We reexamine Smale's alpha theory as a way to certify a numerical solution to an analytic system. For a given point and a system, Smale's alpha theory determines whether Newton's method applied to this point shows the quadratic convergence to an exact solution. We introduce the alpha theory computation using interval arithmetic to avoid costly exact arithmetic. As a straightforward variation of the alpha theory, our work improves computational efficiency compared to software employing the traditional alpha theory.
{"title":"Effective alpha theory certification using interval arithmetic: alpha theory over regions","authors":"Kisun Lee","doi":"arxiv-2405.04842","DOIUrl":"https://doi.org/arxiv-2405.04842","url":null,"abstract":"We reexamine Smale's alpha theory as a way to certify a numerical solution to\u0000an analytic system. For a given point and a system, Smale's alpha theory\u0000determines whether Newton's method applied to this point shows the quadratic\u0000convergence to an exact solution. We introduce the alpha theory computation\u0000using interval arithmetic to avoid costly exact arithmetic. As a\u0000straightforward variation of the alpha theory, our work improves computational\u0000efficiency compared to software employing the traditional alpha theory.","PeriodicalId":501033,"journal":{"name":"arXiv - CS - Symbolic Computation","volume":"7 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140926830","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}
Nils Froleyks, Emily Yu, Armin Biere, Keijo Heljanko
Certification helps to increase trust in formal verification of safety-critical systems which require assurance on their correctness. In hardware model checking, a widely used formal verification technique, phase abstraction is considered one of the most commonly used preprocessing techniques. We present an approach to certify an extended form of phase abstraction using a generic certificate format. As in earlier works our approach involves constructing a witness circuit with an inductive invariant property that certifies the correctness of the entire model checking process, which is then validated by an independent certificate checker. We have implemented and evaluated the proposed approach including certification for various preprocessing configurations on hardware model checking competition benchmarks. As an improvement on previous work in this area, the proposed method is able to efficiently complete certification with an overhead of a fraction of model checking time.
{"title":"Certifying Phase Abstraction","authors":"Nils Froleyks, Emily Yu, Armin Biere, Keijo Heljanko","doi":"arxiv-2405.04297","DOIUrl":"https://doi.org/arxiv-2405.04297","url":null,"abstract":"Certification helps to increase trust in formal verification of\u0000safety-critical systems which require assurance on their correctness. In\u0000hardware model checking, a widely used formal verification technique, phase\u0000abstraction is considered one of the most commonly used preprocessing\u0000techniques. We present an approach to certify an extended form of phase\u0000abstraction using a generic certificate format. As in earlier works our\u0000approach involves constructing a witness circuit with an inductive invariant\u0000property that certifies the correctness of the entire model checking process,\u0000which is then validated by an independent certificate checker. We have\u0000implemented and evaluated the proposed approach including certification for\u0000various preprocessing configurations on hardware model checking competition\u0000benchmarks. As an improvement on previous work in this area, the proposed\u0000method is able to efficiently complete certification with an overhead of a\u0000fraction of model checking time.","PeriodicalId":501033,"journal":{"name":"arXiv - CS - Symbolic Computation","volume":"146 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140927067","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}
Wilf-Zeilberger pairs are fundamental in the algorithmic theory of Wilf and Zeilberger for computer-generated proofs of combinatorial identities. Wilf-Zeilberger forms are their high-dimensional generalizations, which can be used for proving and discovering convergence acceleration formulas. This paper presents a structural description of all possible rational such forms, which can be viewed as an additive analog of the classical Ore-Sato theorem. Based on this analog, we show a structural decomposition of so-called multivariate hyperarithmetic terms, which extend multivariate hypergeometric terms to the additive setting.
{"title":"How to generate all possible rational Wilf-Zeilberger forms?","authors":"Shaoshi Chen, Christoph Koutschan, Yisen Wang","doi":"arxiv-2405.02430","DOIUrl":"https://doi.org/arxiv-2405.02430","url":null,"abstract":"Wilf-Zeilberger pairs are fundamental in the algorithmic theory of Wilf and\u0000Zeilberger for computer-generated proofs of combinatorial identities.\u0000Wilf-Zeilberger forms are their high-dimensional generalizations, which can be\u0000used for proving and discovering convergence acceleration formulas. This paper\u0000presents a structural description of all possible rational such forms, which\u0000can be viewed as an additive analog of the classical Ore-Sato theorem. Based on\u0000this analog, we show a structural decomposition of so-called multivariate\u0000hyperarithmetic terms, which extend multivariate hypergeometric terms to the\u0000additive setting.","PeriodicalId":501033,"journal":{"name":"arXiv - CS - Symbolic Computation","volume":"117 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140887674","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}
We examine the consequences of having a total division operation $frac{x}{y}$ on commutative rings. We consider two forms of binary division, one derived from a unary inverse, the other defined directly as a general operation; each are made total by setting $1/0$ equal to an error value $bot$, which is added to the ring. Such totalised divisions we call common divisions. In a field the two forms are equivalent and we have a finite equational axiomatisation $E$ that is complete for the equational theory of fields equipped with common division, called common meadows. These equational axioms $E$ turn out to be true of commutative rings with common division but only when defined via inverses. We explore these axioms $E$ and their role in seeking a completeness theorem for the conditional equational theory of common meadows. We prove they are complete for the conditional equational theory of commutative rings with inverse based common division. By adding a new proof rule, we can prove a completeness theorem for the conditional equational theory of common meadows. Although, the equational axioms $E$ fail with common division defined directly, we observe that the direct division does satisfies the equations in $E$ under a new congruence for partial terms called eager equality.
我们研究了在交换环上使用总除法运算$frac{x}{y}$ 的后果。我们考虑了二进制除法的两种形式，一种是从一元逆运算衍生出来的，另一种是直接定义为一般运算的；每种形式都是通过设置$1/0$等于误差值$bot$来实现总除法的，误差值被添加到环中。在一个域中，这两种形式是等价的，而且我们有一个有限的等式公理化$E$，它对于具有共分的域sequipped with common division 的等式理论是完备的，称为共草地。这些等式公理 $E$ 在有公分的交换环中也是成立的，但只有在通过倒数定义时才成立。我们探讨了这些公理$E$及其在寻求共面草地的条件等式理论的完备性定理中的作用，并证明了它们对于具有基于逆的共分的交换环的条件等式理论是完备的。通过增加新的证明规则，我们可以证明条件等式公理的完备性定理。尽管在直接定义的公分法下等式公理 $E$ 失效，但我们观察到，在一个新的部分项全等式（称为急切相等）下，直接除法确实满足等式公理 $E$。
{"title":"Rings with common division, common meadows and their conditional equational theories","authors":"Jan A Bergstra, John V Tucker","doi":"arxiv-2405.01733","DOIUrl":"https://doi.org/arxiv-2405.01733","url":null,"abstract":"We examine the consequences of having a total division operation\u0000$frac{x}{y}$ on commutative rings. We consider two forms of binary division,\u0000one derived from a unary inverse, the other defined directly as a general\u0000operation; each are made total by setting $1/0$ equal to an error value $bot$,\u0000which is added to the ring. Such totalised divisions we call common divisions.\u0000In a field the two forms are equivalent and we have a finite equational\u0000axiomatisation $E$ that is complete for the equational theory of fields\u0000equipped with common division, called common meadows. These equational axioms\u0000$E$ turn out to be true of commutative rings with common division but only when\u0000defined via inverses. We explore these axioms $E$ and their role in seeking a\u0000completeness theorem for the conditional equational theory of common meadows.\u0000We prove they are complete for the conditional equational theory of commutative\u0000rings with inverse based common division. By adding a new proof rule, we can\u0000prove a completeness theorem for the conditional equational theory of common\u0000meadows. Although, the equational axioms $E$ fail with common division defined\u0000directly, we observe that the direct division does satisfies the equations in\u0000$E$ under a new congruence for partial terms called eager equality.","PeriodicalId":501033,"journal":{"name":"arXiv - CS - Symbolic Computation","volume":"284 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140887953","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}
Description Logics are a formalism used in the knowledge representation, where the knowledge is captured in the form of concepts constructed in a controlled way from a restricted vocabulary. This allows one to test effectively for consistency of and the subsumption between the concepts. Unification of concepts may likewise become a useful tool in analysing the relations between concepts. The unification problem has been solved for the description logics $mathcal{FL}_0$ and $mathcal{EL}$. These small logics do not provide any means to express negation. Here we show an algorithm solving unification in $mathcal{FL}_bot$, the logic that extends $mathcal{FL}_0$ with the bottom concept. Bottom allows one to express that two concepts are disjoint. Our algorithm runs in exponential time, with respect to the size of the problem.
{"title":"Unification in the description logic $mathcal{FL}_bot$","authors":"Barbara Morawska","doi":"arxiv-2405.00912","DOIUrl":"https://doi.org/arxiv-2405.00912","url":null,"abstract":"Description Logics are a formalism used in the knowledge representation,\u0000where the knowledge is captured in the form of concepts constructed in a\u0000controlled way from a restricted vocabulary. This allows one to test\u0000effectively for consistency of and the subsumption between the concepts.\u0000Unification of concepts may likewise become a useful tool in analysing the\u0000relations between concepts. The unification problem has been solved for the\u0000description logics $mathcal{FL}_0$ and $mathcal{EL}$. These small logics do\u0000not provide any means to express negation. Here we show an algorithm solving\u0000unification in $mathcal{FL}_bot$, the logic that extends $mathcal{FL}_0$\u0000with the bottom concept. Bottom allows one to express that two concepts are\u0000disjoint. Our algorithm runs in exponential time, with respect to the size of\u0000the problem.","PeriodicalId":501033,"journal":{"name":"arXiv - CS - Symbolic Computation","volume":"22 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140840940","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}
We present a new methodology for utilising machine learning technology in symbolic computation research. We explain how a well known human-designed heuristic to make the choice of variable ordering in cylindrical algebraic decomposition may be represented as a constrained neural network. This allows us to then use machine learning methods to further optimise the heuristic, leading to new networks of similar size, representing new heuristics of similar complexity as the original human-designed one. We present this as a form of ante-hoc explainability for use in computer algebra development.
{"title":"Constrained Neural Networks for Interpretable Heuristic Creation to Optimise Computer Algebra Systems","authors":"Dorian Florescu, Matthew England","doi":"arxiv-2404.17508","DOIUrl":"https://doi.org/arxiv-2404.17508","url":null,"abstract":"We present a new methodology for utilising machine learning technology in\u0000symbolic computation research. We explain how a well known human-designed\u0000heuristic to make the choice of variable ordering in cylindrical algebraic\u0000decomposition may be represented as a constrained neural network. This allows\u0000us to then use machine learning methods to further optimise the heuristic,\u0000leading to new networks of similar size, representing new heuristics of similar\u0000complexity as the original human-designed one. We present this as a form of\u0000ante-hoc explainability for use in computer algebra development.","PeriodicalId":501033,"journal":{"name":"arXiv - CS - Symbolic Computation","volume":"75 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140811385","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}
Ou Deng, Shoji Nishimura, Atsushi Ogihara, Qun Jin
This study proposes Evolutionary Causal Discovery (ECD) for causal discovery that tailors response variables, predictor variables, and corresponding operators to research datasets. Utilizing genetic programming for variable relationship parsing, the method proceeds with the Relative Impact Stratification (RIS) algorithm to assess the relative impact of predictor variables on the response variable, facilitating expression simplification and enhancing the interpretability of variable relationships. ECD proposes an expression tree to visualize the RIS results, offering a differentiated depiction of unknown causal relationships compared to conventional causal discovery. The ECD method represents an evolution and augmentation of existing causal discovery methods, providing an interpretable approach for analyzing variable relationships in complex systems, particularly in healthcare settings with Electronic Health Record (EHR) data. Experiments on both synthetic and real-world EHR datasets demonstrate the efficacy of ECD in uncovering patterns and mechanisms among variables, maintaining high accuracy and stability across different noise levels. On the real-world EHR dataset, ECD reveals the intricate relationships between the response variable and other predictive variables, aligning with the results of structural equation modeling and shapley additive explanations analyses.
{"title":"Evolutionary Causal Discovery with Relative Impact Stratification for Interpretable Data Analysis","authors":"Ou Deng, Shoji Nishimura, Atsushi Ogihara, Qun Jin","doi":"arxiv-2404.16361","DOIUrl":"https://doi.org/arxiv-2404.16361","url":null,"abstract":"This study proposes Evolutionary Causal Discovery (ECD) for causal discovery\u0000that tailors response variables, predictor variables, and corresponding\u0000operators to research datasets. Utilizing genetic programming for variable\u0000relationship parsing, the method proceeds with the Relative Impact\u0000Stratification (RIS) algorithm to assess the relative impact of predictor\u0000variables on the response variable, facilitating expression simplification and\u0000enhancing the interpretability of variable relationships. ECD proposes an\u0000expression tree to visualize the RIS results, offering a differentiated\u0000depiction of unknown causal relationships compared to conventional causal\u0000discovery. The ECD method represents an evolution and augmentation of existing\u0000causal discovery methods, providing an interpretable approach for analyzing\u0000variable relationships in complex systems, particularly in healthcare settings\u0000with Electronic Health Record (EHR) data. Experiments on both synthetic and\u0000real-world EHR datasets demonstrate the efficacy of ECD in uncovering patterns\u0000and mechanisms among variables, maintaining high accuracy and stability across\u0000different noise levels. On the real-world EHR dataset, ECD reveals the\u0000intricate relationships between the response variable and other predictive\u0000variables, aligning with the results of structural equation modeling and\u0000shapley additive explanations analyses.","PeriodicalId":501033,"journal":{"name":"arXiv - CS - Symbolic Computation","volume":"50 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140806141","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}
Computer Algebra Systems (e.g. Maple) are used in research, education, and industrial settings. One of their key functionalities is symbolic integration, where there are many sub-algorithms to choose from that can affect the form of the output integral, and the runtime. Choosing the right sub-algorithm for a given problem is challenging: we hypothesise that Machine Learning can guide this sub-algorithm choice. A key consideration of our methodology is how to represent the mathematics to the ML model: we hypothesise that a representation which encodes the tree structure of mathematical expressions would be well suited. We trained both an LSTM and a TreeLSTM model for sub-algorithm prediction and compared them to Maple's existing approach. Our TreeLSTM performs much better than the LSTM, highlighting the benefit of using an informed representation of mathematical expressions. It is able to produce better outputs than Maple's current state-of-the-art meta-algorithm, giving a strong basis for further research.
计算机代数系统（如 Maple）广泛应用于研究、教育和工业领域。它们的主要功能之一是符号积分，其中有许多子算法可供选择，这些算法会影响输出积分的形式和运行时间。为特定问题选择合适的子算法具有挑战性：我们假设机器学习可以指导子算法的选择。我们的方法论的一个关键考虑因素是如何向机器学习模型表示数学：我们假设，对数学表达式的树形结构进行编码的表示方法将非常适合。我们训练了一个 LSTM 模型和一个 TreeLSTM 模型来进行亚算法预测，并将它们与 Maple 的现有方法进行了比较。我们的 TreeLSTM 比 LSTM 的表现要好得多，这凸显了使用数学表达式的知情表示法的好处。它能够产生比 Maple 目前最先进的元算法更好的输出结果，为进一步的研究奠定了坚实的基础。
{"title":"Symbolic Integration Algorithm Selection with Machine Learning: LSTMs vs Tree LSTMs","authors":"Rashid Barket, Matthew England, Jürgen Gerhard","doi":"arxiv-2404.14973","DOIUrl":"https://doi.org/arxiv-2404.14973","url":null,"abstract":"Computer Algebra Systems (e.g. Maple) are used in research, education, and\u0000industrial settings. One of their key functionalities is symbolic integration,\u0000where there are many sub-algorithms to choose from that can affect the form of\u0000the output integral, and the runtime. Choosing the right sub-algorithm for a\u0000given problem is challenging: we hypothesise that Machine Learning can guide\u0000this sub-algorithm choice. A key consideration of our methodology is how to\u0000represent the mathematics to the ML model: we hypothesise that a representation\u0000which encodes the tree structure of mathematical expressions would be well\u0000suited. We trained both an LSTM and a TreeLSTM model for sub-algorithm\u0000prediction and compared them to Maple's existing approach. Our TreeLSTM\u0000performs much better than the LSTM, highlighting the benefit of using an\u0000informed representation of mathematical expressions. It is able to produce\u0000better outputs than Maple's current state-of-the-art meta-algorithm, giving a\u0000strong basis for further research.","PeriodicalId":501033,"journal":{"name":"arXiv - CS - Symbolic Computation","volume":"45 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140797836","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}
Temur KutsiaRISC, Johannes Kepler University Linz, Daniel VenturaINF, Universidade Federal de Goiás, David MonniauxCNRS - Verimag, José F. MoralesIMDEA
This volume contains * The post-proceedings of the Eighteenth Logical and Semantic Frameworks with Applications (LSFA 2023). The meeting was held on July 1-2, 2023, organised by the Sapienza Universit`a di Roma, Italy. LSFA aims to bring researchers and students interested in theoretical and practical aspects of logical and semantic frameworks and their applications. The covered topics include proof theory, type theory and rewriting theory, specification and deduction languages, and formal semantics of languages and systems. * The post-proceedings of the Tenth Workshop on Horn clauses for Verification and Synthesis (HCVS 2023). The meeting was held on April 23, 2023 at the Institut Henri Poincar'e in Paris. HCVS aims to bring together researchers working in the two communities of constraint/ logic programming (e.g., ICLP and CP), program verification (e.g., CAV, TACAS, and VMCAI), and automated deduction (e.g., CADE, IJCAR), on the topics of Horn clause based analysis, verification, and synthesis.
本卷包含 * 第十八届应用逻辑和语义框架会议（LSFA 2023）的论文集。会议于2023年7月1-2日举行，由意大利罗马萨皮恩扎大学主办。LSFA 旨在汇集对逻辑和语义框架及其应用的理论和实践方面感兴趣的研究人员和学生。涵盖的主题包括原理论、类型理论和重写理论、规范和演绎语言以及语言和系统的形式语义学。* 第十届用于验证和合成的Horn子句研讨会（HCVS 2023）论文集。会议于2023年4月23日在巴黎亨利-庞加莱研究所（Institut Henri Poincar'e in Paris）举行。HCVS旨在汇聚约束/逻辑编程（如ICLP和CP）、程序验证（如CAV、TACAS和VMCAI）和自动演绎（如CADE、IJCAR）这两个领域的研究人员，共同探讨基于Horn子句的分析、验证和合成等主题。
{"title":"Proceedings 18th International Workshop on Logical and Semantic Frameworks, with Applications and 10th Workshop on Horn Clauses for Verification and Synthesis","authors":"Temur KutsiaRISC, Johannes Kepler University Linz, Daniel VenturaINF, Universidade Federal de Goiás, David MonniauxCNRS - Verimag, José F. MoralesIMDEA","doi":"arxiv-2404.13672","DOIUrl":"https://doi.org/arxiv-2404.13672","url":null,"abstract":"This volume contains * The post-proceedings of the Eighteenth Logical and Semantic Frameworks with\u0000Applications (LSFA 2023). The meeting was held on July 1-2, 2023, organised by\u0000the Sapienza Universit`a di Roma, Italy. LSFA aims to bring researchers and\u0000students interested in theoretical and practical aspects of logical and\u0000semantic frameworks and their applications. The covered topics include proof\u0000theory, type theory and rewriting theory, specification and deduction\u0000languages, and formal semantics of languages and systems. * The post-proceedings of the Tenth Workshop on Horn clauses for Verification\u0000and Synthesis (HCVS 2023). The meeting was held on April 23, 2023 at the\u0000Institut Henri Poincar'e in Paris. HCVS aims to bring together researchers\u0000working in the two communities of constraint/ logic programming (e.g., ICLP and\u0000CP), program verification (e.g., CAV, TACAS, and VMCAI), and automated\u0000deduction (e.g., CADE, IJCAR), on the topics of Horn clause based analysis,\u0000verification, and synthesis.","PeriodicalId":501033,"journal":{"name":"arXiv - CS - Symbolic Computation","volume":"37 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140797740","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}
Decision-making processes often involve dealing with uncertainty, which is traditionally addressed through probabilistic models. However, in practical scenarios, assessing probabilities reliably can be challenging, compounded by diverse perceptions of probabilistic information among decision makers. To address this variability and accommodate diverse preferences regarding uncertainty, we introduce the Probabilistic Abstract Decision Framework (PADF). PADF offers a structured approach for reasoning across different decision criteria, encompassing the optimistic, pessimistic, and Laplace perspectives, each tailored to distinct perceptions of uncertainty. We illustrate how PADF facilitates the computation of optimal decisions aligned with these criteria by leveraging probabilistic rules. Furthermore, we present strategies for optimizing the computational efficiency of these rules, leveraging appropriate independence assumptions to navigate the extensive search space inherent in PADF. Through these contributions, our framework provides a robust and adaptable tool for effectively navigating the complexities of decision-making under uncertainty.
{"title":"On Modeling Multi-Criteria Decision Making with Uncertain Information using Probabilistic Rules","authors":"Shengxin Hong, Xiuyi Fan","doi":"arxiv-2404.13419","DOIUrl":"https://doi.org/arxiv-2404.13419","url":null,"abstract":"Decision-making processes often involve dealing with uncertainty, which is\u0000traditionally addressed through probabilistic models. However, in practical\u0000scenarios, assessing probabilities reliably can be challenging, compounded by\u0000diverse perceptions of probabilistic information among decision makers. To\u0000address this variability and accommodate diverse preferences regarding\u0000uncertainty, we introduce the Probabilistic Abstract Decision Framework (PADF).\u0000PADF offers a structured approach for reasoning across different decision\u0000criteria, encompassing the optimistic, pessimistic, and Laplace perspectives,\u0000each tailored to distinct perceptions of uncertainty. We illustrate how PADF\u0000facilitates the computation of optimal decisions aligned with these criteria by\u0000leveraging probabilistic rules. Furthermore, we present strategies for\u0000optimizing the computational efficiency of these rules, leveraging appropriate\u0000independence assumptions to navigate the extensive search space inherent in\u0000PADF. Through these contributions, our framework provides a robust and\u0000adaptable tool for effectively navigating the complexities of decision-making\u0000under uncertainty.","PeriodicalId":501033,"journal":{"name":"arXiv - CS - Symbolic Computation","volume":"37 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140797817","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}
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