arXiv - CS - Logic in Computer Science最新文献_第7页

On Woolhouse's Cotton-Spinning Problem 关于伍尔豪斯的棉纺问题

arXiv - CS - Logic in Computer Science Pub Date : 2024-08-15 DOI: arxiv-2408.12623

Jan Friso Groote, Tim A. C. Willemse

引用次数: 0

Derivatives on Graphs for the Positive Calculus of Relations with Transitive Closure 具有传递封闭性的关系正微积分图上的导数

arXiv - CS - Logic in Computer Science Pub Date : 2024-08-15 DOI: arxiv-2408.08236

Yoshiki Nakamura

引用次数: 0

DeepSeek-Prover-V1.5: Harnessing Proof Assistant Feedback for Reinforcement Learning and Monte-Carlo Tree Search DeepSeek-Prover-V1.5：利用证明助手反馈进行强化学习和蒙特卡洛树搜索

arXiv - CS - Logic in Computer Science Pub Date : 2024-08-15 DOI: arxiv-2408.08152

Huajian Xin, Z. Z. Ren, Junxiao Song, Zhihong Shao, Wanjia Zhao, Haocheng Wang, Bo Liu, Liyue Zhang, Xuan Lu, Qiushi Du, Wenjun Gao, Qihao Zhu, Dejian Yang, Zhibin Gou, Z. F. Wu, Fuli Luo, Chong Ruan

{"title":"DeepSeek-Prover-V1.5: Harnessing Proof Assistant Feedback for Reinforcement Learning and Monte-Carlo Tree Search","authors":"Huajian Xin, Z. Z. Ren, Junxiao Song, Zhihong Shao, Wanjia Zhao, Haocheng Wang, Bo Liu, Liyue Zhang, Xuan Lu, Qiushi Du, Wenjun Gao, Qihao Zhu, Dejian Yang, Zhibin Gou, Z. F. Wu, Fuli Luo, Chong Ruan","doi":"arxiv-2408.08152","DOIUrl":"https://doi.org/arxiv-2408.08152","url":null,"abstract":"We introduce DeepSeek-Prover-V1.5, an open-source language model designed for\u0000theorem proving in Lean 4, which enhances DeepSeek-Prover-V1 by optimizing both\u0000training and inference processes. Pre-trained on DeepSeekMath-Base with\u0000specialization in formal mathematical languages, the model undergoes supervised\u0000fine-tuning using an enhanced formal theorem proving dataset derived from\u0000DeepSeek-Prover-V1. Further refinement is achieved through reinforcement\u0000learning from proof assistant feedback (RLPAF). Beyond the single-pass\u0000whole-proof generation approach of DeepSeek-Prover-V1, we propose RMaxTS, a\u0000variant of Monte-Carlo tree search that employs an intrinsic-reward-driven\u0000exploration strategy to generate diverse proof paths. DeepSeek-Prover-V1.5\u0000demonstrates significant improvements over DeepSeek-Prover-V1, achieving new\u0000state-of-the-art results on the test set of the high school level miniF2F\u0000benchmark ($63.5%$) and the undergraduate level ProofNet benchmark ($25.3%$).","PeriodicalId":501208,"journal":{"name":"arXiv - CS - Logic in Computer Science","volume":"41 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142192476","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Inductive Learning of Logical Theories with LLMs: A Complexity-graded Analysis 用 LLMs 归纳学习逻辑理论：完备性分级分析

arXiv - CS - Logic in Computer Science Pub Date : 2024-08-15 DOI: arxiv-2408.16779

João Pedro Gandarela, Danilo S. Carvalho, André Freitas

{"title":"Inductive Learning of Logical Theories with LLMs: A Complexity-graded Analysis","authors":"João Pedro Gandarela, Danilo S. Carvalho, André Freitas","doi":"arxiv-2408.16779","DOIUrl":"https://doi.org/arxiv-2408.16779","url":null,"abstract":"This work presents a novel systematic methodology to analyse the capabilities\u0000and limitations of Large Language Models (LLMs) with feedback from a formal\u0000inference engine, on logic theory induction. The analysis is complexity-graded\u0000w.r.t. rule dependency structure, allowing quantification of specific inference\u0000challenges on LLM performance. Integrating LLMs with formal methods is a\u0000promising frontier in the Natural Language Processing field, as an important\u0000avenue for improving model inference control and explainability. In particular,\u0000inductive learning over complex sets of facts and rules, poses unique\u0000challenges for current autoregressive models, as they lack explicit symbolic\u0000grounding. While they can be complemented by formal systems, the properties\u0000delivered by LLMs regarding inductive learning, are not well understood and\u0000quantified. Empirical results indicate that the largest LLMs can achieve\u0000competitive results against a SOTA Inductive Logic Programming (ILP) system\u0000baseline, but also that tracking long predicate relationship chains is a more\u0000difficult obstacle than theory complexity for the LLMs.","PeriodicalId":501208,"journal":{"name":"arXiv - CS - Logic in Computer Science","volume":"131 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142192484","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Optimising Dynamic Traffic Distribution for Urban Networks with Answer Set Programming 利用答案集编程优化城市网络的动态流量分配

arXiv - CS - Logic in Computer Science Pub Date : 2024-08-14 DOI: arxiv-2408.07521

Matteo Cardellini, Carmine Dodaro, Marco Maratea, Mauro Vallati

引用次数: 0

Relational Graph Convolutional Networks Do Not Learn Sound Rules 关系图卷积网络无法学习合理规则

arXiv - CS - Logic in Computer Science Pub Date : 2024-08-14 DOI: arxiv-2408.10261

Matthew Morris, David J. Tena Cucala, Bernardo Cuenca Grau, Ian Horrocks

{"title":"Relational Graph Convolutional Networks Do Not Learn Sound Rules","authors":"Matthew Morris, David J. Tena Cucala, Bernardo Cuenca Grau, Ian Horrocks","doi":"arxiv-2408.10261","DOIUrl":"https://doi.org/arxiv-2408.10261","url":null,"abstract":"Graph neural networks (GNNs) are frequently used to predict missing facts in\u0000knowledge graphs (KGs). Motivated by the lack of explainability for the outputs\u0000of these models, recent work has aimed to explain their predictions using\u0000Datalog, a widely used logic-based formalism. However, such work has been\u0000restricted to certain subclasses of GNNs. In this paper, we consider one of the\u0000most popular GNN architectures for KGs, R-GCN, and we provide two methods to\u0000extract rules that explain its predictions and are sound, in the sense that\u0000each fact derived by the rules is also predicted by the GNN, for any input\u0000dataset. Furthermore, we provide a method that can verify that certain classes\u0000of Datalog rules are not sound for the R-GCN. In our experiments, we train\u0000R-GCNs on KG completion benchmarks, and we are able to verify that no Datalog\u0000rule is sound for these models, even though the models often obtain high to\u0000near-perfect accuracy. This raises some concerns about the ability of R-GCN\u0000models to generalise and about the explainability of their predictions. We\u0000further provide two variations to the training paradigm of R-GCN that encourage\u0000it to learn sound rules and find a trade-off between model accuracy and the\u0000number of learned sound rules.","PeriodicalId":501208,"journal":{"name":"arXiv - CS - Logic in Computer Science","volume":"19 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142224944","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

On-the-fly Synthesis for LTL over Finite Traces: An Efficient Approach that Counts 有限轨迹上 LTL 的即时合成：一种高效的计算方法

arXiv - CS - Logic in Computer Science Pub Date : 2024-08-14 DOI: arxiv-2408.07324

Shengping Xiao, Yongkang Li, Shufang Zhu, Jun Sun, Jianwen Li, Geguang Pu, Moshe Y. Vardi

{"title":"On-the-fly Synthesis for LTL over Finite Traces: An Efficient Approach that Counts","authors":"Shengping Xiao, Yongkang Li, Shufang Zhu, Jun Sun, Jianwen Li, Geguang Pu, Moshe Y. Vardi","doi":"arxiv-2408.07324","DOIUrl":"https://doi.org/arxiv-2408.07324","url":null,"abstract":"We present an on-the-fly synthesis framework for Linear Temporal Logic over\u0000finite traces (LTLf) based on top-down deterministic automata construction.\u0000Existing approaches rely on constructing a complete Deterministic Finite\u0000Automaton (DFA) corresponding to the LTLf specification, a process with doubly\u0000exponential complexity relative to the formula size in the worst case. In this\u0000case, the synthesis procedure cannot be conducted until the entire DFA is\u0000constructed. This inefficiency is the main bottleneck of existing approaches.\u0000To address this challenge, we first present a method for converting LTLf into\u0000Transition-based DFA (TDFA) by directly leveraging LTLf semantics,\u0000incorporating intermediate results as direct components of the final automaton\u0000to enable parallelized synthesis and automata construction. We then explore the\u0000relationship between LTLf synthesis and TDFA games and subsequently develop an\u0000algorithm for performing LTLf synthesis using on-the-fly TDFA game solving.\u0000This algorithm traverses the state space in a global forward manner combined\u0000with a local backward method, along with the detection of strongly connected\u0000components. Moreover, we introduce two optimization techniques -- model-guided\u0000synthesis and state entailment -- to enhance the practical efficiency of our\u0000approach. Experimental results demonstrate that our on-the-fly approach\u0000achieves the best performance on the tested benchmarks and effectively\u0000complements existing tools and approaches.","PeriodicalId":501208,"journal":{"name":"arXiv - CS - Logic in Computer Science","volume":"75 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142192483","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Fast Inference for Probabilistic Answer Set Programs via the Residual Program 通过残差程序快速推断概率答案集程序

arXiv - CS - Logic in Computer Science Pub Date : 2024-08-14 DOI: arxiv-2408.07524

Damiano Azzolini, Fabrizio Riguzzi

引用次数: 0

Model Counting in the Wild 野外模型计数

arXiv - CS - Logic in Computer Science Pub Date : 2024-08-13 DOI: arxiv-2408.07059

Arijit Shaw, Kuldeep S. Meel

{"title":"Model Counting in the Wild","authors":"Arijit Shaw, Kuldeep S. Meel","doi":"arxiv-2408.07059","DOIUrl":"https://doi.org/arxiv-2408.07059","url":null,"abstract":"Model counting is a fundamental problem in automated reasoning with\u0000applications in probabilistic inference, network reliability, neural network\u0000verification, and more. Although model counting is computationally intractable\u0000from a theoretical perspective due to its #P-completeness, the past decade has\u0000seen significant progress in developing state-of-the-art model counters to\u0000address scalability challenges. In this work, we conduct a rigorous assessment of the scalability of model\u0000counters in the wild. To this end, we surveyed 11 application domains and\u0000collected an aggregate of 2262 benchmarks from these domains. We then evaluated\u0000six state-of-the-art model counters on these instances to assess scalability\u0000and runtime performance. Our empirical evaluation demonstrates that the performance of model counters\u0000varies significantly across different application domains, underscoring the\u0000need for careful selection by the end user. Additionally, we investigated the\u0000behavior of different counters with respect to two parameters suggested by the\u0000model counting community, finding only a weak correlation. Our analysis\u0000highlights the challenges and opportunities for portfolio-based approaches in\u0000model counting.","PeriodicalId":501208,"journal":{"name":"arXiv - CS - Logic in Computer Science","volume":"163 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142192486","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Annotated Dependency Pairs for Full Almost-Sure Termination of Probabilistic Term Rewriting 注释依赖对，实现概率术语重写的完全几乎确定终止

arXiv - CS - Logic in Computer Science Pub Date : 2024-08-13 DOI: arxiv-2408.06768

Jan-Christoph Kassing, Jürgen Giesl

引用次数: 0