability.
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This paper involves generalizing the Goldblatt-Thomason and the Lindström characterization theorems to first-order modal logic.
Modal languages for topology: expressivity and definability
本文研究解释在拓扑空间上的（扩展）模态语言的表达能力和可定义性。我们提供的范Benthem特征定理和Goldblatt-Goldblason可定义性定理的良好建立的一阶拓扑语言$L_t$的拓扑类似物。
Let ML(U^+) denote the fragment of modal logic extended with the universal modality in which the universal modality occurs only positively. We characterize the relative definability of ML(U^+) relative to finite transitive frames in the spirit of the well-known Goldblatt-Thomason theorem. We show that a class F of Kripke frames is definable in ML(U^+) relative to finite transitive frames if and only if F is closed under taking generated subframes and bounded morphic images. In addition, we study modal definability in team-based logics. We study (extended) modal dependence logic, (extended) mod…
Modal definability in Euclidean modal logics
本文研究欧几里得模态逻辑框架类中模态可定义性问题的可计算性，刻画了哪些欧几里得模态逻辑会导致该问题不可判定。
In this paper we study frame definability in finitely-valued modal logics and establish two main results via suitable translations: (1) in finitely-valued modal logics one cannot define more classes of frames than are already definable in classical modal logic (cf.~\citep[Thm.~8]{tho}), and (2) a large family of finitely-valued modal logics define exactly the same classes of frames as classical modal logic (including modal logics based on finite Heyting and \MV-algebras, or even \BL-algebras). In this way one may observe, for example, that the celebrated Goldblatt--Thomason theorem applies imm…
Modal definability in Kripke's theory of truth
本文为克里普克真理论中的非正式模态定义引入模态语言，证明根基性和悖论性可表达而内在性不可表达，并刻画模态可定义关系及完全公理化其语义。
We study model and frame definability of various modal logics. Let ML(A+) denote the fragment of modal logic extended with the universal modality in which the universal modality occurs only positively. We show that a class of Kripke models is definable in ML(A+) if and only if the class is elementary and closed under disjoint unions and surjective bisimulations. We also characterise the definability of ML(A+) in the spirit of the well-known Goldblatt--Thomason theorem. We show that an elementary class F of Kripke frames is definable in ML(A+) if and only if F is closed under taking generated s…
Characterization and definability in modal first-order fragments
模型论的结果，如特征和可定义性，提供了关于不同逻辑的重要信息。众所周知，这些结果的几个模态逻辑的证明，不知何故，相同的“味道”。对于一阶以下的大多数模态逻辑的一般证明仍然过于雄心勃勃。在这篇论文中，我们计划隔离充分条件的特征和定义定理，以保持在广泛的逻辑。随着这些条件，我们将证明，无论哪个逻辑满足它们，满足这两个定理。因此，人们可以用已知的结果给出逻辑的统一证明。此外，人们将能够证明尚未研究的逻辑的特征和可定义性结果。在这两种情况下，只需要检查逻辑是否满足自动导出所需结果的要求。
Frame definability in second-order arithmetic
该文研究模态逻辑框架可定义性的反数学强度，证明估值扩张引理等相关原则与二阶算术子系统$\text{ACA}^{+}_0}$等价，还考察了CTL、LTL对应原则的强度。
We investigate the relationship between recursive enumerability and elementary frame definability in first-order predicate modal logic. On the one hand, it is well-known that every first-order predicate modal logic complete with respect to an elementary class of Kripke frames, i.e., a class of frames definable by a classical first-order formula, is recursively enumerable. On the other, numerous examples are known of predicate modal logics, based on `natural' propositional modal logics with essentially second-order Kripke semantics, that are either not recursively enumerable or Kripke incomplet…
Definability of Functional Properties in the Basic Modal-Temporal Language over Ordered Frames
研究基本模态-时态语言在有序框架上对九种功能性质的可定义性，发现原始多流设置表达能力弱，限制为最小功能框架后表达能力增强，但非线序中仍有不可定义性质。
An extension of Kracht's theorem to generalized Sahlqvist formulas
Sahlqvist公式是由Hendrik Sahlqvist在1975年提出的一类在语法上指定的模态公式。它们是重要的，因为它们的一阶可定义性和规范性，因此公理化完全模态逻辑。由Sahlqvist公式定义的一阶性质是由Marcus Kracht在1993年在语法上描述的。本文将Kracht定理推广到Goranko和Vakarelov提出的“广义Sahlqvist公式”类，并描述了Kracht公式的一个适当的推广.
First-Order Modal Logic via Logical Categories
本文将逻辑范畴框架扩展至一阶模态逻辑，证明Joyal风格表示定理并引入模态预拓扑os概念，最后展示如何从一阶模态理论构建语法范畴。
Validity and Entailment in Modal and Propositional Dependence Logics
本文全面分类了模态与命题依赖逻辑中有效性与蕴涵的复杂性，证明模态依赖逻辑的有效性问题是NEXPTIME完全的，反驳了先前更高的复杂性猜想。
Base-extension Semantics for S5 Modal Logic
本文为多主体S5模态逻辑提出基扩展语义，以证明而非真值为基础，通过基之间的关系结构建立可靠性与完全性，并探讨向动态认知逻辑的扩展。
Modal Logics that Bound the Circumference of Transitive Frames
本研究定义了约束传递框架循环长度的模态逻辑序列，证明其可判定与有限模型性质，拓展至自反框架得到S4扩展序列，给出拓扑语义解释并分析对应模态代数簇的结构。
Interpolation for the two-way modal mu-calculus
本文为双向模态 μ-演算引入非良基与循环证明演算，利用迹原子应用 Vardi 自动机证明其可靠性与完备性，并据此确立 Craig 插值与 Beth 可定义性。
In this article, we study logics of unknown truths and false beliefs under neighborhood semantics. We compare the relative expressivity of the two logics. It turns out that they are incomparable over various classes of neighborhood models, and the combination of the two logics are equally expressive as standard modal logic over any class of neighborhood models. We propose morphisms for each logic, which can help us explore the frame definability problem, show a general soundness and completeness result, and generalize some results in the literature. We axiomatize the two logics over various cl…
Simple tableaux for two expansions of Gödel modal logic
本文研究哥德尔模态逻辑的两种扩张KG_inv与KG_bl，通过采用具有限模型性质的替代语义，构建可显式构造反模型的统一表演算与判定算法，证明二者的可满足性与有效性问题为PSpace完全。
We further develop the paraconsistent Gödel modal logic. In this paper, we consider its version endowed with Kripke semantics on $[0,1]$-valued frames with two fuzzy relations $R^+$ and $R^-$ (degrees of trust in assertions and denials) and two valuations $v_1$ and $v_2$ (support of truth and support of falsity) linked with a De Morgan negation $\neg$. We demonstrate that it \emph{does not} extend Gödel modal logic and that $\Box$ and $\lozenge$ are not interdefinable. We also show that several important classes of frames are $\birelKGsquare$ definable (in particular, crisp, mono-relational, a…
Base-extension Semantics for Modal Logic
本文为经典命题模态系统 K、KT、K4 和 S4 开发了基扩展语义，以 $\square$ 为主算子，建立了可靠性与完备性定理及 $\square$ 与 $\lozenge$ 的对偶性，并指出该语义对欧几里得模态逻辑不完备。
Base-extension Semantics for Intuitionistic Modal Logics
本文为Simpson直觉主义模态逻辑建立基扩展语义，并证明其相对自然演绎系统的可靠性与完备性。
Combining swap structures: the case of Paradefinite Ivlev-like modal logics based on FDE
本文提出基于快照叠加的交换结构组合新方法，将四值Ivlev型模态系统与FDE的四值扩展IDM4结合，得到6种保守扩张的六值超有限模态逻辑，给出其希尔伯特公理系统与Prolog判定程序。
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