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Journal of Automated Reasoning最新文献

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SAT Meets Tableaux for Linear Temporal Logic Satisfiability 线性时态逻辑满足性的 SAT Meets Tableaux
IF 1.1 3区 计算机科学
Journal of Automated Reasoning Pub Date : 2024-03-15 DOI: 10.1007/s10817-023-09691-1
Luca Geatti, Nicola Gigante, Angelo Montanari, Gabriele Venturato
{"title":"SAT Meets Tableaux for Linear Temporal Logic Satisfiability","authors":"Luca Geatti, Nicola Gigante, Angelo Montanari, Gabriele Venturato","doi":"10.1007/s10817-023-09691-1","DOIUrl":"https://doi.org/10.1007/s10817-023-09691-1","url":null,"abstract":"<p><i>Linear temporal logic</i> (<span>(textsf{LTL},)</span>) and its variant interpreted on <i>finite traces</i> (<span>(textsf{LTL}_{textsf{f},})</span>) are among the most popular specification languages in the fields of formal verification, artificial intelligence, and others. In this paper, we focus on the satisfiability problem for <span>(textsf{LTL},)</span>and <span>(textsf{LTL}_{textsf{f},})</span>formulas, for which many techniques have been devised during the last decades. Among these are <i>tableau systems</i>, of which the most recent is Reynolds’ tree-shaped tableau. We provide a SAT-based algorithm for <span>(textsf{LTL},)</span>and <span>(textsf{LTL}_{textsf{f},})</span>satisfiability checking based on Reynolds’ tableau, proving its correctness and discussing experimental results obtained through its implementation in the BLACK satisfiability checker.</p>","PeriodicalId":15082,"journal":{"name":"Journal of Automated Reasoning","volume":"24 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2024-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140147813","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Should Decisions in QCDCL Follow Prefix Order? QCDCL 中的决定是否应遵循前缀顺序？
IF 1.1 3区 计算机科学
Journal of Automated Reasoning Pub Date : 2024-02-09 DOI: 10.1007/s10817-024-09694-6
{"title":"Should Decisions in QCDCL Follow Prefix Order?","authors":"","doi":"10.1007/s10817-024-09694-6","DOIUrl":"https://doi.org/10.1007/s10817-024-09694-6","url":null,"abstract":"<h3>Abstract</h3> <p>Quantified conflict-driven clause learning (QCDCL) is one of the main solving approaches for quantified Boolean formulas (QBF). One of the differences between QCDCL and propositional CDCL is that QCDCL typically follows the prefix order of the QBF for making decisions. We investigate an alternative model for QCDCL solving where decisions can be made in arbitrary order. The resulting system <span> <span>(textsf{QCDCL}^textsf {{Atiny {MakeUppercase {ny}}}})</span> </span> is still sound and terminating, but does not necessarily allow to always learn asserting clauses or cubes. To address this potential drawback, we additionally introduce two subsystems that guarantee to always learn asserting clauses (<span> <span>(textsf{QCDCL}^textsf {{Utiny {MakeUppercase {ni}}-Atiny {MakeUppercase {ny}}}})</span> </span>) and asserting cubes (<span> <span>(textsf{QCDCL}^textsf {{Etiny {MakeUppercase {xi}}-Atiny {MakeUppercase {ny}}}})</span> </span>), respectively. We model all four approaches by formal proof systems and show that <span> <span>(textsf{QCDCL}^textsf {{Utiny {MakeUppercase {ni}}-Atiny {MakeUppercase {ny}}}})</span> </span> is exponentially better than <span> <span>(mathsf{{QCDCL}} )</span> </span> on false formulas, whereas <span> <span>(textsf{QCDCL}^textsf {{Etiny {MakeUppercase {xi}}-Atiny {MakeUppercase {ny}}}})</span> </span> is exponentially better than <span> <span>(mathsf{{QCDCL}} )</span> </span> on true QBFs. Technically, this involves constructing specific QBF families and showing lower and upper bounds in the respective proof systems. We complement our theoretical study with some initial experiments that confirm our theoretical findings.</p>","PeriodicalId":15082,"journal":{"name":"Journal of Automated Reasoning","volume":"80 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2024-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139768227","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Non-termination in Term Rewriting and Logic Programming 术语重写和逻辑编程中的非终结性
IF 1.1 3区 计算机科学
Journal of Automated Reasoning Pub Date : 2024-02-02 DOI: 10.1007/s10817-023-09693-z
Étienne Payet
{"title":"Non-termination in Term Rewriting and Logic Programming","authors":"Étienne Payet","doi":"10.1007/s10817-023-09693-z","DOIUrl":"https://doi.org/10.1007/s10817-023-09693-z","url":null,"abstract":"<p>In this paper, we define two particular forms of non-termination, namely <i>loops</i> and <i>binary chains</i>, in an abstract framework that encompasses term rewriting and logic programming. The definition of loops relies on the notion of <i>compatibility</i> of binary relations. We also present a syntactic criterion for the detection of a special case of binary chains. Moreover, we describe our implementation <span>NTI</span> and compare its results at the Termination Competition 2023 with those of leading analyzers.</p>","PeriodicalId":15082,"journal":{"name":"Journal of Automated Reasoning","volume":"13 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2024-02-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139664196","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Matroid-Based Automatic Prover and Coq Proof Generator for Projective Incidence Geometry 基于 Matroid 的投影入射几何自动证明器和 Coq 证明生成器
IF 1.1 3区 计算机科学
Journal of Automated Reasoning Pub Date : 2024-01-18 DOI: 10.1007/s10817-023-09690-2
{"title":"A Matroid-Based Automatic Prover and Coq Proof Generator for Projective Incidence Geometry","authors":"","doi":"10.1007/s10817-023-09690-2","DOIUrl":"https://doi.org/10.1007/s10817-023-09690-2","url":null,"abstract":"<h3>Abstract</h3> <p>We present an automatic theorem prover for projective incidence geometry. This prover does not consider coordinates. Instead, it follows a combinatorial approach based on the concept of rank. This allows to deal only with sets of points and to capture relations between objects of the projective space (equality, collinearity, coplanarity, etc.) in a homogenous way. Taking advantage of the computational aspect of this approach, we automatically compute by saturation the ranks of all sets of the powerset of the points of the geometric configuration we consider. Upon completion of the saturation phase, our prover then retraces the proof process and generates the corresponding Coq code. This code is then formally checked by the Coq proof assistant, thus ensuring that the proof is actually correct. We use the prover to verify some well-known, non-trivial theorems in projective space geometry, among them: Desargues’ theorem and Dandelin–Gallucci’s theorem.</p>","PeriodicalId":15082,"journal":{"name":"Journal of Automated Reasoning","volume":"14 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2024-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139498054","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Formalization of the CHSH Inequality and Tsirelson’s Upper-bound in Isabelle/HOL Isabelle/HOL 中 CHSH 不等式和齐雷尔森上界的形式化
IF 1.1 3区 计算机科学
Journal of Automated Reasoning Pub Date : 2023-12-19 DOI: 10.1007/s10817-023-09689-9
{"title":"A Formalization of the CHSH Inequality and Tsirelson’s Upper-bound in Isabelle/HOL","authors":"","doi":"10.1007/s10817-023-09689-9","DOIUrl":"https://doi.org/10.1007/s10817-023-09689-9","url":null,"abstract":"<h3>Abstract</h3> <p>We present a formalization of several fundamental notions and results from Quantum Information theory in the proof assistant Isabelle/HOL, including density matrices and projective measurements, along with the proof that the local hidden-variable hypothesis advocated by Einstein to model quantum mechanics cannot hold. The proof of the latter result is based on the so-called CHSH inequality, and it is the violation of this inequality that was experimentally evidenced by Aspect, who earned the Nobel Prize in 2022 for his work. We also formalize various results related to the violation of the CHSH inequality, such as Tsirelson’s bound, which quantifies the amount to which this inequality can be violated in a quantum setting.</p>","PeriodicalId":15082,"journal":{"name":"Journal of Automated Reasoning","volume":"19 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138741175","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Formally-Verified Round-Off Error Analysis of Runge–Kutta Methods Runge-Kutta 方法的形式验证舍入误差分析
IF 1.1 3区 计算机科学
Journal of Automated Reasoning Pub Date : 2023-12-06 DOI: 10.1007/s10817-023-09686-y
Florian Faissole
{"title":"Formally-Verified Round-Off Error Analysis of Runge–Kutta Methods","authors":"Florian Faissole","doi":"10.1007/s10817-023-09686-y","DOIUrl":"https://doi.org/10.1007/s10817-023-09686-y","url":null,"abstract":"<p>Numerical errors are insidious, difficult to predict and inherent in different levels of critical systems design. Indeed, numerical algorithms generally constitute approximations of an ideal mathematical model, which itself constitutes an approximation of a physical reality which has undergone multiple measurement errors. To this are added rounding errors due to computer arithmetic implementations, often neglected even if they can significantly distort the results obtained. This applies to Runge–Kutta methods used for the numerical integration of ordinary differential equations, that are ubiquitous to model fundamental laws of physics, chemistry, biology or economy. We provide a Coq formalization of the rounding error analysis of Runge–Kutta methods applied to linear systems and implemented in floating-point arithmetic. We propose a generic methodology to build a bound on the error accumulated over the iterations, taking gradual underflow into account. We then instantiate this methodology for two classic Runge–Kutta methods, namely Euler and RK2. The formalization of the results include the definition of matrix norms, the proof of rounding error bounds of matrix operations and the formalization of the generic results and their applications on examples. In order to support the proposed approach, we provide numerical experiments on examples coming from nuclear physics applications.</p>","PeriodicalId":15082,"journal":{"name":"Journal of Automated Reasoning","volume":"101 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138547562","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Formal Verification of Termination Criteria for First-Order Recursive Functions 一阶递归函数终止准则的形式化验证
IF 1.1 3区 计算机科学
Journal of Automated Reasoning Pub Date : 2023-11-29 DOI: 10.1007/s10817-023-09669-z
Cesar A. Muñoz, Mauricio Ayala-Rincón, Mariano M. Moscato, Aaron M. Dutle, Anthony J. Narkawicz, Ariane Alves Almeida, Andréia B. Avelar da Silva, Thiago M. Ferreira Ramos
{"title":"Formal Verification of Termination Criteria for First-Order Recursive Functions","authors":"Cesar A. Muñoz, Mauricio Ayala-Rincón, Mariano M. Moscato, Aaron M. Dutle, Anthony J. Narkawicz, Ariane Alves Almeida, Andréia B. Avelar da Silva, Thiago M. Ferreira Ramos","doi":"10.1007/s10817-023-09669-z","DOIUrl":"https://doi.org/10.1007/s10817-023-09669-z","url":null,"abstract":"<p>This paper presents a formalization of several termination criteria for first-order recursive functions. The formalization, which is developed in the Prototype Verification System (PVS), includes the specification and proof of equivalence of semantic termination, Turing termination, size change principle, calling context graphs, and matrix-weighted graphs. These termination criteria are defined on a computational model that consists of a basic functional language called PVS0, which is an embedding of recursive first-order functions. Through this embedding, the native mechanism for checking termination of recursive functions in PVS could be soundly extended with semi-automatic termination criteria such as calling contexts graphs.</p>","PeriodicalId":15082,"journal":{"name":"Journal of Automated Reasoning","volume":"10 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138520705","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Saturation-Based Boolean Conjunctive Query Answering and Rewriting for the Guarded Quantification Fragments 基于饱和的布尔连词查询回答与改写保护量化片段
IF 1.1 3区 计算机科学
Journal of Automated Reasoning Pub Date : 2023-11-23 DOI: 10.1007/s10817-023-09687-x
Sen Zheng, Renate A. Schmidt
{"title":"Saturation-Based Boolean Conjunctive Query Answering and Rewriting for the Guarded Quantification Fragments","authors":"Sen Zheng, Renate A. Schmidt","doi":"10.1007/s10817-023-09687-x","DOIUrl":"https://doi.org/10.1007/s10817-023-09687-x","url":null,"abstract":"<p>Query answering is an important problem in AI, database and knowledge representation. In this paper, we develop saturation-based Boolean conjunctive query answering and rewriting procedures for the guarded, the loosely guarded and the clique-guarded fragments. Our query answering procedure improves existing resolution-based decision procedures for the guarded and the loosely guarded fragments and this procedure solves Boolean conjunctive query answering problems for the guarded, the loosely guarded and the clique-guarded fragments. Based on this query answering procedure, we also introduce a novel saturation-based query rewriting procedure for these guarded fragments. Unlike mainstream query answering and rewriting methods, our procedures derive a compact and reusable saturation, namely a closure of formulas, to handle the challenge of querying for distributed datasets. This paper lays the theoretical foundations for the first automated deduction decision procedures for Boolean conjunctive query answering and the first saturation-based Boolean conjunctive query rewriting in the guarded, the loosely guarded and the clique-guarded fragments.</p>","PeriodicalId":15082,"journal":{"name":"Journal of Automated Reasoning","volume":"100 3","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138520703","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Self-evident Automated Geometric Theorem Proving Based on Complex Number Identity 基于复数恒等式的自明自动几何定理证明
IF 1.1 3区 计算机科学
Journal of Automated Reasoning Pub Date : 2023-11-20 DOI: 10.1007/s10817-023-09688-w
Xicheng Peng, Jingzhong Zhang, Mao Chen, Sannyuya Liu
{"title":"Self-evident Automated Geometric Theorem Proving Based on Complex Number Identity","authors":"Xicheng Peng, Jingzhong Zhang, Mao Chen, Sannyuya Liu","doi":"10.1007/s10817-023-09688-w","DOIUrl":"https://doi.org/10.1007/s10817-023-09688-w","url":null,"abstract":"<p>How to automatically generate short and easy-to-understand proofs for geometric theorems has long been an issue of concern in mathematics education. A novel automated geometric theorem proving method based on complex number identities is proposed in this paper, which acts as a bridge between geometry and algebra. According to the proposed method, the geometric relations in the given proposition are first transformed into a complex number expression, then the complex number identity is generated by the elimination method; finally, the closure property under all four operations of real numbers is employed to prove the proposition. A test on more than 300 geometric problems shows that the proposed method is highly effective, and the corresponding proofs are short, with obvious geometric meaning.</p>","PeriodicalId":15082,"journal":{"name":"Journal of Automated Reasoning","volume":"91 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138542397","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Bisequent Calculus for Four-Valued Quasi-Relevant Logics: Cut Elimination and Interpolation 四值拟相关逻辑的等列演算:切消和插值
IF 1.1 3区 计算机科学
Journal of Automated Reasoning Pub Date : 2023-11-16 DOI: 10.1007/s10817-023-09685-z
Andrzej Indrzejczak
{"title":"Bisequent Calculus for Four-Valued Quasi-Relevant Logics: Cut Elimination and Interpolation","authors":"Andrzej Indrzejczak","doi":"10.1007/s10817-023-09685-z","DOIUrl":"https://doi.org/10.1007/s10817-023-09685-z","url":null,"abstract":"<p>We present a uniform syntactical characterisation of the class of quasi-relevant logics which are four-valued extensions of the basic relevant logic B of Meyer and Routley. All these logics are obtained by the addition of suitable quasi-relevant implications to the four-valued logic of First Degree Entailment FDE. So far they were characterised axiomatically and semantically in several ways but did not obtain a special proof-theoretic treatment. To this aim a generalised form of sequent calculus called bisequent calculus (BSC) is applied. In BSC rules operate on the ordered pairs of ordinary sequents. It may be treated as the weakest kind of system in the rich family of generalised sequent calculi operating on items which are some collections of ordinary sequents, like hypersequents or nested sequents. It is shown that all logics under consideration have cut-free characterisation in BSC which satisfies the subformula property and yields decidability. It is also shown that the interpolation theorem holds for these logics if their language is enriched with additional negation.</p>","PeriodicalId":15082,"journal":{"name":"Journal of Automated Reasoning","volume":"4 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138520657","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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