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A Reliable Common-Sense Reasoning Socialbot Built Using LLMs and Goal-Directed ASP 利用 LLM 和目标导向 ASP 构建可靠的常识推理社交机器人
Pub Date : 2024-07-26 DOI: arxiv-2407.18498
Yankai Zeng, Abhiramon Rajashekharan, Kinjal Basu, Huaduo Wang, Joaquín Arias, Gopal Gupta
The development of large language models (LLMs), such as GPT, has enabled theconstruction of several socialbots, like ChatGPT, that are receiving a lot ofattention for their ability to simulate a human conversation. However, theconversation is not guided by a goal and is hard to control. In addition,because LLMs rely more on pattern recognition than deductive reasoning, theycan give confusing answers and have difficulty integrating multiple topics intoa cohesive response. These limitations often lead the LLM to deviate from themain topic to keep the conversation interesting. We propose AutoCompanion, asocialbot that uses an LLM model to translate natural language into predicates(and vice versa) and employs commonsense reasoning based on Answer SetProgramming (ASP) to hold a social conversation with a human. In particular, werely on s(CASP), a goal-directed implementation of ASP as the backend. Thispaper presents the framework design and how an LLM is used to parse usermessages and generate a response from the s(CASP) engine output. To validateour proposal, we describe (real) conversations in which the chatbot's goal isto keep the user entertained by talking about movies and books, and s(CASP)ensures (i) correctness of answers, (ii) coherence (and precision) during theconversation, which it dynamically regulates to achieve its specific purpose,and (iii) no deviation from the main topic.
大型语言模型(LLMs)(如 GPT)的发展使得一些社交机器人(如 ChatGPT)的构建成为可能,这些机器人因其模拟人类对话的能力而备受关注。然而,对话没有目标引导,难以控制。此外,由于 LLM 更多地依赖于模式识别而非演绎推理,因此它们给出的答案可能令人困惑,而且很难将多个话题整合为一个连贯的回答。这些限制往往会导致 LLM 偏离主要话题,以保持对话的趣味性。我们提出的 AutoCompanion 是一种社交机器人,它使用 LLM 模型将自然语言翻译成谓词(反之亦然),并采用基于答案集编程(ASP)的常识推理与人类进行社交对话。特别是,我们将以 S(CASP)--ASP 的目标导向实现--作为后端。本文介绍了该框架的设计,以及如何使用 LLM 来解析用户信息并从 s(CASP) 引擎输出中生成响应。为了验证我们的提议,我们描述了(真实的)对话,在对话中,聊天机器人的目标是通过谈论电影和书籍让用户保持娱乐,而 s(CASP) 则确保:(i) 答案的正确性;(ii) 对话过程中的连贯性(和精确性),它可以动态调节以实现其特定目的;(iii) 不偏离主要话题。
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引用次数: 0
Repairing Networks of $mathcal{EL_perp}$ Ontologies using Weakening and Completing -- Extended version 使用弱化和补全修复 $mathcal{EL_perp}$ 本体网络 -- 扩展版
Pub Date : 2024-07-26 DOI: arxiv-2407.18848
Ying Li, Patrick Lambrix
The quality of ontologies and their alignments is crucial for developinghigh-quality semantics-based applications. Traditional debugging techniquesrepair ontology networks by removing unwanted axioms and mappings, but maythereby remove consequences that are correct in the domain of the ontologynetwork. In this paper we propose a framework for repairing ontology networksthat deals with this issue. It defines basic operations such as debugging,weakening and completing. Further, it defines combination operators thatreflect choices in how and when to use the basic operators, as well as choicesregarding the autonomy level of the ontologies and alignments in the ontologynetwork. We show the influence of the combination operators on the quality ofthe repaired network and present an implemented tool. By using our frameworktogether with existing algorithms for debugging, weakening and completing, weessentially provide a blueprint for extending previous work and systems.
本体及其排列的质量对于开发基于语义的高质量应用至关重要。传统的调试技术通过删除不需要的公理和映射来修复本体网络,但可能会因此删除本体网络领域中正确的结果。在本文中,我们提出了一个修复本体网络的框架来解决这个问题。它定义了调试、弱化和补全等基本操作。此外,它还定义了组合运算符,这些运算符反映了对如何以及何时使用基本运算符的选择,以及对本体网络中本体和配准的自治级别的选择。我们展示了组合运算符对修复网络质量的影响,并介绍了一个实现工具。通过将我们的框架与现有的调试、弱化和补全算法结合使用,我们基本上为扩展以前的工作和系统提供了一个蓝图。
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引用次数: 0
Supercritical Size-Width Tree-Like Resolution Trade-Offs for Graph Isomorphism 图形同构的超临界大小-宽度树状分辨率权衡
Pub Date : 2024-07-25 DOI: arxiv-2407.17947
Christoph Berkholz, Moritz Lichter, Harry Vinall-Smeeth
We study the refutation complexity of graph isomorphism in the tree-likeresolution calculus. Tor'an and W"orz (TOCL 2023) showed that there is aresolution refutation of narrow width $k$ for two graphs if and only if theycan be distinguished in ($k+1$)-variable first-order logic (FO$^{k+1}$) andhence by a count-free variant of the $k$-dimensional Weisfeiler-Lemanalgorithm. While DAG-like narrow width $k$ resolution refutations have size atmost $n^k$, tree-like refutations may be much larger. We show that there aregraphs of order n, whose isomorphism can be refuted in narrow width $k$ butonly in tree-like size $2^{Omega(n^{k/2})}$. This is a supercritical trade-offwhere bounding one parameter (the narrow width) causes the other parameter (thesize) to grow above its worst case. The size lower bound is super-exponentialin the formula size and improves a related supercritical width versus tree-likesize trade-off by Razborov (JACM 2016). To prove our result, we develop a newvariant of the $k$-pebble EF-game for FO$^k$ to reason about tree-likerefutation size in a similar way as the Prover-Delayer games in proofcomplexity. We analyze this game on a modified variant of the compressed CFIgraphs introduced by Grohe, Lichter, Neuen, and Schweitzer (FOCS 2023). Using arecent improved robust compressed CFI construction of Janett, Nordstr"om, andPang (unpublished manuscript), we obtain a similar bound for width $k$ (insteadof the stronger but less common narrow width) and make the result more robust.
我们研究了树状解析微积分中图同构的驳斥复杂性。Tor'an和W"orz(TOCL 2023)的研究表明,当且仅当两个图可以在($k+1$)变量一阶逻辑(FO$^{k+1}$)中区分,并因此可以通过$k$维Weisfeiler-Leman算法的无计数变体来区分时,两个图才存在窄宽度为$k$的解析驳斥。类似于 DAG 的窄宽 $k$ 解析驳斥的大小最多为 $n^k$,而类似于树的驳斥则可能大得多。我们证明,有一些阶数为 n 的图,其同构可以在窄宽 $k$ 的情况下被驳倒,但只能在树状大小为 $2^{Omega(n^{k/2})}$ 的情况下被驳倒。这是一种超临界权衡,即限制一个参数(窄宽)会导致另一个参数(大小)的增长超过其最坏情况。大小下限是公式大小的超指数,并改进了 Razborov(JACM 2016)提出的相关超临界宽度与树形大小权衡。为了证明我们的结果,我们为 FO$^k$ 开发了一个 $k$-pebble EF 游戏的新变量,以类似于证明复杂性中的 Prover-Delayer 游戏的方式推理树状异构大小。我们在 Grohe、Lichter、Neuen 和 Schweitzer(FOCS 2023)提出的压缩 CFI 图的改进变体上分析了这一博弈。通过使用 Janett、Nordstr"om 和 Pang(未发表手稿)最近改进的稳健压缩 CFI 结构,我们得到了宽度 $k$ 的类似约束(而不是更强但不常见的窄宽度),并使结果更加稳健。
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引用次数: 0
C2P: Featuring Large Language Models with Causal Reasoning C2P:具有因果推理功能的大型语言模型
Pub Date : 2024-07-25 DOI: arxiv-2407.18069
Abdolmahdi Bagheri, Matin Alinejad, Kevin Bello, Alireza Akhondi-Asl
Causal reasoning is the primary bottleneck that Large Language Models (LLMs)must overcome to attain human-level intelligence. To address this, we introducethe Causal Chain of Prompting (C2P) as the first reasoning framework thatequips current LLMs with causal reasoning capabilities. C2P operatesautonomously, avoiding reliance on external tools or modules during both thecausal learning and reasoning phases, and can be seamlessly implemented duringthe training or fine-tuning of LLMs. Experimental results across variousbenchmark datasets demonstrate a significant improvement in causal learning andsubsequent reasoning accuracy of LLMs. We illustrate how C2P enhances LLMs'ability to causally reason in real-world scenarios, addressing complex problemsin fields such as healthcare, medicine, economics, education, social sciences,environmental science, and marketing. With few-shot learning, GPT-4 Turbo usingC2P with as few as six examples achieves significant performance improvements,boasting over a 33% increase in reasoning accuracy over the moststate-of-the-art LLMs, which perform nearly randomly in similar circumstances.This demonstrates the transformative potential of integrating C2P into LLMtraining or fine-tuning processes, thereby empowering these models withadvanced causal reasoning capabilities.
因果推理是大型语言模型(LLM)达到人类智能水平必须克服的主要瓶颈。为了解决这个问题,我们引入了因果链提示(C2P)作为第一个推理框架,为当前的 LLM 赋予因果推理能力。C2P 可自主运行,避免在因果学习和推理阶段依赖外部工具或模块,并可在 LLM 的训练或微调过程中无缝实施。各种基准数据集的实验结果表明,LLM 的因果学习和后续推理的准确性有了显著提高。我们展示了 C2P 如何增强 LLM 在现实世界场景中的因果推理能力,从而解决医疗保健、医学、经济学、教育、社会科学、环境科学和市场营销等领域的复杂问题。与最先进的 LLM 相比,GPT-4 Turbo 的推理准确率提高了 33% 以上,而最先进的 LLM 在类似情况下的表现几乎是随机的。
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引用次数: 0
On Polynomial-Time Decidability of k-Negations Fragments of First-Order Theories 论一阶理论 k 否定片段的多项式时间可决性
Pub Date : 2024-07-25 DOI: arxiv-2407.18420
Christoph Haase, Alessio Mansutti, Amaury Pouly
This paper introduces a generic framework that provides sufficient conditionsfor guaranteeing polynomial-time decidability of fixed-negation fragments offirst-order theories that adhere to certain fixed-parameter tractabilityrequirements. It enables deciding sentences of such theories with arbitraryexistential quantification, conjunction and a fixed number of negation symbolsin polynomial time. It was recently shown by Nguyen and Pak [SIAM J. Comput.51(2): 1--31 (2022)] that an even more restricted such fragment of Presburgerarithmetic (the first-order theory of the integers with addition and order) isNP-hard. In contrast, by application of our framework, we show that the fixednegation fragment of weak Presburger arithmetic, which drops the order relationfrom Presburger arithmetic in favour of equality, is decidable in polynomialtime.
本文介绍了一个通用框架,它为保证一阶理论的固定否定片段的多项式时间可解性提供了充分条件,这些一阶理论遵守了某些固定参数的可操作性要求。它能在多项式时间内判定具有任意存在定量、连词和固定数量否定符号的这类理论的句子。最近,Nguyen 和 Pak [SIAM J. Comput.51(2): 1--31 (2022)]证明,Presburgerarithmetic(带加法和阶的整数一阶理论)的一个更为有限的片段是 NP-困难的。与此相反,通过应用我们的框架,我们证明了弱普雷斯伯格算术的固定否定片段在多项式时间内是可解的。
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引用次数: 0
Pruning Boolean d-DNNF Circuits Through Tseitin-Awareness 通过 Tseitin-Awareness 修剪布尔 d-DNNF 电路
Pub Date : 2024-07-25 DOI: arxiv-2407.17951
Vincent Derkinderen
Boolean circuits in d-DNNF form enable tractable probabilistic inference.However, as a key insight of this work, we show that commonly used d-DNNFcompilation approaches introduce irrelevant subcircuits. We call thesesubcircuits Tseitin artifacts, as they are introduced due to the Tseitintransformation step -- a well-established procedure to transform any circuitinto the CNF format required by several d-DNNF knowledge compilers. We discusshow to detect and remove both Tseitin variables and Tseitin artifacts, leadingto more succinct circuits. We empirically observe an average size reduction of77.5% when removing both Tseitin variables and artifacts. The additionalpruning of Tseitin artifacts reduces the size by 22.2% on average. Thissignificantly improves downstream tasks that benefit from a more succinctcircuit, e.g., probabilistic inference tasks.
d-DNNF形式的布尔电路可以实现可控的概率推理。然而,作为这项工作的一个关键见解,我们表明,常用的d-DNNF编译方法会引入无关的子电路。我们将这些子电路称为 Tseitin 人工制品,因为它们是由于 Tseitintransformation 步骤而引入的--该步骤是将任何电路转换为若干 d-DNNF 知识编译器所需的 CNF 格式的既定程序。我们讨论了如何检测并移除 Tseitin 变量和 Tseitin 伪影,从而实现更简洁的电路。我们根据经验观察到,在同时移除 Tseitin 变量和假象时,电路的平均大小减少了 77.5%。对 Tseitin 伪变量的额外剪枝平均减少了 22.2%。这显著改善了受益于更简洁电路的下游任务,例如概率推理任务。
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引用次数: 0
The Existential Theory of the Reals as a Complexity Class: A Compendium 作为复杂性类别的实数存在论:简编
Pub Date : 2024-07-25 DOI: arxiv-2407.18006
Marcus Schaefer, Jean Cardinal, Tillmann Miltzow
We survey the complexity class $exists mathbb{R}$, which captures thecomplexity of deciding the existential theory of the reals. The class $existsmathbb{R}$ has roots in two different traditions, one based on theBlum-Shub-Smale model of real computation, and the other following work byMn"{e}v and Shor on the universality of realization spaces of orientedmatroids. Over the years the number of problems for which $exists mathbb{R}$rather than NP has turned out to be the proper way of measuring theircomplexity has grown, particularly in the fields of computational geometry,graph drawing, game theory, and some areas in logic and algebra. $existsmathbb{R}$ has also started appearing in the context of machine learning,Markov decision processes, and probabilistic reasoning. We have aimed at collecting a comprehensive compendium of problems completeand hard for $exists mathbb{R}$, as well as a long list of open problems. Thecompendium is presented in the third part of our survey; a tour through thecompendium and the areas it touches on makes up the second part. The first partintroduces the reader to the existential theory of the reals as a complexityclass, discussing its history, motivation and prospects as well as sometechnical aspects.
我们研究了复杂性类$exists mathbb{R}$,它捕捉了决定实数存在论的复杂性。$exists/mathbb{R}$类起源于两个不同的传统,一个是基于实数计算的布鲁姆-舒布-斯马尔模型,另一个是在姆恩(Mn"{e}v)和肖尔(Shor)关于面向matroids的实现空间的普遍性的研究之后产生的。多年来,$exists mathbb{R}$而不是NP被证明是衡量问题复杂性的正确方法的问题数量不断增加,尤其是在计算几何、图绘制、博弈论以及逻辑和代数的某些领域。$exists/mathbb{R}$也开始出现在机器学习、马尔可夫决策过程和概率推理中。我们的目标是为 $exists mathbb{R}$收集一份完整和困难问题的综合汇编,以及一长串开放问题。我们将在第三部分介绍这份汇编;第二部分将介绍汇编及其涉及的领域。第一部分向读者介绍了作为复杂性类别的有实数存在论,讨论了它的历史、动机和前景,以及一些技术方面的问题。
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引用次数: 0
A quantitative probabilistic relational Hoare logic 定量概率关系胡尔逻辑
Pub Date : 2024-07-24 DOI: arxiv-2407.17127
Martin Avanzini, Gilles Barthe, Davide Davoli, Benjamin Grégoire
We introduce eRHL, a program logic for reasoning about relational expectationproperties of pairs of probabilistic programs. eRHL is quantitative, i.e., itspre- and post-conditions take values in the extended non-negative reals. Thanksto its quantitative assertions, eRHL overcomes randomness alignmentrestrictions from prior logics, including PRHL, a popular relational programlogic used to reason about security of cryptographic constructions, and apRHL,a variant of PRHL for differential privacy. As a result, eRHL is the firstrelational probabilistic program logic to be supported by non-trivial soundnessand completeness results for all almost surely terminating programs. We showthat eRHL is sound and complete with respect to program equivalence,statistical distance, and differential privacy. We also show that every PRHLjudgment is valid iff it is provable in eRHL. We showcase the practicalbenefits of eRHL with examples that are beyond reach of PRHL and apRHL.
我们介绍的 eRHL 是一种程序逻辑,用于推理概率程序对的关系期望属性。eRHL 是定量的,即它的前置条件和后置条件在扩展的非负实数中取值。得益于其定量断言,eRHL 克服了先前逻辑中的随机性对齐限制,包括用于推理密码构造安全性的流行关系程序逻辑 PRHL,以及用于差分隐私的 PRHL 变体 apRHL。因此,eRHL 是第一个为所有几乎肯定终止的程序提供非难健全性和完备性结果支持的关系型概率程序逻辑。我们证明了 eRHL 在程序等价性、统计距离和差分隐私性方面是健全和完备的。我们还证明,如果每个 PRHL 判断在 eRHL 中是可证明的,那么它就是有效的。我们用 PRHL 和 apRHL 无法解决的例子展示了 eRHL 的实用优势。
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引用次数: 0
Static and Dynamic Verification of OCaml Programs: The Gospel Ecosystem (Extended Version) OCaml 程序的静态和动态验证:福音生态系统(扩展版)
Pub Date : 2024-07-24 DOI: arxiv-2407.17289
Tiago Lopes Soares, Ion Chririca, Mário Pereira
We present our work on the collaborative use of dynamic and static analysistools for the verification of software written in the OCaml language. We buildupon Gospel, a specification language for OCaml that can be used both indynamic and static analyses. We employ Ortac, for runtime assertion checking,and Cameleer and CFML for the deductive verification of OCaml code. We reporton the use of such tools to build a case study of collaborative analysis of anon-trivial OCaml program. This shows how these tools nicely complement eachothers, while at the same highlights the differences when writing specificationtargeting dynamic or static analysis methods.
我们介绍了在验证用 OCaml 语言编写的软件时协同使用动态和静态分析工具的工作。Gospel 是一种 OCaml 规范语言,可用于动态和静态分析。我们使用 Ortac 进行运行时断言检查,使用 Cameleer 和 CFML 对 OCaml 代码进行演绎验证。我们报告了使用这些工具对一个非琐碎的 OCaml 程序进行协作分析的案例研究。这表明了这些工具如何很好地互补,同时也突出了在编写以规范为目标的动态或静态分析方法时的差异。
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引用次数: 0
A process algebraic framework for multi-agent dynamic epistemic systems 多代理动态认识系统的过程代数框架
Pub Date : 2024-07-24 DOI: arxiv-2407.17537
Alessandro Aldini
This paper combines the classical model of labeled transition systems withthe epistemic model for reasoning about knowledge. The result is a unifyingframework for modeling and analyzing multi-agent, knowledge-based, dynamicsystems. On the modeling side, we propose a process algebraic, agent-orientedspecification language that makes such a framework easy to use for practicalpurposes. On the verification side, we define a modal logic encompassingtemporal and epistemic operators.
本文将标记转换系统的经典模型与知识推理的认识论模型相结合。这就为建模和分析基于知识的多代理动态系统提供了一个统一的框架。在建模方面,我们提出了一种过程代数、面向代理的规范语言,使这种框架易于用于实际目的。在验证方面,我们定义了一种模态逻辑,其中包含时态和表态操作符。
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引用次数: 0
期刊
arXiv - CS - Logic in Computer Science
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