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76
The DLV System for Knowledge Representation and Reasoning
 ACM Transactions on Computational Logic
, 2002
"... Disjunctive Logic Programming (DLP) is an advanced formalism for knowledge representation and reasoning, which is very expressive in a precise mathematical sense: it allows to express every property of finite structures that is decidable in the complexity class ΣP 2 (NPNP). Thus, under widely believ ..."
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Cited by 456 (102 self)
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Disjunctive Logic Programming (DLP) is an advanced formalism for knowledge representation and reasoning, which is very expressive in a precise mathematical sense: it allows to express every property of finite structures that is decidable in the complexity class ΣP 2 (NPNP). Thus, under widely believed assumptions, DLP is strictly more expressive than normal (disjunctionfree) logic programming, whose expressiveness is limited to properties decidable in NP. Importantly, apart from enlarging the class of applications which can be encoded in the language, disjunction often allows for representing problems of lower complexity in a simpler and more natural fashion. This paper presents the DLV system, which is widely considered the stateoftheart implementation of disjunctive logic programming, and addresses several aspects. As for problem solving, we provide a formal definition of its kernel language, functionfree disjunctive logic programs (also known as disjunctive datalog), extended by weak constraints, which are a powerful tool to express optimization problems. We then illustrate the usage of DLV as a tool for knowledge representation and reasoning, describing a new declarative programming methodology which allows one to encode complex problems (up to ∆P 3complete problems) in a declarative fashion. On the foundational side, we provide a detailed analysis of the computational complexity of the language of
The Refined Extension Principle for Semantics of Dynamic Logic Programming
, 2005
"... Over recent years, various semantics have been proposed for dealing with updates in the setting of logic programs. The availability of different semantics naturally raises the question of which are most adequate to model updates. A systematic approach to face this question is to identify general pri ..."
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Cited by 64 (23 self)
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Over recent years, various semantics have been proposed for dealing with updates in the setting of logic programs. The availability of different semantics naturally raises the question of which are most adequate to model updates. A systematic approach to face this question is to identify general principles against which such semantics could be evaluated. In this paper we motivate and introduce a new such principle  the refined extension principle. Such principle is complied with by the stable model semantics for (single) logic programs. It turns out that none of the existing semantics for logic program updates, even though generalisations of the stable model semantics, comply with this principle. For this reason, we define a refinement of the dynamic stable model semantics for Dynamic Logic Programs that complies with the principle.
Semantic Forgetting in Answer Set Programming
, 2008
"... The notion of forgetting, also known as variable elimination, has been investigated extensively in the context of classical logic, but less so in (nonmonotonic) logic programming and nonmonotonic reasoning. The few approaches that exist are based on syntactic modifications of a program at hand. In t ..."
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Cited by 29 (9 self)
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The notion of forgetting, also known as variable elimination, has been investigated extensively in the context of classical logic, but less so in (nonmonotonic) logic programming and nonmonotonic reasoning. The few approaches that exist are based on syntactic modifications of a program at hand. In this paper, we establish a declarative theory of forgetting for disjunctive logic programs under answer set semantics that is fully based on semantic grounds. The suitability of this theory is justified by a number of desirable properties. In particular, one of our results shows that our notion of forgetting can be entirely captured by classical forgetting. We present several algorithms for computing a representation of the result of forgetting, and provide a characterization of the computational complexity of reasoning from a logic program under forgetting. As applications of our approach, we present a fairly general framework for resolving conflicts in inconsistent knowledge bases that are represented by disjunctive logic programs, and we show how the semantics of inheritance logic programs and update logic programs from the literature can be characterized through forgetting. The basic idea of the conflict resolution framework is to weaken the preferences of each agent by forgetting certain knowledge that causes inconsistency. In particular, we show how to use the notion of forgetting to provide an elegant solution for preference elicitation in disjunctive logic programming.
Updating action domain descriptions
 in Proc. IJCAI
, 2005
"... How can an intelligent agent update her knowledge base about an action domain, relative to some conditions (possibly obtained from earlier observations)? We study this question in a formal framework for reasoning about actions and change, in which the meaning of an action domain description can be r ..."
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Cited by 24 (5 self)
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How can an intelligent agent update her knowledge base about an action domain, relative to some conditions (possibly obtained from earlier observations)? We study this question in a formal framework for reasoning about actions and change, in which the meaning of an action domain description can be represented by a directed graph whose nodes correspond to states and whose edges correspond to action occurrences. We define the update of an action domain description in this framework, and show among other results that a solution to this problem can be obtained by a divideandconquer approach in some cases. We also introduce methods to compute a solution and an approximate solution to this problem, and analyze the computational complexity of these problems. Finally, we discuss techniques to improve the quality of solutions. 1
A PreferenceBased Framework for Updating Logic Programs
, 2007
"... We present a framework for updating logic programs under the answerset semantics that builds on existing work on preferences in logic programming. The approach is simple and general, making use of two distinct complementary techniques: defaultification and preference. While defaultification resolve ..."
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Cited by 19 (3 self)
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We present a framework for updating logic programs under the answerset semantics that builds on existing work on preferences in logic programming. The approach is simple and general, making use of two distinct complementary techniques: defaultification and preference. While defaultification resolves potential conflicts by inducing more answer sets, preferences then select among these answer sets, yielding the answer sets generated by those rules that have been added more recently. We examine instances of the framework with respect to various desirable properties; for the most part, these properties are satisfied by instances of our framework. Finally, the proposed framework is also easily implementable by offtheshelf systems.
On semantic update operators for answerset programs
 In Proceedings of the 19th European Conference on Artificial Intelligence (ECAI
, 2010
"... Abstract. Logic programs under the stable models semantics, or answerset programs, provide an expressive rule based knowledge representation framework, featuring formal, declarative and wellunderstood semantics. However, handling the evolution of rule bases is still a largely open problem. The AGM ..."
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Cited by 19 (9 self)
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Abstract. Logic programs under the stable models semantics, or answerset programs, provide an expressive rule based knowledge representation framework, featuring formal, declarative and wellunderstood semantics. However, handling the evolution of rule bases is still a largely open problem. The AGM framework for belief change was shown to give inappropriate results when directly applied to logic programs under a nonmonotonic semantics such as the stable models. Most approaches to address this issue, developed so far, proposed update operators based on syntactic conditions for rule rejection. More recently, AGM revision has been successfully applied to a significantly more expressive semantic characterisation of logic programs based on SE models. This is an important step, as it changes the focus from the evolution of a syntactic representation of a rule base to the evolution of its semantic content. In this paper, we borrow results from the area of belief update to tackle the problem of updating (instead of revising) logic programs. We prove a representation theorem which makes it possible to constructively define any operator satisfying a set of postulates derived from Katsuno and Mendelzon’s postulates for belief update. We define a specific operator based on this theorem and compare the behaviour of this operator with syntactic update operators defined in the literature. Perhaps surprisingly, we uncover a very serious drawback in a large class of semantic update operators to which it belongs. 1
Towards automated integration of guess and check programs in answer set programming: a metainterpreter and applications
, 2004
"... Answer set programming (ASP) with disjunction offers a powerful tool for declaratively representing and solving hard problems. Many NPcomplete problems can be encoded in the answer set semantics of logic programs in a very concise and intuitive way, where the encoding reflects the typical " ..."
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Cited by 16 (2 self)
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Answer set programming (ASP) with disjunction offers a powerful tool for declaratively representing and solving hard problems. Many NPcomplete problems can be encoded in the answer set semantics of logic programs in a very concise and intuitive way, where the encoding reflects the typical "guess and check" nature of NP problems: The property is encoded in a way such that polynomial size certificates for it correspond to stable models of a program. However, the problemsolving capacity of full disjunctive logic programs (DLPs) is beyond NP, and captures a class of problems at the second level of the polynomial hierarchy. While these problems also have a clear "guess and check" structure, an encoding in a DLP reflecting it intuitively may sometimes be a nonobvious task, in particular if the "check" itself is a coNPcomplete problem; usually, such problems are solved by interleaving separate guess and check programs, where the check is expressed by inconsistency of the check program. In this paper, we present general transformations of headcycle free (extended) logic programs into stratified and positive (extended) disjunctive logic programs based on metainterpretation techniques. The answer sets of the original and the transformed program are in simple correspondence, and, moreover, inconsistency of the original program is indicated by a designated answer set of the transformed program. This enables one to integrate separate "guess" and "check" programs, which are often easy to obtain, automatically into a single disjunctive logic program. Our results complement recent results on metainterpretation in ASP, and extend methods and techniques for a declarative "guess and check" problem solving paradigm through ASP.
Robust Equivalence Models for Semantic Updates of AnswerSet Programs
 PROCEEDINGS OF THE THIRTEENTH INTERNATIONAL CONFERENCE ON PRINCIPLES OF KNOWLEDGE REPRESENTATION AND REASONING
"... Existing methods for dealing with knowledge updates differ greatly depending on the underlying knowledge representation formalism. When Classical Logic is used, update operators are typically based on manipulating the knowledge base on the modeltheoretic level. On the opposite side of the spectrum ..."
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Cited by 15 (6 self)
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Existing methods for dealing with knowledge updates differ greatly depending on the underlying knowledge representation formalism. When Classical Logic is used, update operators are typically based on manipulating the knowledge base on the modeltheoretic level. On the opposite side of the spectrum stand the semantics for updating AnswerSet Programs where most approaches need to rely on rule syntax. Yet, a unifying perspective that could embrace all these approaches is of great importance as it enables a deeper understanding of all involved methods and principles and creates room for their crossfertilisation, ripening and further development. This paper bridges these seemingly irreconcilable approaches to updates. It introduces a novel monotonic characterisation of rules, dubbed REmodels, and shows it to be a more suitable semantic foundation for rule updates than SEmodels. A generic framework for defining semantic rule update operators is then proposed. It is based on the idea of viewing a program as the set of sets of REmodels of its rules; updates are performed by introducing additional interpretations to the sets of REmodels of rules in the original program. It is shown that particular instances of the framework are closely related to both belief update principles and traditional approaches to rule updates and enjoy a range of plausible syntactic as well as semantic properties.
Solving logic program conflicts through strong and weak forgettings
 IN PROCEEDINGS OF THE INTERNATIONAL JOINT CONFERENCE ON ARTIFICIAL INTELLIGENCE
, 2005
"... We consider how to forget a set of atoms in a logic program. Intuitively, when a set of atoms is forgotten from a logic program, all atoms in the set should be eliminated from this program in some way, and other atoms related to them in the program might also be affected. We define notions of strong ..."
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Cited by 15 (6 self)
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We consider how to forget a set of atoms in a logic program. Intuitively, when a set of atoms is forgotten from a logic program, all atoms in the set should be eliminated from this program in some way, and other atoms related to them in the program might also be affected. We define notions of strong and weak forgettings in logic programs to capture such intuition and reveal their close connections to the notion of forgetting in classical propositional theories. Based on these notions, we then propose a framework for conflict solving in logic programs, which is general enough to represent many important conflict solving problems. We also study some essential semantic and computational properties in relation to strong and weak forgettings and conflict solving in our framework.
Semantics for dynamic logic programming: a principled based approach
 In 7th Int. Conf. on Logic Programming and Nonmonotonic Reasoning (LPNMR7), volume 1730 of LNAI
, 2004
"... Abstract. Over recent years, various semantics have been proposed for dealing with updates in the setting of logic programs. The availability of different semantics naturally raises the question of which are most adequate to model updates. A systematic approach to face this question is to identify g ..."
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Cited by 14 (6 self)
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Abstract. Over recent years, various semantics have been proposed for dealing with updates in the setting of logic programs. The availability of different semantics naturally raises the question of which are most adequate to model updates. A systematic approach to face this question is to identify general principles against which such semantics could be evaluated. In this paper we motivate and introduce a new such principle – the refined extension principle – which is complied with by the stable model semantics for (single) logic programs. It turns out that none of the existing semantics for logic program updates, even though based on stable models, complies with this principle. For this reason, we define a refinement of the dynamic stable model semantics for Dynamic Logic Programs that complies with the principle. 1