Pub Date : 2023-12-20DOI: 10.1017/s1471068423000388
SIMONE CARUSO, CARMINE DODARO, MARCO MARATEA, MARCO MOCHI, FRANCESCO RICCIO
Answer set programming (ASP) is a popular declarative programming language for solving hard combinatorial problems. Although ASP has gained widespread acceptance in academic and industrial contexts, there are certain user groups who may find it more advantageous to employ a higher-level language that closely resembles natural language when specifying ASP programs. In this paper, we propose a novel tool, called CNL2ASP, for translating English sentences expressed in a controlled natural language (CNL) form into ASP. In particular, we first provide a definition of the type of sentences allowed by our CNL and their translation as ASP rules and then exemplify the usage of the CNL for the specification of both synthetic and real-world combinatorial problems. Finally, we report the results of an experimental analysis conducted on the real-world problems to compare the performance of automatically generated encodings with the ones written by ASP practitioners, showing that our tool can obtain satisfactory performance on these benchmarks.
答案集编程（ASP）是一种流行的声明式编程语言，用于解决难以解决的组合问题。虽然 ASP 已在学术和工业领域获得广泛认可，但某些用户群体可能会发现，在指定 ASP 程序时，使用一种与自然语言非常相似的高级语言会更有优势。在本文中，我们提出了一种名为 CNL2ASP 的新工具，用于将以受控自然语言（CNL）形式表达的英语句子翻译成 ASP。具体而言，我们首先定义了 CNL 所允许的句子类型，并将其翻译为 ASP 规则，然后举例说明了如何使用 CNL 来规范合成问题和现实世界中的组合问题。最后，我们报告了对真实世界问题进行实验分析的结果，以比较自动生成的编码与 ASP 从业人员编写的编码的性能，结果表明我们的工具可以在这些基准上获得令人满意的性能。
{"title":"CNL2ASP: Converting Controlled Natural Language Sentences into ASP","authors":"SIMONE CARUSO, CARMINE DODARO, MARCO MARATEA, MARCO MOCHI, FRANCESCO RICCIO","doi":"10.1017/s1471068423000388","DOIUrl":"https://doi.org/10.1017/s1471068423000388","url":null,"abstract":"<p>Answer set programming (ASP) is a popular declarative programming language for solving hard combinatorial problems. Although ASP has gained widespread acceptance in academic and industrial contexts, there are certain user groups who may find it more advantageous to employ a higher-level language that closely resembles natural language when specifying ASP programs. In this paper, we propose a novel tool, called CNL2ASP, for translating English sentences expressed in a controlled natural language (CNL) form into ASP. In particular, we first provide a definition of the type of sentences allowed by our CNL and their translation as ASP rules and then exemplify the usage of the CNL for the specification of both synthetic and real-world combinatorial problems. Finally, we report the results of an experimental analysis conducted on the real-world problems to compare the performance of automatically generated encodings with the ones written by ASP practitioners, showing that our tool can obtain satisfactory performance on these benchmarks.</p>","PeriodicalId":49436,"journal":{"name":"Theory and Practice of Logic Programming","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2023-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138816479","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-12-14DOI: 10.1017/s1471068423000376
CHIAKI SAKAMA
Given a conditional sentence “${varphi}Rightarrow psi$" (if ${varphi}$ then $psi$) and respective facts, four different types of inferences are observed in human reasoning: Affirming the antecedent (AA) (or modus ponens) reasons $psi$ from ${varphi}$; affirming the consequent (AC) reasons ${varphi}$ from $psi$; denying the antecedent (DA) reasons $negpsi$ from $neg{varphi}$; and denying the consequent (DC) (or m
{"title":"Human Conditional Reasoning in Answer Set Programming","authors":"CHIAKI SAKAMA","doi":"10.1017/s1471068423000376","DOIUrl":"https://doi.org/10.1017/s1471068423000376","url":null,"abstract":"<p>Given a conditional sentence “<span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20231213121345464-0823:S1471068423000376:S1471068423000376_inline1.png\"><span data-mathjax-type=\"texmath\"><span>${varphi}Rightarrow psi$</span></span></img></span></span>\" (if <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20231213121345464-0823:S1471068423000376:S1471068423000376_inline2.png\"><span data-mathjax-type=\"texmath\"><span>${varphi}$</span></span></img></span></span> then <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20231213121345464-0823:S1471068423000376:S1471068423000376_inline3.png\"><span data-mathjax-type=\"texmath\"><span>$psi$</span></span></img></span></span>) and respective facts, four different types of inferences are observed in human reasoning: <span>Affirming the antecedent</span> (AA) (or <span>modus ponens</span>) reasons <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20231213121345464-0823:S1471068423000376:S1471068423000376_inline4.png\"><span data-mathjax-type=\"texmath\"><span>$psi$</span></span></img></span></span> from <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20231213121345464-0823:S1471068423000376:S1471068423000376_inline5.png\"><span data-mathjax-type=\"texmath\"><span>${varphi}$</span></span></img></span></span>; <span>affirming the consequent</span> (AC) reasons <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20231213121345464-0823:S1471068423000376:S1471068423000376_inline6.png\"><span data-mathjax-type=\"texmath\"><span>${varphi}$</span></span></img></span></span> from <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20231213121345464-0823:S1471068423000376:S1471068423000376_inline7.png\"><span data-mathjax-type=\"texmath\"><span>$psi$</span></span></img></span></span>; <span>denying the antecedent</span> (DA) reasons <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20231213121345464-0823:S1471068423000376:S1471068423000376_inline8.png\"><span data-mathjax-type=\"texmath\"><span>$negpsi$</span></span></img></span></span> from <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20231213121345464-0823:S1471068423000376:S1471068423000376_inline9.png\"><span data-mathjax-type=\"texmath\"><span>$neg{varphi}$</span></span></img></span></span>; and <span>denying the consequent</span> (DC) (or <span>m","PeriodicalId":49436,"journal":{"name":"Theory and Practice of Logic Programming","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2023-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138629303","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-28DOI: 10.1017/s1471068423000364
AMÉLIE GHEERBRANT, LEONID LIBKIN, ALEXANDRA ROGOVA, CRISTINA SIRANGELO
To answer database queries over incomplete data, the gold standard is finding certain answers: those that are true regardless of how incomplete data is interpreted. Such answers can be found efficiently for conjunctive queries and their unions, even in the presence of constraints. With negation added, the problem becomes intractable however. We concentrate on the complexity of certain answers under constraints and on effficiently answering queries outside the usual classes of (unions) of conjunctive queries by means of rewriting as Datalog and first-order queries. We first notice that there are three different ways in which query answering can be cast as a decision problem. We complete the existing picture and provide precise complexity bounds on all versions of the decision problem, for certain and best answers. We then study a well-behaved class of queries that extends unions of conjunctive queries with a mild form of negation. We show that for them, certain answers can be expressed in Datalog with negation, even in the presence of functional dependencies, thus making them tractable in data complexity. We show that in general, Datalog cannot be replaced by first-order logic, but without constraints such a rewriting can be done in first order.
{"title":"Querying Incomplete Data: Complexity and Tractability via Datalog and First-Order Rewritings","authors":"AMÉLIE GHEERBRANT, LEONID LIBKIN, ALEXANDRA ROGOVA, CRISTINA SIRANGELO","doi":"10.1017/s1471068423000364","DOIUrl":"https://doi.org/10.1017/s1471068423000364","url":null,"abstract":"To answer database queries over incomplete data, the gold standard is finding certain answers: those that are true regardless of how incomplete data is interpreted. Such answers can be found efficiently for conjunctive queries and their unions, even in the presence of constraints. With negation added, the problem becomes intractable however. We concentrate on the complexity of certain answers under constraints and on effficiently answering queries outside the usual classes of (unions) of conjunctive queries by means of rewriting as Datalog and first-order queries. We first notice that there are three different ways in which query answering can be cast as a decision problem. We complete the existing picture and provide precise complexity bounds on all versions of the decision problem, for certain and best answers. We then study a well-behaved class of queries that extends unions of conjunctive queries with a mild form of negation. We show that for them, certain answers can be expressed in Datalog with negation, even in the presence of functional dependencies, thus making them tractable in data complexity. We show that in general, Datalog cannot be replaced by first-order logic, but without constraints such a rewriting can be done in first order.","PeriodicalId":49436,"journal":{"name":"Theory and Practice of Logic Programming","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2023-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138540392","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-18DOI: 10.1017/s1471068423000352
JOSÉ A. RIAZA
Abstract Tau Prolog is a client-side Prolog interpreter fully implemented in JavaScript, which aims at implementing the ISO Prolog Standard. Tau Prolog has been developed to be used with either Node.js or a browser seamlessly, and therefore, it has been developed following a non-blocking, callback-based approach to avoid blocking web browsers. Taking the best from JavaScript and Prolog, Tau Prolog allows the programmer to handle browser events and manipulate the Document Object Model (DOM) of a web using Prolog predicates. In this paper we describe the architecture of Tau Prolog and its main packages for interacting with the Web, and we present its programming environment.
Tau Prolog是一个完全用JavaScript实现的客户端Prolog解释器，旨在实现ISO Prolog标准。Tau Prolog已经被开发为可以与Node.js或浏览器无缝使用，因此，它遵循非阻塞，基于回调的方法来开发，以避免阻塞web浏览器。利用JavaScript和Prolog的精华，Tau Prolog允许程序员使用Prolog谓词处理浏览器事件和操作web的文档对象模型(DOM)。本文描述了Tau Prolog的体系结构及其与Web交互的主要包，并给出了它的编程环境。
{"title":"Tau Prolog: A Prolog Interpreter for the Web","authors":"JOSÉ A. RIAZA","doi":"10.1017/s1471068423000352","DOIUrl":"https://doi.org/10.1017/s1471068423000352","url":null,"abstract":"Abstract Tau Prolog is a client-side Prolog interpreter fully implemented in JavaScript, which aims at implementing the ISO Prolog Standard. Tau Prolog has been developed to be used with either Node.js or a browser seamlessly, and therefore, it has been developed following a non-blocking, callback-based approach to avoid blocking web browsers. Taking the best from JavaScript and Prolog, Tau Prolog allows the programmer to handle browser events and manipulate the Document Object Model (DOM) of a web using Prolog predicates. In this paper we describe the architecture of Tau Prolog and its main packages for interacting with the Web, and we present its programming environment.","PeriodicalId":49436,"journal":{"name":"Theory and Practice of Logic Programming","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135109880","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-08-31DOI: 10.1017/s1471068423000340
ÓSCAR MARTÍN, ALBERTO VERDEJO, NARCISO MARTÍ-OLIET
Abstract In previous work, summarized in this paper, we proposed an operation of parallel composition for rewriting-logic theories, allowing compositional specification of systems and reusability of components. The present paper focuses on compositional verification. We show how the assume/guarantee technique can be transposed to our setting, by giving appropriate definitions of satisfaction based on transition structures and path semantics. We also show that simulation and equational abstraction can be done componentwise. Appropriate concepts of fairness and deadlock for our composition operation are discussed, as they affect satisfaction of temporal formulas. We keep in parallel a distributed and a global view of composed systems. We show that these views are equivalent and interchangeable, which may help our intuition and also has practical uses as, for example, it allows global-style verification of a modularly specified system. Under consideration in Theory and Practice of Logic Programming (TPLP).
{"title":"Compositional Verification in Rewriting Logic","authors":"ÓSCAR MARTÍN, ALBERTO VERDEJO, NARCISO MARTÍ-OLIET","doi":"10.1017/s1471068423000340","DOIUrl":"https://doi.org/10.1017/s1471068423000340","url":null,"abstract":"Abstract In previous work, summarized in this paper, we proposed an operation of parallel composition for rewriting-logic theories, allowing compositional specification of systems and reusability of components. The present paper focuses on compositional verification. We show how the assume/guarantee technique can be transposed to our setting, by giving appropriate definitions of satisfaction based on transition structures and path semantics. We also show that simulation and equational abstraction can be done componentwise. Appropriate concepts of fairness and deadlock for our composition operation are discussed, as they affect satisfaction of temporal formulas. We keep in parallel a distributed and a global view of composed systems. We show that these views are equivalent and interchangeable, which may help our intuition and also has practical uses as, for example, it allows global-style verification of a modularly specified system. Under consideration in Theory and Practice of Logic Programming (TPLP).","PeriodicalId":49436,"journal":{"name":"Theory and Practice of Logic Programming","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135831505","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-08-24DOI: 10.1017/s1471068423000327
GEORG GOTTLOB, MARCO MANNA, CINZIA MARTE
Abstract Existential rules form an expressive ${{textsf{Datalog}}}$ -based language to specify ontological knowledge. The presence of existential quantification in rule-heads, however, makes the main reasoning tasks undecidable. To overcome this limitation, in the last two decades, a number of classes of existential rules guaranteeing the decidability of query answering have been proposed. Unfortunately, only some of these classes fully encompass ${{textsf{Datalog}}}$ and, often, this comes at the price of higher computational complexity. Moreover, expressive classes are typically unable to exploit tools developed for classes exhibiting lower expressiveness. To mitigate these shortcomings, this paper introduces a novel general syntactic condition that allows us to define, systematically and in a uniform way, from any decidable class $mathcal{C}$ of existential rules, a new class called ${{textsf{Dyadic-}mathcal{C}}}$ enjoying the following properties: ( i ) it is decidable; ( ii ) it generalizes ${{textsf{Datalog}}}$ ; ( iii ) it generalizes $mathcal{C}$ ; ( iv ) it can effectively exploit any reasoner for query answering over $mathcal{C}$ ; and ( v ) its computational complexity does not exceed the highest between the one of $mathcal{C}$ and the one of ${{textsf{Datalog}}}$ .
{"title":"Dyadic Existential Rules","authors":"GEORG GOTTLOB, MARCO MANNA, CINZIA MARTE","doi":"10.1017/s1471068423000327","DOIUrl":"https://doi.org/10.1017/s1471068423000327","url":null,"abstract":"Abstract Existential rules form an expressive ${{textsf{Datalog}}}$ -based language to specify ontological knowledge. The presence of existential quantification in rule-heads, however, makes the main reasoning tasks undecidable. To overcome this limitation, in the last two decades, a number of classes of existential rules guaranteeing the decidability of query answering have been proposed. Unfortunately, only some of these classes fully encompass ${{textsf{Datalog}}}$ and, often, this comes at the price of higher computational complexity. Moreover, expressive classes are typically unable to exploit tools developed for classes exhibiting lower expressiveness. To mitigate these shortcomings, this paper introduces a novel general syntactic condition that allows us to define, systematically and in a uniform way, from any decidable class $mathcal{C}$ of existential rules, a new class called ${{textsf{Dyadic-}mathcal{C}}}$ enjoying the following properties: ( i ) it is decidable; ( ii ) it generalizes ${{textsf{Datalog}}}$ ; ( iii ) it generalizes $mathcal{C}$ ; ( iv ) it can effectively exploit any reasoner for query answering over $mathcal{C}$ ; and ( v ) its computational complexity does not exceed the highest between the one of $mathcal{C}$ and the one of ${{textsf{Datalog}}}$ .","PeriodicalId":49436,"journal":{"name":"Theory and Practice of Logic Programming","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135420397","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-08-15DOI: 10.1017/s1471068423000339
MARCO CALAUTTI, SERGIO GRECO, CRISTIAN MOLINARO, IRINA TRUBITSYNA
Abstract Data exchange, the problem of transferring data from a source schema to a target schema, has been studied for several years. The semantics of answering positive queries over the target schema has been defined in early work, but little attention has been paid to more general queries. A few proposals of semantics for more general queries exist but they either do not properly extend the standard semantics under positive queries, giving rise to counterintuitive answers, or they make query answering undecidable even for the most important data exchange settings, for example, with weakly-acyclic dependencies. The goal of this paper is to provide a new semantics for data exchange that is able to deal with general queries. At the same time, we want our semantics to coincide with the classical one when focusing on positive queries, and to not trade-off too much in terms of complexity of query answering. We show that query answering is undecidable in general under the new semantics, but it is $text{co}text{NP}text{-complete}$ when the dependencies are weakly-acyclic. Moreover, in the latter case, we show that exact answers under our semantics can be computed by means of logic programs with choice, thus exploiting existing efficient systems. For more efficient computations, we also show that our semantics allows for the construction of a representative target instance, similar in spirit to a universal solution, that can be exploited for computing approximate answers in polynomial time.
{"title":"Querying Data Exchange Settings Beyond Positive Queries","authors":"MARCO CALAUTTI, SERGIO GRECO, CRISTIAN MOLINARO, IRINA TRUBITSYNA","doi":"10.1017/s1471068423000339","DOIUrl":"https://doi.org/10.1017/s1471068423000339","url":null,"abstract":"Abstract Data exchange, the problem of transferring data from a source schema to a target schema, has been studied for several years. The semantics of answering positive queries over the target schema has been defined in early work, but little attention has been paid to more general queries. A few proposals of semantics for more general queries exist but they either do not properly extend the standard semantics under positive queries, giving rise to counterintuitive answers, or they make query answering undecidable even for the most important data exchange settings, for example, with weakly-acyclic dependencies. The goal of this paper is to provide a new semantics for data exchange that is able to deal with general queries. At the same time, we want our semantics to coincide with the classical one when focusing on positive queries, and to not trade-off too much in terms of complexity of query answering. We show that query answering is undecidable in general under the new semantics, but it is $text{co}text{NP}text{-complete}$ when the dependencies are weakly-acyclic. Moreover, in the latter case, we show that exact answers under our semantics can be computed by means of logic programs with choice, thus exploiting existing efficient systems. For more efficient computations, we also show that our semantics allows for the construction of a representative target instance, similar in spirit to a universal solution, that can be exploited for computing approximate answers in polynomial time.","PeriodicalId":49436,"journal":{"name":"Theory and Practice of Logic Programming","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135115300","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-08-02DOI: 10.1017/s1471068423000315
PRZEMYSŁAW A. WAŁĘGA, DAVID J. TENA CUCALA, BERNARDO CUENCA GRAU, EGOR V. KOSTYLEV
Abstract We introduce negation under the stable model semantics in DatalogMTL – a temporal extension of Datalog with metric temporal operators. As a result, we obtain a rule language which combines the power of answer set programming with the temporal dimension provided by metric operators. We show that, in this setting, reasoning becomes undecidable over the rational timeline, and decidable in ${{rm E}{smallrm XP}{rm S}{smallrm PACE}}$ in data complexity over the integer timeline. We also show that, if we restrict our attention to forward-propagating programs, reasoning over the integer timeline becomes ${{rm PS}{smallrm PACE}}$ -complete in data complexity, and hence, no harder than over positive programs; however, reasoning over the rational timeline in this fragment remains undecidable.
{"title":"The Stable Model Semantics of Datalog with Metric Temporal Operators","authors":"PRZEMYSŁAW A. WAŁĘGA, DAVID J. TENA CUCALA, BERNARDO CUENCA GRAU, EGOR V. KOSTYLEV","doi":"10.1017/s1471068423000315","DOIUrl":"https://doi.org/10.1017/s1471068423000315","url":null,"abstract":"Abstract We introduce negation under the stable model semantics in DatalogMTL – a temporal extension of Datalog with metric temporal operators. As a result, we obtain a rule language which combines the power of answer set programming with the temporal dimension provided by metric operators. We show that, in this setting, reasoning becomes undecidable over the rational timeline, and decidable in ${{rm E}{smallrm XP}{rm S}{smallrm PACE}}$ in data complexity over the integer timeline. We also show that, if we restrict our attention to forward-propagating programs, reasoning over the integer timeline becomes ${{rm PS}{smallrm PACE}}$ -complete in data complexity, and hence, no harder than over positive programs; however, reasoning over the rational timeline in this fragment remains undecidable.","PeriodicalId":49436,"journal":{"name":"Theory and Practice of Logic Programming","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135016527","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-01DOI: 10.1017/s1471068423000273
MASOOD FEYZBAKHSH RANKOOH, TOMI JANHUNEN
Abstract We establish a novel relation between delete-free planning, an important task for the AI planning community also known as relaxed planning, and logic programming. We show that given a planning problem, all subsets of actions that could be ordered to produce relaxed plans for the problem can be bijectively captured with stable models of a logic program describing the corresponding relaxed planning problem. We also consider the supported model semantics of logic programs, and introduce one causal and one diagnostic encoding of the relaxed planning problem as logic programs, both capturing relaxed plans with their supported models. Our experimental results show that these new encodings can provide major performance gain when computing optimal relaxed plans, with our diagnostic encoding outperforming state-of-the-art approaches to relaxed planning regardless of the given time limit when measured on a wide collection of STRIPS planning benchmarks.
{"title":"Capturing (Optimal) Relaxed Plans with Stable and Supported Models of Logic Programs","authors":"MASOOD FEYZBAKHSH RANKOOH, TOMI JANHUNEN","doi":"10.1017/s1471068423000273","DOIUrl":"https://doi.org/10.1017/s1471068423000273","url":null,"abstract":"Abstract We establish a novel relation between delete-free planning, an important task for the AI planning community also known as relaxed planning, and logic programming. We show that given a planning problem, all subsets of actions that could be ordered to produce relaxed plans for the problem can be bijectively captured with stable models of a logic program describing the corresponding relaxed planning problem. We also consider the supported model semantics of logic programs, and introduce one causal and one diagnostic encoding of the relaxed planning problem as logic programs, both capturing relaxed plans with their supported models. Our experimental results show that these new encodings can provide major performance gain when computing optimal relaxed plans, with our diagnostic encoding outperforming state-of-the-art approaches to relaxed planning regardless of the given time limit when measured on a wide collection of STRIPS planning benchmarks.","PeriodicalId":49436,"journal":{"name":"Theory and Practice of Logic Programming","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135569085","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-01DOI: 10.1017/s1471068423000224
VLADIMIR LIFSCHITZ
Abstract This paper describes a generalization of Clark’s completion that is applicable to logic programs containing arithmetic operations and produces syntactically simple, natural looking formulas. If a set of first-order axioms is equivalent to the completion of a program, then we may be able to find standard models of these axioms by running an answer set solver. As an example, we apply this “reverse completion” procedure to the Sum and Product Puzzle.
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