Jim de Groot
We prove a Goldblatt-Thomason theorem for dialgebraic intuitionistic logics, and instantiate it to Goldblatt-Thomason theorems for a wide variety of modal intuitionistic logics from the literature.
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Duality for Constructive Modal Logics: from Sahqlvist to Goldblatt-Thomason
本文研究了构造模态逻辑CK的语义学，建立代数与双关系语义的对偶性，并由此证明了萨尔奎维斯特类型的对应性和完备性结果，以及戈德布拉特-托马森类型的框架类可定义性定理。
We prove a uniform version of the Goldblatt-Thomason theorem for logics algebraically captured by normal lattice expansions (normal LE-logics).
Goldblat-Thomason Theorems for Fundamental (Modal) Logic
本文针对Holliday提出的基础逻辑的关系语义，证明了其Goldblatt-Thomason定理，给出基础框架类可公理化的充要条件，并将结果推广至基础模态逻辑。
This paper involves generalizing the Goldblatt-Thomason and the Lindström characterization theorems to first-order modal logic.
Definable Classes of Models and Frames in Bi-intuitionistic Logic
研究双直觉逻辑语言对框架和模型的表达能力，通过提供类似戈德布拉特 - 托马森定理的结果，结合先前成果，完整刻画了命题双直觉逻辑的表达能力。
The system of intuitionistic modal logic ${\bf IEL}^{-}$ was proposed by S. Artemov and T. Protopopescu as the intuitionistic version of belief logic \cite{Artemov}. We construct the modal lambda calculus which is Curry-Howard isomorphic to ${\bf IEL}^{-}$ as the type-theoretical representation of applicative computation widely known in functional programming. We also provide a categorical interpretation of this modal lambda calculus considering coalgebras associated with a monoidal functor on a cartesian closed category. Finally, we study Heyting algebras and locales with corresponding operat…
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…
In this paper we study the expressive power and definability for (extended) modal languages interpreted on topological spaces. We provide topological analogues of the van Benthem characterization theorem and the Goldblatt-Thomason definability theorem in terms of the well established first-order topological language $L_t$.
Fundamental Logic Through the Lens of Modality
本文利用模态逻辑，通过Gödel-McKinsey-Tarski和Goldblatt翻译，证明了基础逻辑与正交逻辑、直觉主义逻辑之间的完全忠实嵌入关系。
We investigate the role of coalgebraic predicate logic, a logic for neighborhood frames first proposed by Chang, in the study of monotonic modal logics. We prove analogues of the Goldblatt-Thomason Theorem and Fine's Canonicity Theorem for classes of monotonic neighborhood frames closed under elementary equivalence in coalgebraic predicate logic. The elementary equivalence here can be relativized to the classes of monotonic, quasi-filter, augmented quasi-filter, filter, or augmented filter neighborhood frames, respectively. The original, Kripke-semantic versions of the theorems follow as a spe…
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…
Fundamental Propositional Logic with Preconditional: Strong Completeness, Finite Model Property, and Modal Translations
研究带前提条件的基本命题逻辑，通过给出后承关系表示结合基本逻辑与前提条件，研究其扩展$\mathsf{T}$和$\mathsf{F}$，证明强完备性与有限模型性质，适配模态嵌入到正交$\mathsf{S4}$和直觉主义$\mathsf{KTB}$，给出新条件从句及框架构造。
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…
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