Formal Verification of Proofs from Automated Theorem Provers for Higher-Order Logic
研究解决了自动定理证明器生成证明的验证问题，通过在Dedukti框架下开发一种通用方法来编码规则和证明步骤，并应用于高阶逻辑EP演算。
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Abstract computation over first-order structures. Extras: From programs to decision trees I
本文通过引入程序路径和转换系统来分析BSS RAMs在初等结构上的决策过程，并提供算法枚举有限的程序路径。
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Nonparametric Testing of Spatial Dependence in 2D and 3D Random Fields
This paper addresses the nonparametric testing of spatial dependence in two- and three-dimensional random fields. The proposed method maps spatial grid data onto a one-dimensional sequence via space-filling curves—specifically Hilbert and generalized Gilbert curves—and subsequently applies ordinal pattern-based statistical tests to detect dependence structures. Its key contribution lies in the first integration of locality-preserving space-filling curve mappings with nonparametric ordinal pattern analysis, thereby overcoming dimensional and grid-shape constraints inherent in conventional approaches. The framework supports arbitrary-size regular or irregular grids and extends naturally to higher dimensions. Experimental results demonstrate that the method is robust, computationally efficient, and achieves superior detection accuracy compared to existing spatial ordinal-pattern-based techniques, while maintaining conceptual simplicity and ease of implementation.
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Global Permutation Entropy
Traditional permutation entropy (PE) considers only contiguous subsequences, neglecting non-contiguous patterns and thus inadequately characterizing time-series complexity. To address this limitation, we propose Global Permutation Entropy (GPE), a novel complexity measure for real-valued time series. GPE systematically incorporates *all* length-𝑘 subsequences—regardless of temporal contiguity—thereby capturing the full combinatorial structure of ordinal patterns beyond local continuity constraints. Leveraging an efficient algorithm for extracting the complete permutation spectrum and quantifying it via Shannon entropy, GPE enables unbiased characterization of deep structural dynamics. Extensive evaluation on synthetic benchmarks demonstrates that GPE exhibits markedly enhanced sensitivity to dynamical transitions compared to standard PE. An open-source Julia package implementing GPE is publicly available.
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A Reduction of Input/Output Logics to SAT
This work addresses the challenge of automated reasoning for conditional norms in input/output (I/O) logic. We propose a novel SAT-based reduction framework that, unlike conventional approaches requiring truth assignments to normative statements, systematically encodes I/O conditional inference problems into propositional logic formulas solvable by off-the-shelf SAT solvers. Based on this framework, we implement rio, a prototype symbolic reasoning system supporting multiple I/O logics—including basic, simple-minded, and through variants. Experimental evaluation demonstrates that rio achieves both strong expressive power and competitive computational efficiency, successfully verifying several canonical normative examples. To our knowledge, this is the first scalable, formally verifiable automation framework for non-truth-functional normative reasoning.
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Formal Verification of Proofs from Automated Theorem Provers for Higher-Order Logic
研究解决了自动定理证明器生成证明的验证问题，通过在Dedukti框架下开发一种通用方法来编码规则和证明步骤，并应用于高阶逻辑EP演算。
0 citationsRead paper
Abstract computation over first-order structures. Extras: From programs to decision trees I
本文通过引入程序路径和转换系统来分析BSS RAMs在初等结构上的决策过程，并提供算法枚举有限的程序路径。
0 citationsRead paper
Nonparametric Testing of Spatial Dependence in 2D and 3D Random Fields
This paper addresses the nonparametric testing of spatial dependence in two- and three-dimensional random fields. The proposed method maps spatial grid data onto a one-dimensional sequence via space-filling curves—specifically Hilbert and generalized Gilbert curves—and subsequently applies ordinal pattern-based statistical tests to detect dependence structures. Its key contribution lies in the first integration of locality-preserving space-filling curve mappings with nonparametric ordinal pattern analysis, thereby overcoming dimensional and grid-shape constraints inherent in conventional approaches. The framework supports arbitrary-size regular or irregular grids and extends naturally to higher dimensions. Experimental results demonstrate that the method is robust, computationally efficient, and achieves superior detection accuracy compared to existing spatial ordinal-pattern-based techniques, while maintaining conceptual simplicity and ease of implementation.
0 citationsRead paper
Global Permutation Entropy
Traditional permutation entropy (PE) considers only contiguous subsequences, neglecting non-contiguous patterns and thus inadequately characterizing time-series complexity. To address this limitation, we propose Global Permutation Entropy (GPE), a novel complexity measure for real-valued time series. GPE systematically incorporates *all* length-𝑘 subsequences—regardless of temporal contiguity—thereby capturing the full combinatorial structure of ordinal patterns beyond local continuity constraints. Leveraging an efficient algorithm for extracting the complete permutation spectrum and quantifying it via Shannon entropy, GPE enables unbiased characterization of deep structural dynamics. Extensive evaluation on synthetic benchmarks demonstrates that GPE exhibits markedly enhanced sensitivity to dynamical transitions compared to standard PE. An open-source Julia package implementing GPE is publicly available.
0 citationsRead paper
A Reduction of Input/Output Logics to SAT
This work addresses the challenge of automated reasoning for conditional norms in input/output (I/O) logic. We propose a novel SAT-based reduction framework that, unlike conventional approaches requiring truth assignments to normative statements, systematically encodes I/O conditional inference problems into propositional logic formulas solvable by off-the-shelf SAT solvers. Based on this framework, we implement rio, a prototype symbolic reasoning system supporting multiple I/O logics—including basic, simple-minded, and through variants. Experimental evaluation demonstrates that rio achieves both strong expressive power and competitive computational efficiency, successfully verifying several canonical normative examples. To our knowledge, this is the first scalable, formally verifiable automation framework for non-truth-functional normative reasoning.
0 citationsRead paper