Pub Date : 2021-09-03DOI: 10.1017/s1471068421000533
D. Miller
Several formal systems, such as resolution and minimal model semantics, provide a framework for logic programming. In this article, we will survey the use of structural proof theory as an alternative foundation. Researchers have been using this foundation for the past 35 years to elevate logic programming from its roots in first-order classical logic into higher-order versions of intuitionistic and linear logic. These more expressive logic programming languages allow for capturing stateful computations and rich forms of abstractions, including higher-order programming, modularity, and abstract data types. Term-level bindings are another kind of abstraction, and these are given an elegant and direct treatment within both proof theory and these extended logic programming languages. Logic programming has also inspired new results in proof theory, such as those involving polarity and focused proofs. These recent results provide a high-level means for presenting the differences between forward-chaining and backward-chaining style inferences. Anchoring logic programming in proof theory has also helped identify its connections and differences with functional programming, deductive databases, and model checking.
{"title":"A Survey of the Proof-Theoretic Foundations of Logic Programming","authors":"D. Miller","doi":"10.1017/s1471068421000533","DOIUrl":"https://doi.org/10.1017/s1471068421000533","url":null,"abstract":"\u0000 Several formal systems, such as resolution and minimal model semantics, provide a framework for logic programming. In this article, we will survey the use of structural proof theory as an alternative foundation. Researchers have been using this foundation for the past 35 years to elevate logic programming from its roots in first-order classical logic into higher-order versions of intuitionistic and linear logic. These more expressive logic programming languages allow for capturing stateful computations and rich forms of abstractions, including higher-order programming, modularity, and abstract data types. Term-level bindings are another kind of abstraction, and these are given an elegant and direct treatment within both proof theory and these extended logic programming languages. Logic programming has also inspired new results in proof theory, such as those involving polarity and focused proofs. These recent results provide a high-level means for presenting the differences between forward-chaining and backward-chaining style inferences. Anchoring logic programming in proof theory has also helped identify its connections and differences with functional programming, deductive databases, and model checking.","PeriodicalId":49436,"journal":{"name":"Theory and Practice of Logic Programming","volume":"62 1","pages":"859-904"},"PeriodicalIF":1.4,"publicationDate":"2021-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86064928","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}
{"title":"Introduction to the 37th International Conference on Logic Programming Special Issue I","authors":"A. Brik, A. Formisano, Yanhong A. Liu, Joost Vennekens","doi":"10.1017/S1471068421000442","DOIUrl":"https://doi.org/10.1017/S1471068421000442","url":null,"abstract":"programming, Constraint logic programming, Answer set programming, Interaction with SAT, SMT and CSP solvers, Theorem proving, Argumentation, Probabilistic programming, Machine learning.","PeriodicalId":49436,"journal":{"name":"Theory and Practice of Logic Programming","volume":"21 1","pages":"521 - 526"},"PeriodicalIF":1.4,"publicationDate":"2021-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48787012","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 : 2021-08-17DOI: 10.1017/s147106842100048x
Jorge Fandinno, Wolfgang Faber, M. Gelfond
The language of epistemic specifications and epistemic logic programs extends disjunctive logic programs under the stable model semantics with modal constructs called subjective literals. Using subjective literals, it is possible to check whether a regular literal is true in every or some stable models of the program, those models, in this context also called belief sets, being collected in a set called world view. This allows for representing, within the language, whether some proposition should be understood accordingly to the open or the closed world assumption. Several attempts for capturing the intuitions underlying the language by means of a formal semantics were given, resulting in a multitude of proposals that makes it difficult to understand the current state of the art. In this article, we provide an overview of the inception of the field and the knowledge representation and reasoning tasks it is suitable for. We also provide a detailed analysis of properties of proposed semantics, and an outlook of challenges to be tackled by future research in the area.
{"title":"Thirty years of Epistemic Specifications","authors":"Jorge Fandinno, Wolfgang Faber, M. Gelfond","doi":"10.1017/s147106842100048x","DOIUrl":"https://doi.org/10.1017/s147106842100048x","url":null,"abstract":"\u0000 The language of epistemic specifications and epistemic logic programs extends disjunctive logic programs under the stable model semantics with modal constructs called subjective literals. Using subjective literals, it is possible to check whether a regular literal is true in every or some stable models of the program, those models, in this context also called belief sets, being collected in a set called world view. This allows for representing, within the language, whether some proposition should be understood accordingly to the open or the closed world assumption. Several attempts for capturing the intuitions underlying the language by means of a formal semantics were given, resulting in a multitude of proposals that makes it difficult to understand the current state of the art. In this article, we provide an overview of the inception of the field and the knowledge representation and reasoning tasks it is suitable for. We also provide a detailed analysis of properties of proposed semantics, and an outlook of challenges to be tackled by future research in the area.","PeriodicalId":49436,"journal":{"name":"Theory and Practice of Logic Programming","volume":"13 1","pages":"1043-1083"},"PeriodicalIF":1.4,"publicationDate":"2021-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91323082","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 : 2021-08-13DOI: 10.1017/S1471068421000259
Jorge Fandinno, Franccois Laferriere, J. Romero, Torsten Schaub, Tran Cao Son New Mexico State University, Usa, Omaha State University, U. Potsdam, H Germany
Abstract We present a general approach to planning with incomplete information in Answer Set Programming (ASP). More precisely, we consider the problems of conformant and conditional planning with sensing actions and assumptions. We represent planning problems using a simple formalism where logic programs describe the transition function between states, the initial states and the goal states. For solving planning problems, we use Quantified Answer Set Programming (QASP), an extension of ASP with existential and universal quantifiers over atoms that is analogous to Quantified Boolean Formulas (QBFs). We define the language of quantified logic programs and use it to represent the solutions different variants of conformant and conditional planning. On the practical side, we present a translation-based QASP solver that converts quantified logic programs into QBFs and then executes a QBF solver, and we evaluate experimentally the approach on conformant and conditional planning benchmarks.
{"title":"Planning with Incomplete Information in Quantified Answer Set Programming","authors":"Jorge Fandinno, Franccois Laferriere, J. Romero, Torsten Schaub, Tran Cao Son New Mexico State University, Usa, Omaha State University, U. Potsdam, H Germany","doi":"10.1017/S1471068421000259","DOIUrl":"https://doi.org/10.1017/S1471068421000259","url":null,"abstract":"Abstract We present a general approach to planning with incomplete information in Answer Set Programming (ASP). More precisely, we consider the problems of conformant and conditional planning with sensing actions and assumptions. We represent planning problems using a simple formalism where logic programs describe the transition function between states, the initial states and the goal states. For solving planning problems, we use Quantified Answer Set Programming (QASP), an extension of ASP with existential and universal quantifiers over atoms that is analogous to Quantified Boolean Formulas (QBFs). We define the language of quantified logic programs and use it to represent the solutions different variants of conformant and conditional planning. On the practical side, we present a translation-based QASP solver that converts quantified logic programs into QBFs and then executes a QBF solver, and we evaluate experimentally the approach on conformant and conditional planning benchmarks.","PeriodicalId":49436,"journal":{"name":"Theory and Practice of Logic Programming","volume":"21 1","pages":"663 - 679"},"PeriodicalIF":1.4,"publicationDate":"2021-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46738828","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 : 2021-08-11DOI: 10.1017/s1471068421000119
Stefan Borgwardt, Walter Forkel, Alisa Kovtunova
Ontology-mediated query answering is a popular paradigm for enriching answers to user queries with background knowledge. For querying the absence of information, however, there exist only few ontology-based approaches. Moreover, these proposals conflate the closed-domain and closed-world assumption and, therefore, are not suited to deal with the anonymous objects that are common in ontological reasoning. Many real-world applications, like processing electronic health records, also contain a temporal dimension and require efficient reasoning algorithms. Moreover, since medical data are not recorded on a regular basis, reasoners must deal with sparse data with potentially large temporal gaps. Our contribution consists of two main parts: In the first part, we introduce a new closed-world semantics for answering conjunctive queries (CQs) with negation over ontologies formulated in the description logic $${mathcal E}{mathcal L}{{mathcal H}_ bot }$$ , which is based on the minimal canonical model. We propose a rewriting strategy for dealing with negated query atoms, which shows that query answering is possible in polynomial time in data complexity. In the second part, we extend this minimal-world semantics for answering metric temporal CQs with negation over the lightweight temporal logic and obtain similar rewritability and complexity results.
{"title":"Temporal Minimal-World Query Answering over Sparse ABoxes","authors":"Stefan Borgwardt, Walter Forkel, Alisa Kovtunova","doi":"10.1017/s1471068421000119","DOIUrl":"https://doi.org/10.1017/s1471068421000119","url":null,"abstract":"Ontology-mediated query answering is a popular paradigm for enriching answers to user queries with background knowledge. For querying the absence of information, however, there exist only few ontology-based approaches. Moreover, these proposals conflate the closed-domain and closed-world assumption and, therefore, are not suited to deal with the anonymous objects that are common in ontological reasoning. Many real-world applications, like processing electronic health records, also contain a temporal dimension and require efficient reasoning algorithms. Moreover, since medical data are not recorded on a regular basis, reasoners must deal with sparse data with potentially large temporal gaps. Our contribution consists of two main parts: In the first part, we introduce a new closed-world semantics for answering conjunctive queries (CQs) with negation over ontologies formulated in the description logic $${mathcal E}{mathcal L}{{mathcal H}_ bot }$$ , which is based on the minimal canonical model. We propose a rewriting strategy for dealing with negated query atoms, which shows that query answering is possible in polynomial time in data complexity. In the second part, we extend this minimal-world semantics for answering metric temporal CQs with negation over the lightweight temporal logic and obtain similar rewritability and complexity results.","PeriodicalId":49436,"journal":{"name":"Theory and Practice of Logic Programming","volume":"3 1","pages":"193-228"},"PeriodicalIF":1.4,"publicationDate":"2021-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86639784","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 : 2021-08-11DOI: 10.1017/S1471068421000429
L. Chrpa, Wolfgang Faber, Daniel Fiser, Michael Morak
Abstract In the context of planning and reasoning about actions and change, we call an action reversible when its effects can be reverted by applying other actions, returning to the original state. Renewed interest in this area has led to several results in the context of the PDDL language, widely used for describing planning tasks. In this paper, we propose several solutions to the computational problem of deciding the reversibility of an action. In particular, we leverage an existing translation from PDDL to Answer Set Programming (ASP), and then use several different encodings to tackle the problem of action reversibility for the STRIPS fragment of PDDL. For these, we use ASP, as well as Epistemic Logic Programming (ELP), an extension of ASP with epistemic operators, and compare and contrast their strengths and weaknesses.
{"title":"Determining Action Reversibility in STRIPS Using Answer Set and Epistemic Logic Programming","authors":"L. Chrpa, Wolfgang Faber, Daniel Fiser, Michael Morak","doi":"10.1017/S1471068421000429","DOIUrl":"https://doi.org/10.1017/S1471068421000429","url":null,"abstract":"Abstract In the context of planning and reasoning about actions and change, we call an action reversible when its effects can be reverted by applying other actions, returning to the original state. Renewed interest in this area has led to several results in the context of the PDDL language, widely used for describing planning tasks. In this paper, we propose several solutions to the computational problem of deciding the reversibility of an action. In particular, we leverage an existing translation from PDDL to Answer Set Programming (ASP), and then use several different encodings to tackle the problem of action reversibility for the STRIPS fragment of PDDL. For these, we use ASP, as well as Epistemic Logic Programming (ELP), an extension of ASP with epistemic operators, and compare and contrast their strengths and weaknesses.","PeriodicalId":49436,"journal":{"name":"Theory and Practice of Logic Programming","volume":"21 1","pages":"646 - 662"},"PeriodicalIF":1.4,"publicationDate":"2021-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41551960","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 : 2021-08-10DOI: 10.1017/s1471068421000326
Paul S. Brown, V. Dimitrova, G. Hart, A. Cohn, P. Moura
Whitby is the server-side of an Intelligent Tutoring System application for learning System-Theoretic Process Analysis (STPA), a methodology used to ensure the safety of anything that can be represented with a systems model. The underlying logic driving the reasoning behind Whitby is Situation Calculus, which is a many-sorted logic with situation, action, and object sorts. The Situation Calculus is applied to Ontology Authoring and Contingent Scaffolding: the primary activities within Whitby. Thus many fluents and actions are aggregated in Whitby from these two sub-applications and from Whitby itself, but all are available through a common situation query interface that does not depend upon any of the fluents or actions. Each STPA project in Whitby is a single situation term, which is queried for fluents that include the ontology, and to determine what pedagogical interventions to offer. Initially Whitby was written in Prolog using a module system. In the interest of a cleaner architecture and implementation with improved code reuse and extensibility, the initial application was refactored into Logtalk. This refactoring includes decoupling the Situation Calculus reasoner, Ontology Authoring framework, and Contingent Scaffolding framework into third-party libraries that can be reused in other applications. This extraction was achieved by inverting dependencies via Logtalk protocols and categories, which are reusable interfaces and components that provide functionally cohesive sets of predicate declarations and predicate definitions. In this paper the architectures of two iterations of Whitby are evaluated with respect to the motivations behind the refactor: clean architecture enabling code reuse and extensibility.
Whitby是一个用于学习系统理论过程分析(System- theoretical Process Analysis, STPA)的智能辅导系统应用程序的服务器端，STPA是一种用于确保任何可以用系统模型表示的事物的安全性的方法。驱动Whitby背后推理的底层逻辑是情景演算(Situation Calculus)，这是一种包含情景、动作和对象排序的多排序逻辑。情境演算应用于本体创作和偶然脚手架:惠特比的主要活动。因此，Whitby从这两个子应用程序和Whitby本身聚合了许多流畅度和操作，但所有这些都可以通过一个不依赖于任何流畅度或操作的公共情况查询接口获得。Whitby的每个STPA项目都是一个单独的情境术语，它被查询包括本体的流利程度，并确定提供什么样的教学干预。最初Whitby是用Prolog使用模块系统编写的。为了更清晰的体系结构和实现，以及改进的代码重用和可扩展性，最初的应用程序被重构到Logtalk中。这种重构包括将Situation Calculus推理器、本体创作框架和Contingent Scaffolding框架解耦到可以在其他应用程序中重用的第三方库中。这种提取是通过Logtalk协议和类别反转依赖关系实现的，这些协议和类别是可重用的接口和组件，提供功能上内聚的谓词声明和谓词定义集。在本文中，Whitby的两次迭代的架构根据重构背后的动机进行了评估:干净的架构支持代码重用和可扩展性。
{"title":"Refactoring the Whitby Intelligent Tutoring System for Clean Architecture","authors":"Paul S. Brown, V. Dimitrova, G. Hart, A. Cohn, P. Moura","doi":"10.1017/s1471068421000326","DOIUrl":"https://doi.org/10.1017/s1471068421000326","url":null,"abstract":"\u0000 Whitby is the server-side of an Intelligent Tutoring System application for learning System-Theoretic Process Analysis (STPA), a methodology used to ensure the safety of anything that can be represented with a systems model. The underlying logic driving the reasoning behind Whitby is Situation Calculus, which is a many-sorted logic with situation, action, and object sorts. The Situation Calculus is applied to Ontology Authoring and Contingent Scaffolding: the primary activities within Whitby. Thus many fluents and actions are aggregated in Whitby from these two sub-applications and from Whitby itself, but all are available through a common situation query interface that does not depend upon any of the fluents or actions. Each STPA project in Whitby is a single situation term, which is queried for fluents that include the ontology, and to determine what pedagogical interventions to offer. Initially Whitby was written in Prolog using a module system. In the interest of a cleaner architecture and implementation with improved code reuse and extensibility, the initial application was refactored into Logtalk. This refactoring includes decoupling the Situation Calculus reasoner, Ontology Authoring framework, and Contingent Scaffolding framework into third-party libraries that can be reused in other applications. This extraction was achieved by inverting dependencies via Logtalk protocols and categories, which are reusable interfaces and components that provide functionally cohesive sets of predicate declarations and predicate definitions. In this paper the architectures of two iterations of Whitby are evaluated with respect to the motivations behind the refactor: clean architecture enabling code reuse and extensibility.","PeriodicalId":49436,"journal":{"name":"Theory and Practice of Logic Programming","volume":"21 1","pages":"818-834"},"PeriodicalIF":1.4,"publicationDate":"2021-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88912907","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 : 2021-08-09DOI: 10.1017/S1471068421000247
Mario Alviano, Sotiris Batsakis, George Baryannis
Abstract Modal logic S5 has attracted significant attention and has led to several practical applications, owing to its simplified approach to dealing with nesting modal operators. Efficient implementations for evaluating satisfiability of S5 formulas commonly rely on Skolemisation to convert them into propositional logic formulas, essentially by introducing copies of propositional atoms for each set of interpretations (possible worlds). This approach is simple, but often results into large formulas that are too difficult to process, and therefore more parsimonious constructions are required. In this work, we propose to use Answer Set Programming for implementing such constructions, and in particular for identifying the propositional atoms that are relevant in every world by means of a reachability relation. The proposed encodings are designed to take advantage of other properties such as entailment relations of subformulas rooted by modal operators. An empirical assessment of the proposed encodings shows that the reachability relation is very effective and leads to comparable performance to a state-of-the-art S5 solver based on SAT, while entailment relations are possibly too expensive to reason about and may result in overhead.
{"title":"Modal Logic S5 Satisfiability in Answer Set Programming","authors":"Mario Alviano, Sotiris Batsakis, George Baryannis","doi":"10.1017/S1471068421000247","DOIUrl":"https://doi.org/10.1017/S1471068421000247","url":null,"abstract":"Abstract Modal logic S5 has attracted significant attention and has led to several practical applications, owing to its simplified approach to dealing with nesting modal operators. Efficient implementations for evaluating satisfiability of S5 formulas commonly rely on Skolemisation to convert them into propositional logic formulas, essentially by introducing copies of propositional atoms for each set of interpretations (possible worlds). This approach is simple, but often results into large formulas that are too difficult to process, and therefore more parsimonious constructions are required. In this work, we propose to use Answer Set Programming for implementing such constructions, and in particular for identifying the propositional atoms that are relevant in every world by means of a reachability relation. The proposed encodings are designed to take advantage of other properties such as entailment relations of subformulas rooted by modal operators. An empirical assessment of the proposed encodings shows that the reachability relation is very effective and leads to comparable performance to a state-of-the-art S5 solver based on SAT, while entailment relations are possibly too expensive to reason about and may result in overhead.","PeriodicalId":49436,"journal":{"name":"Theory and Practice of Logic Programming","volume":"21 1","pages":"527 - 542"},"PeriodicalIF":1.4,"publicationDate":"2021-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49488199","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 : 2021-08-08DOI: 10.1017/S1471068421000405
Pascual Julián-Iranzo, F. Sáenz-Pérez
Abstract This paper explores the integration of hypothetical reasoning into an efficient implementation of the fuzzy logic language Bousi∼Prolog. To this end, we first analyse what would be expected from a logic inference system, equipped with what is called embedded implication, to model solving goals with respect to assumptions. We start with a propositional system and incrementally build more complex systems and implementations to satisfy the requirements imposed by a system like Bousi∼Prolog. Finally, we propose an inference system, operational semantics and the translation function to generate efficient Prolog programmes from Bousi∼Prolog programmes.
{"title":"Planning for an Efficient Implementation of Hypothetical Bousi∼Prolog","authors":"Pascual Julián-Iranzo, F. Sáenz-Pérez","doi":"10.1017/S1471068421000405","DOIUrl":"https://doi.org/10.1017/S1471068421000405","url":null,"abstract":"Abstract This paper explores the integration of hypothetical reasoning into an efficient implementation of the fuzzy logic language Bousi∼Prolog. To this end, we first analyse what would be expected from a logic inference system, equipped with what is called embedded implication, to model solving goals with respect to assumptions. We start with a propositional system and incrementally build more complex systems and implementations to satisfy the requirements imposed by a system like Bousi∼Prolog. Finally, we propose an inference system, operational semantics and the translation function to generate efficient Prolog programmes from Bousi∼Prolog programmes.","PeriodicalId":49436,"journal":{"name":"Theory and Practice of Logic Programming","volume":"21 1","pages":"680 - 697"},"PeriodicalIF":1.4,"publicationDate":"2021-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47865918","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 : 2021-08-07DOI: 10.1017/S1471068421000235
A. Charalambidis, P. Rondogiannis, Antonis Troumpoukis
Abstract Logic programs with ordered disjunction (LPODs) extend classical logic programs with the capability of expressing alternatives with decreasing degrees of preference in the heads of program rules. Despite the fact that the operational meaning of ordered disjunction is clear, there exists an important open issue regarding its semantics. In particular, there does not exist a purely model-theoretic approach for determining the most preferred models of an LPOD. At present, the selection of the most preferred models is performed using a technique that is not based exclusively on the models of the program and in certain cases produces counterintuitive results. We provide a novel, model-theoretic semantics for LPODs, which uses an additional truth value in order to identify the most preferred models of a program. We demonstrate that the proposed approach overcomes the shortcomings of the traditional semantics of LPODs. Moreover, the new approach can be used to define the semantics of a natural class of logic programs that can have both ordered and classical disjunctions in the heads of clauses. This allows programs that can express not only strict levels of preferences but also alternatives that are equally preferred.
{"title":"A Logical Characterization of the Preferred Models of Logic Programs with Ordered Disjunction","authors":"A. Charalambidis, P. Rondogiannis, Antonis Troumpoukis","doi":"10.1017/S1471068421000235","DOIUrl":"https://doi.org/10.1017/S1471068421000235","url":null,"abstract":"Abstract Logic programs with ordered disjunction (LPODs) extend classical logic programs with the capability of expressing alternatives with decreasing degrees of preference in the heads of program rules. Despite the fact that the operational meaning of ordered disjunction is clear, there exists an important open issue regarding its semantics. In particular, there does not exist a purely model-theoretic approach for determining the most preferred models of an LPOD. At present, the selection of the most preferred models is performed using a technique that is not based exclusively on the models of the program and in certain cases produces counterintuitive results. We provide a novel, model-theoretic semantics for LPODs, which uses an additional truth value in order to identify the most preferred models of a program. We demonstrate that the proposed approach overcomes the shortcomings of the traditional semantics of LPODs. Moreover, the new approach can be used to define the semantics of a natural class of logic programs that can have both ordered and classical disjunctions in the heads of clauses. This allows programs that can express not only strict levels of preferences but also alternatives that are equally preferred.","PeriodicalId":49436,"journal":{"name":"Theory and Practice of Logic Programming","volume":"21 1","pages":"629 - 645"},"PeriodicalIF":1.4,"publicationDate":"2021-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46828846","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}
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