First-Order Modal Logic: Frame Definability and Lindström Theorems
英文摘要：
This paper involves generalizing the Goldblatt-Thomason and the Lindström characterization theorems to first-order modal logic.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
相关论文
Modal definability based on Łukasiewicz validity relations
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.
math.LO
拓扑学的模态语言：表达性和可定义性
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。
math.LO
The Lindstrom's Characterizability of Abstract Logic Systems for Analytic Structures Based on Measures
In 1969, Per Lindstrom proved his celebrated theorem characterising the first-order logic and established criteria for the first-order definability of formal theories for discrete structures. K. J. Barwise, S. Shelah, J. Vaananen and others extended Lindstrom's characterizability program to classes of infinitary logic systems, including a recent paper by M. Dzamonja and J. Vaananen on Karp's chain logic, which satisfies interpolation, undefinability of well-order, and is maximal in the class of logic systems with these properties. The novelty of the chain logic is in its new definition of sati…
cs.CLcs.LOmath.LO
Characterizing Relative Frame Definability in Team Semantics via the Universal Modality
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…
math.LO
Frame definability in finitely-valued modal logics
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…
math.LO
克里普克真理论中的模态可定义性
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。
math.LO
更多相关论文收起更多论文
欧几里得模态逻辑中的模态可定义性
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。
cs.LOmath.LO
Characterising Modal Definability of Team-Based Logics via the Universal Modality
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…
cs.LOmath.LO
模态一阶片段的特征化和可定义性
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。
cs.LOmath.LO
二阶算术中的框架可定义性
Frame definability in second-order arithmetic
Mathematical Institute, Tohoku University（东北大学数学研究所）
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。
math.LO
Recursive enumerability and elementary frame definability in predicate modal logic
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…
cs.LOmath.LO
Maximality of bi-intuitionistic propositional logic
In the style of Lindström's theorem for classical first-order logic, this article characterizes propositional bi-intuitionistic logic as the maximal (with respect to expressive power) abstract logic satisfying a certain form of compactness, the Tarski union property and preservation under bi-asimulations. Since bi-intuitionistic logic introduces new complexities in the intuitionistic setting by adding the analogue of a backwards looking modality, the present paper constitutes a non-trivial modification of previous work done by the authors for intuitionistic logic in: G. Badia and G. Olkhovikov…
math.LO
有序框架上基本模态-时态语言中功能性质的可定义性
Definability of Functional Properties in the Basic Modal-Temporal Language over Ordered Frames
University of Malaga（马拉加大学）
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。
cs.LOmath.LO
微分模态逻辑的差分模态
Derivational modal logics with the difference modality
在这一章中，我们用导模态和差模态研究了组合语言中拓扑空间的模态逻辑。我们给出公理化和证明以下类的完备性：所有的空间，$T_1$ -空间，稠密的本身空间，一个零维稠密的本身可分度量空间，$R^n$ $(n\ge 2)$。我们还讨论了语言之间的相关性与不同的组合的拓扑，派生，普遍和差异形式的可定义性。
math.LO
A dichotomy for some elementarily generated modal logics
In this paper we consider the normal modal logics of elementary classes defined by first-order formulas of the form $\forall x_0 \exists x_1 \dots \exists x_n \bigwedge x_i R_λx_j$. We prove that many properties of these logics, such as finite axiomatisability, elementarity, axiomatisability by a set of canonical formulas or by a single generalised Sahlqvist formula, together with modal definability of the initial formula, either simultaneously hold or simultaneously do not hold.
math.LO
构造模态逻辑的对偶性：从萨尔奎维斯特到戈德布拉特-托马森
Duality for Constructive Modal Logics: from Sahqlvist to Goldblatt-Thomason
Mathematical Institute, University of Bern（伯尔尼大学数学研究所）；School of Computer Science, University of Birimingham（伯明翰大学计算机学院）；School of Computing, The Australian National University（澳大利亚国立大学计算学院）
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。
cs.LOmath.LO
Kracht定理在广义Sahlqvist公式上的推广
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.
math.LO
通过逻辑范畴的一阶模态逻辑
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。
cs.LOmath.LO
动态概率逻辑：公理化与可定义性
Dynamic Probability Logics: Axiomatization & Definability
本文引入动态概率逻辑DPL及其无穷扩张，给出希尔伯特式公理化并证明强完全性，进而研究保测、遍历、混合等性质的可定义性，并证明带初始分布的马尔可夫过程的平稳性、不变性、不可约性和常返性在无穷概率逻辑中可定义。
math.LO
四个直觉主义模态连接词
Four intuitionistic modal connectives
Institut de recherche en informatique de Toulouse（图卢兹信息技术研究所）；CNRS – Toulouse INP – Université de Toulouse（法国国家科学研究中心-图卢兹国立理工学院-图卢兹大学）
本文引入基于Prenosil和Wijesekera两种风格的菱形及其对偶方框的直觉主义模态逻辑，分析框架类的模态可定义性、完全公理化，并证明最小直觉主义模态逻辑的可判定性。
cs.LOmath.LO
A Finitely Supported Frame for the Turing Schmerl Calculus
In arXiv:1604.08705 we introduced the propositional modal logic $\textbf{TSC}$ (which stands for Turing Schmerl Calculus) which adequately describes the provable interrelations between different kinds of Turing progressions. In arXiv:1709.04715 we defined a model $\mathcal{J}$ which is proven to be a universal model for $\textbf{TSC}$ based on the intensively studied Ignatiev's universal model for the closed fragment of $\textbf{GLP}$ (Gödel Löb's polymodal provability logic). In the current paper we present a new universal frame $\mathcal{H}$, which is a slight modification of $\mathcal{J}$, …
math.LO
k元逻辑中的一类广义量化词
A Class of Generalised Quantifiers for k-Variable Logics
本文提出了一种k元逻辑中的一类广义量化词，展示了其在多种逻辑系统中的应用，并通过双射关系和Lindström定理证明了其表达能力的唯一性。
math.LO
模态逻辑中的可靠性与完全性导入
Importing soundness and completeness in modal logics
Scuola Normale Superiore di Pisa（比萨高等师范学院）
提出从表达能力更强的模态语言向较弱语言传递可靠性与完全性的通用策略，统一了多种算子可定义性概念，并通过语义不敏感性和保真翻译实现。
cs.LOmath.LO
凸团队逻辑
Convex Team Logics
University of Padua（帕多瓦大学）；University of Amsterdam（阿姆斯特丹大学）
本文证明凸命题和模态团队逻辑的表达完备性，引入多种完备逻辑，并回答经典命题逻辑加非空原子NE的开放问题，推广统一定义性概念。
math.LO
模态逻辑的可能性框架与力迫
Possibility Frames and Forcing for Modal Logic
University of California, Berkeley（加州大学伯克利分校）
该文基于部分“可能性”发展正规模态逻辑模型理论，其可能性框架基于带可达关系的偏序集，公式解释为正则开集，标准世界框架是其特殊情况，还开展了对偶、可定义性/对应及完全性理论的初步研究。
cs.LOmath.LO
模态逻辑 K、GL 和 iSL 的机械化一致插值
Mechanised uniform interpolation for modal logics K, GL, and iSL
本文在 Coq 中机械化计算并证明了模态逻辑 K、GL 和 iSL 的命题量词可定义性（一致插值），完善了 GL 的现有证明，实现了 iSL 的首次证明论构造，并提供了经过验证的计算程序。
cs.LOmath.LO
约束传递框架周长的模态逻辑
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。
math.LO
双向模态 μ-演算的插值
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。
cs.LOmath.LO
双直觉逻辑中模型和框架的可定义类
Definable Classes of Models and Frames in Bi-intuitionistic Logic
University of Queensland（昆士兰大学）；Jagiellonian University（雅盖隆大学）；Ruhr University Bochum（鲁尔大学波鸿分校）
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。
math.LO
嵌套序列为直觉多模逻辑：切消和Lyndon插值
Nested Sequents for Intuitionistic Multi-Modal Logics: Cut-Elimination and Lyndon Interpolation
本文提出了一种单结论嵌套序列表演算，用于直觉多模逻辑，并证明了切消性和Lyndon插值性质。
cs.LOmath.LO
命题量化模态逻辑的若干一般性完全性结果
Some General Completeness Results for Propositionally Quantified Modal Logics
本文研究命题量化模态逻辑的完全性问题，证明含Barcan模式的正规逻辑在可量化一般框架下强完全，给出公式真值在框架过渡中保持的充分条件，并基于有限多样性得到一类Kripke完全的逻辑及欧几里得框架逻辑的有限公理化。
cs.LOmath.LO
Notes on neighborhood semantics for logics of unknown truths and false beliefs
School of Humanities, University of Chinese Academy of Sciences（中国科学院大学人文学院）
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…
cs.AImath.LO
Fitchean无知与一阶无知：一种邻域视角
Fitchean Ignorance and First-order Ignorance: A Neighborhood Look
本文在邻域语义学下将Fitchean无知和一阶无知视为原始模态词进行研究，提供表达力、框架可定义性及公理化等模型论结果，并通过交集语义扩展至公开宣告的动态情形。
cs.LOmath.LO
