Pub Date : 2022-10-18DOI: 10.1017/s1471068422000394
Thomas Eiter, M. Maher, Enrico Pontelli, Luc de Raedt, M. Truszczynski
{"title":"The Collection of Papers Celebrating the 20th Anniversary of TPLP, Part II","authors":"Thomas Eiter, M. Maher, Enrico Pontelli, Luc de Raedt, M. Truszczynski","doi":"10.1017/s1471068422000394","DOIUrl":"https://doi.org/10.1017/s1471068422000394","url":null,"abstract":"","PeriodicalId":49436,"journal":{"name":"Theory and Practice of Logic Programming","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2022-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76595058","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 : 2022-09-22DOI: 10.1017/s1471068422000345
Thomas Eiter, M. Maher, Enrico Pontelli, Luc de Raedt, M. Truszczynski
The first issue of the journal Theory and Practice of Logic Programming, or TPLP, was published in January 2001. This issue, the last one in the present volume, and the following issue, the first one in the next volume, comprise a collection of papers com-memorating and celebrating the twentieth anniversary of the journal. This celebratory collection comes with about one year delay due to the COVID-19 pandemic (but also, if we were to be entirely honest, because of a common human tendency to put things off). Whatever the true reason for the delay, the collection is finally here. We hope and expect it will prove to be a demonstration of the vitality of logic programming, and of a broad range of research directions it spawned in the past and continues to generate today. Logic programming computer a of research on automated theorem proving in logic the of the programming The these original of inspiration of
《逻辑程序设计理论与实践》(Theory and Practice of Logic Programming, TPLP)杂志的第一期于2001年1月出版。这一期是本卷的最后一期，下一期是下一卷的第一期，包括纪念和庆祝该杂志二十周年的论文集。由于COVID-19大流行，这个庆祝系列推迟了大约一年(但如果我们完全诚实的话，也是因为人类普遍倾向于推迟事情)。不管延迟的真正原因是什么，藏品终于来了。我们希望并期待它将证明逻辑程序设计的生命力，以及它在过去和今天所产生的广泛的研究方向。逻辑程序设计计算机对逻辑程序设计中自动定理证明的研究，这些原始的启发
{"title":"Introduction to the Collection of Papers Celebrating the 20th Anniversary of TPLP","authors":"Thomas Eiter, M. Maher, Enrico Pontelli, Luc de Raedt, M. Truszczynski","doi":"10.1017/s1471068422000345","DOIUrl":"https://doi.org/10.1017/s1471068422000345","url":null,"abstract":"The first issue of the journal Theory and Practice of Logic Programming, or TPLP, was published in January 2001. This issue, the last one in the present volume, and the following issue, the first one in the next volume, comprise a collection of papers com-memorating and celebrating the twentieth anniversary of the journal. This celebratory collection comes with about one year delay due to the COVID-19 pandemic (but also, if we were to be entirely honest, because of a common human tendency to put things off). Whatever the true reason for the delay, the collection is finally here. We hope and expect it will prove to be a demonstration of the vitality of logic programming, and of a broad range of research directions it spawned in the past and continues to generate today. Logic programming computer a of research on automated theorem proving in logic the of the programming The these original of inspiration of","PeriodicalId":49436,"journal":{"name":"Theory and Practice of Logic Programming","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2022-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82962759","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 : 2022-09-19DOI: 10.1017/s1471068422000357
ANDRE THEVAPALAN, GABRIELE KERN-ISBERNER
Answer set programs used in real-world applications often require that the program is usable with different input data. This, however, can often lead to contradictory statements and consequently to an inconsistent program. Causes for potential contradictions in a program are conflicting rules. In this paper, we show how to ensure that a program $mathcal{P}$ remains non-contradictory given any allowed set of such input data. For that, we introduce the notion of conflict-resolving ${lambda}$ -extensions. A conflict-resolving ${lambda}$ -extension for a conflicting rule r is a set ${lambda}$ of (default) literals such that extending the body of r by ${lambda}$ resolves all conflicts of r at once. We investigate the properties that suitable ${lambda}$ -extensions should possess and building on that, we develop a strategy to compute all such conflict-resolving ${lambda}$ -extensions for each conflicting rule in
{"title":"On Establishing Robust Consistency in Answer Set Programs","authors":"ANDRE THEVAPALAN, GABRIELE KERN-ISBERNER","doi":"10.1017/s1471068422000357","DOIUrl":"https://doi.org/10.1017/s1471068422000357","url":null,"abstract":"<p>Answer set programs used in real-world applications often require that the program is usable with different input data. This, however, can often lead to contradictory statements and consequently to an inconsistent program. Causes for potential contradictions in a program are conflicting rules. In this paper, we show how to ensure that a program <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20220916112821223-0181:S1471068422000357:S1471068422000357_inline1.png\"/><span data-mathjax-type=\"texmath\"><span>\u0000$mathcal{P}$\u0000</span></span></span></span> remains non-contradictory given any allowed set of such input data. For that, we introduce the notion of conflict-resolving <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20220916112821223-0181:S1471068422000357:S1471068422000357_inline2.png\"/><span data-mathjax-type=\"texmath\"><span>\u0000${lambda}$\u0000</span></span></span></span>-extensions. A conflict-resolving <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20220916112821223-0181:S1471068422000357:S1471068422000357_inline3.png\"/><span data-mathjax-type=\"texmath\"><span>\u0000${lambda}$\u0000</span></span></span></span>-extension for a conflicting rule <span>r</span> is a set <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20220916112821223-0181:S1471068422000357:S1471068422000357_inline4.png\"/><span data-mathjax-type=\"texmath\"><span>\u0000${lambda}$\u0000</span></span></span></span> of (default) literals such that extending the body of <span>r</span> by <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20220916112821223-0181:S1471068422000357:S1471068422000357_inline5.png\"/><span data-mathjax-type=\"texmath\"><span>\u0000${lambda}$\u0000</span></span></span></span> resolves all conflicts of <span>r</span> at once. We investigate the properties that suitable <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20220916112821223-0181:S1471068422000357:S1471068422000357_inline6.png\"/><span data-mathjax-type=\"texmath\"><span>\u0000${lambda}$\u0000</span></span></span></span>-extensions should possess and building on that, we develop a strategy to compute all such conflict-resolving <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20220916112821223-0181:S1471068422000357:S1471068422000357_inline7.png\"/><span data-mathjax-type=\"texmath\"><span>\u0000${lambda}$\u0000</span></span></span></span>-extensions for each conflicting rule in <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:c","PeriodicalId":49436,"journal":{"name":"Theory and Practice of Logic Programming","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2022-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138540403","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 : 2022-08-23DOI: 10.1017/s1471068422000333
JORGE FANDINNO, VLADIMIR LIFSCHITZ
Theory of stable models is the mathematical basis of answer set programming. Several results in that theory refer to the concept of the positive dependency graph of a logic program. We describe a modification of that concept and show that the new understanding of positive dependency makes it possible to strengthen some of these results.
{"title":"Positive Dependency Graphs Revisited","authors":"JORGE FANDINNO, VLADIMIR LIFSCHITZ","doi":"10.1017/s1471068422000333","DOIUrl":"https://doi.org/10.1017/s1471068422000333","url":null,"abstract":"<p>Theory of stable models is the mathematical basis of answer set programming. Several results in that theory refer to the concept of the positive dependency graph of a logic program. We describe a modification of that concept and show that the new understanding of positive dependency makes it possible to strengthen some of these results.</p>","PeriodicalId":49436,"journal":{"name":"Theory and Practice of Logic Programming","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2022-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138540407","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 : 2022-08-15DOI: 10.1017/s1471068422000291
Y. Lierler, J. Morales
This is the second issue with the selected papers of the 38th International Conference on Logic Programming (ICLP 2022), held in Haifa, Israel, from July 31 to August 6, 2022. The two issues contain 16 papers selected from several tracks of the conference program for publication in Theory and Practice of Logic Programming. The preceding issue of this volume of the journal contains a detailed editorial by the conference chairs (Lierler et al. 2022), as well as eight papers selected for publication. This issue contains the remaining eight of the papers selected for publication in the Theory and Practice of Logic Programming.
{"title":"Introduction to the 38th International Conference on Logic Programming Special Issue II","authors":"Y. Lierler, J. Morales","doi":"10.1017/s1471068422000291","DOIUrl":"https://doi.org/10.1017/s1471068422000291","url":null,"abstract":"This is the second issue with the selected papers of the 38th International Conference on Logic Programming (ICLP 2022), held in Haifa, Israel, from July 31 to August 6, 2022. The two issues contain 16 papers selected from several tracks of the conference program for publication in Theory and Practice of Logic Programming. The preceding issue of this volume of the journal contains a detailed editorial by the conference chairs (Lierler et al. 2022), as well as eight papers selected for publication. This issue contains the remaining eight of the papers selected for publication in the Theory and Practice of Logic Programming.","PeriodicalId":49436,"journal":{"name":"Theory and Practice of Logic Programming","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2022-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43261401","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 : 2022-07-11DOI: 10.1017/S1471068422000266
Simon Marynissen, J. Heyninck, B. Bogaerts, M. Denecker
Abstract Justification theory is a general framework for the definition of semantics of rule-based languages that has a high explanatory potential. Nested justification systems, first introduced by Denecker et al., allow for the composition of justification systems. This notion of nesting thus enables the modular definition of semantics of rule-based languages, and increases the representational capacities of justification theory. As we show in this paper, the original characterization of semantics for nested justification systems leads to the loss of information relevant for explanations. In view of this problem, we provide an alternative characterization of their semantics and show that it is equivalent to the original one. Furthermore, we show how nested justification systems allow representing fixpoint definitions.
{"title":"On Nested Justification Systems","authors":"Simon Marynissen, J. Heyninck, B. Bogaerts, M. Denecker","doi":"10.1017/S1471068422000266","DOIUrl":"https://doi.org/10.1017/S1471068422000266","url":null,"abstract":"Abstract Justification theory is a general framework for the definition of semantics of rule-based languages that has a high explanatory potential. Nested justification systems, first introduced by Denecker et al., allow for the composition of justification systems. This notion of nesting thus enables the modular definition of semantics of rule-based languages, and increases the representational capacities of justification theory. As we show in this paper, the original characterization of semantics for nested justification systems leads to the loss of information relevant for explanations. In view of this problem, we provide an alternative characterization of their semantics and show that it is equivalent to the original one. Furthermore, we show how nested justification systems allow representing fixpoint definitions.","PeriodicalId":49436,"journal":{"name":"Theory and Practice of Logic Programming","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2022-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41515136","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 : 2022-07-01DOI: 10.1017/S147106842200028X
Y. Lierler, J. Morales
This issue and its companion, the following one in this volume, contain the regular papers of the 38th International Conference on Logic Programming (ICLP 2022), held in Haifa, Israel, from July 31 to August 6, 2022. In 2022, ICLP was a part of the Federal Logic Conference (FLoC) 2022 (https://floc2022.org/). Since the first conference held in Marseille in 1982, ICLP has been the premier international event for presenting research in logic programming. The scope of the conference covers all areas of logic programming including: Foundations: semantics, formalisms, nonmonotonic reasoning, knowledge representation.
{"title":"Introduction to the 38th International Conference on Logic Programming Special Issue","authors":"Y. Lierler, J. Morales","doi":"10.1017/S147106842200028X","DOIUrl":"https://doi.org/10.1017/S147106842200028X","url":null,"abstract":"This issue and its companion, the following one in this volume, contain the regular papers of the 38th International Conference on Logic Programming (ICLP 2022), held in Haifa, Israel, from July 31 to August 6, 2022. In 2022, ICLP was a part of the Federal Logic Conference (FLoC) 2022 (https://floc2022.org/). Since the first conference held in Marseille in 1982, ICLP has been the premier international event for presenting research in logic programming. The scope of the conference covers all areas of logic programming including: Foundations: semantics, formalisms, nonmonotonic reasoning, knowledge representation.","PeriodicalId":49436,"journal":{"name":"Theory and Practice of Logic Programming","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2022-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48593247","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 : 2022-05-17DOI: 10.1017/S1471068422000138
Joaquín Arias, S. Törmä, M. Carro, G. Gupta
Abstract Building Information Modeling (BIM) produces three-dimensional object-oriented models of buildings combining the geometrical information with a wide range of properties about materials, products, safety, to name just a few. BIM is slowly but inevitably revolutionizing the architecture, engineering, and construction industry. Buildings need to be compliant with regulations about stability, safety, and environmental impact. Manual compliance checking is tedious and error-prone, and amending flaws discovered only at construction time causes huge additional costs and delays. Several tools can check BIM models for conformance with rules/guidelines. For example, Singapore’s CORENET e-Submission System checks fire safety. But since the current BIM exchange format only contains basic information about building objects, a separate, ad-hoc model pre-processing is required to determine, for example, evacuation routes. Moreover, they face difficulties in adapting existing built-in rules and/or adding new ones (to cater for building regulations, that can vary not only among countries but also among parts of the same city), if at all possible. We propose the use of logic-based executable formalisms (CLP and Constraint ASP) to couple BIM models with advanced knowledge representation and reasoning capabilities. Previous experience shows that such formalisms can be used to uniformly capture and reason with knowledge (including ambiguity) in a large variety of domains. Additionally, incorporating checking within design tools makes it possible to ensure that models are rule-compliant at every step. This also prevents erroneous designs from having to be (partially) redone, which is also costly and burdensome. To validate our proposal, we implemented a preliminary reasoner under CLP(Q/R) and ASP with constraints and evaluated it with several BIM models.
{"title":"Building Information Modeling Using Constraint Logic Programming","authors":"Joaquín Arias, S. Törmä, M. Carro, G. Gupta","doi":"10.1017/S1471068422000138","DOIUrl":"https://doi.org/10.1017/S1471068422000138","url":null,"abstract":"Abstract Building Information Modeling (BIM) produces three-dimensional object-oriented models of buildings combining the geometrical information with a wide range of properties about materials, products, safety, to name just a few. BIM is slowly but inevitably revolutionizing the architecture, engineering, and construction industry. Buildings need to be compliant with regulations about stability, safety, and environmental impact. Manual compliance checking is tedious and error-prone, and amending flaws discovered only at construction time causes huge additional costs and delays. Several tools can check BIM models for conformance with rules/guidelines. For example, Singapore’s CORENET e-Submission System checks fire safety. But since the current BIM exchange format only contains basic information about building objects, a separate, ad-hoc model pre-processing is required to determine, for example, evacuation routes. Moreover, they face difficulties in adapting existing built-in rules and/or adding new ones (to cater for building regulations, that can vary not only among countries but also among parts of the same city), if at all possible. We propose the use of logic-based executable formalisms (CLP and Constraint ASP) to couple BIM models with advanced knowledge representation and reasoning capabilities. Previous experience shows that such formalisms can be used to uniformly capture and reason with knowledge (including ambiguity) in a large variety of domains. Additionally, incorporating checking within design tools makes it possible to ensure that models are rule-compliant at every step. This also prevents erroneous designs from having to be (partially) redone, which is also costly and burdensome. To validate our proposal, we implemented a preliminary reasoner under CLP(Q/R) and ASP with constraints and evaluated it with several BIM models.","PeriodicalId":49436,"journal":{"name":"Theory and Practice of Logic Programming","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2022-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41351181","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 : 2022-05-16DOI: 10.1017/S1471068422000217
Mohammed M. S. El-Kholany, M. Gebser, Konstantin Schekotihin
Abstract Scheduling methods are important for effective production and logistics management, where tasks need to be allocated and performed with limited resources. In particular, the Job-shop Scheduling Problem (JSP) is a well known and challenging combinatorial optimization problem in which tasks sharing a machine are to be arranged in a sequence such that encompassing jobs can be completed as early as possible. Given that already moderately sized JSP instances can be highly combinatorial, and neither optimal schedules nor the runtime to termination of complete optimization methods is known, efficient approaches to approximate good-quality schedules are of interest. In this paper, we propose problem decomposition into time windows whose operations can be successively scheduled and optimized by means of multi-shot Answer Set Programming (ASP) solving. From a computational perspective, decomposition aims to split highly complex scheduling tasks into better manageable subproblems with a balanced number of operations so that good-quality or even optimal partial solutions can be reliably found in a small fraction of runtime. Regarding the feasibility and quality of solutions, problem decomposition must respect the precedence of operations within their jobs and partial schedules optimized by time windows should yield better global solutions than obtainable in similar runtime on the entire instance. We devise and investigate a variety of decomposition strategies in terms of the number and size of time windows as well as heuristics for choosing their operations. Moreover, we incorporate time window overlapping and compression techniques into the iterative scheduling process to counteract window-wise optimization limitations restricted to partial schedules. Our experiments on JSP benchmark sets of several sizes show that successive optimization by multi-shot ASP solving leads to substantially better schedules within the runtime limit than global optimization on the full problem, where the gap increases with the number of operations to schedule. While the obtained solution quality still remains behind a state-of-the-art Constraint Programming system, our multi-shot solving approach comes closer the larger the instance size, demonstrating good scalability by problem decomposition.
{"title":"Problem Decomposition and Multi-shot ASP Solving for Job-shop Scheduling","authors":"Mohammed M. S. El-Kholany, M. Gebser, Konstantin Schekotihin","doi":"10.1017/S1471068422000217","DOIUrl":"https://doi.org/10.1017/S1471068422000217","url":null,"abstract":"Abstract Scheduling methods are important for effective production and logistics management, where tasks need to be allocated and performed with limited resources. In particular, the Job-shop Scheduling Problem (JSP) is a well known and challenging combinatorial optimization problem in which tasks sharing a machine are to be arranged in a sequence such that encompassing jobs can be completed as early as possible. Given that already moderately sized JSP instances can be highly combinatorial, and neither optimal schedules nor the runtime to termination of complete optimization methods is known, efficient approaches to approximate good-quality schedules are of interest. In this paper, we propose problem decomposition into time windows whose operations can be successively scheduled and optimized by means of multi-shot Answer Set Programming (ASP) solving. From a computational perspective, decomposition aims to split highly complex scheduling tasks into better manageable subproblems with a balanced number of operations so that good-quality or even optimal partial solutions can be reliably found in a small fraction of runtime. Regarding the feasibility and quality of solutions, problem decomposition must respect the precedence of operations within their jobs and partial schedules optimized by time windows should yield better global solutions than obtainable in similar runtime on the entire instance. We devise and investigate a variety of decomposition strategies in terms of the number and size of time windows as well as heuristics for choosing their operations. Moreover, we incorporate time window overlapping and compression techniques into the iterative scheduling process to counteract window-wise optimization limitations restricted to partial schedules. Our experiments on JSP benchmark sets of several sizes show that successive optimization by multi-shot ASP solving leads to substantially better schedules within the runtime limit than global optimization on the full problem, where the gap increases with the number of operations to schedule. While the obtained solution quality still remains behind a state-of-the-art Constraint Programming system, our multi-shot solving approach comes closer the larger the instance size, demonstrating good scalability by problem decomposition.","PeriodicalId":49436,"journal":{"name":"Theory and Practice of Logic Programming","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2022-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45922822","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 : 2022-05-16DOI: 10.1017/S147106842200014X
Rafael Kiesel, Pietro Totis, Angelika Kimmig
Abstract Quantitative extensions of logic programming often require the solution of so called second level inference tasks, that is, problems that involve a third operation, such as maximization or normalization, on top of addition and multiplication, and thus go beyond the well-known weighted or algebraic model counting setting of probabilistic logic programming under the distribution semantics. We introduce Second Level Algebraic Model Counting (2AMC) as a generic framework for these kinds of problems. As 2AMC is to (algebraic) model counting what forall-exists-SAT is to propositional satisfiability, it is notoriously hard to solve. First level techniques based on Knowledge Compilation (KC) have been adapted for specific 2AMC instances by imposing variable order constraints on the resulting circuit. However, those constraints can severely increase the circuit size and thus decrease the efficiency of such approaches. We show that we can exploit the logical structure of a 2AMC problem to omit parts of these constraints, thus limiting the negative effect. Furthermore, we introduce and implement a strategy to generate a sufficient set of constraints statically, with a priori guarantees for the performance of KC. Our empirical evaluation on several benchmarks and tasks confirms that our theoretical results can translate into more efficient solving in practice.
{"title":"Efficient Knowledge Compilation Beyond Weighted Model Counting","authors":"Rafael Kiesel, Pietro Totis, Angelika Kimmig","doi":"10.1017/S147106842200014X","DOIUrl":"https://doi.org/10.1017/S147106842200014X","url":null,"abstract":"Abstract Quantitative extensions of logic programming often require the solution of so called second level inference tasks, that is, problems that involve a third operation, such as maximization or normalization, on top of addition and multiplication, and thus go beyond the well-known weighted or algebraic model counting setting of probabilistic logic programming under the distribution semantics. We introduce Second Level Algebraic Model Counting (2AMC) as a generic framework for these kinds of problems. As 2AMC is to (algebraic) model counting what forall-exists-SAT is to propositional satisfiability, it is notoriously hard to solve. First level techniques based on Knowledge Compilation (KC) have been adapted for specific 2AMC instances by imposing variable order constraints on the resulting circuit. However, those constraints can severely increase the circuit size and thus decrease the efficiency of such approaches. We show that we can exploit the logical structure of a 2AMC problem to omit parts of these constraints, thus limiting the negative effect. Furthermore, we introduce and implement a strategy to generate a sufficient set of constraints statically, with a priori guarantees for the performance of KC. Our empirical evaluation on several benchmarks and tasks confirms that our theoretical results can translate into more efficient solving in practice.","PeriodicalId":49436,"journal":{"name":"Theory and Practice of Logic Programming","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2022-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42718281","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}
$mathcal{P}$ remains non-contradictory given any allowed set of such input data. For that, we introduce the notion of conflict-resolving 
${lambda}$ -extensions. A conflict-resolving 
${lambda}$ -extension for a conflicting rule r is a set 
${lambda}$ of (default) literals such that extending the body of r by 
${lambda}$ resolves all conflicts of r at once. We investigate the properties that suitable 
${lambda}$ -extensions should possess and building on that, we develop a strategy to compute all such conflict-resolving 
${lambda}$ -extensions for each conflicting rule in 
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