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Wellfounded semantics for description logic programs in the Semantic Web
, 2009
"... The realization of the Semantic Web vision, in which computational logic has a prominent role, has stimulated a lot of research on combining rules and ontologies, which are formulated in different formalisms, into a framework that is more useful for describing semantic content. In particular, combin ..."
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Cited by 57 (17 self)
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The realization of the Semantic Web vision, in which computational logic has a prominent role, has stimulated a lot of research on combining rules and ontologies, which are formulated in different formalisms, into a framework that is more useful for describing semantic content. In particular, combining logic programming with the Web Ontology Language (OWL), which is a standard based on description logics, emerged as an important issue for linking the Rules and Ontology Layers of the Semantic Web. Nonmonotonic description logic programs (or dlprograms) were introduced for such a combination, in which a pair (L,P) of a description logic knowledge base L and a set of rules P with negation as failure is given a modelbased semantics that generalizes the answer set semantics of logic programs. In this paper, we reconsider dlprograms and present a wellfounded semantics for them as an analog for the other main semantics of logic programs. It generalizes the canonical definition of the wellfounded semantics based on unfounded sets, and, as we show, lifts many of the wellknown properties from ordinary logic programs to dlprograms. Among these properties: our semantics amounts to a partial model approximating the answer set semantics, which yields for positive and stratified dlprograms a total model coinciding with the answer set semantics; it has polynomial data complexity provided the access to the description logic
Ultimate Wellfounded and Stable Semantics for Logic Programs With Aggregates (Extended Abstract)
 In Proceedings of ICLP01, LNCS 2237
, 2001
"... is relatively straightforward. Another advantage of the ultimate approximation is that in cases where TP is monotone the ultimate wellfounded model will be 2valued and will coincide with the least fixpoint of TP . This is not the case for the standard wellfounded semantics. For example in the sta ..."
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Cited by 44 (7 self)
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is relatively straightforward. Another advantage of the ultimate approximation is that in cases where TP is monotone the ultimate wellfounded model will be 2valued and will coincide with the least fixpoint of TP . This is not the case for the standard wellfounded semantics. For example in the standard wellfounded model of the program: # p. p. p is undefined while the associated TP operator is monotone and p is true in the ultimate wellfounded model. One disadvantage of using the ultimate semantics is that it has a higher computational cost even for programs without aggregates. The complexity goes one level higher in the polynomial hierarchy to # 2 for the wellfounded model and to 2 for a stable model which is also complete for this class [2]. Fortunately, by adding aggregates the complexity does not increase further. To give an example of a logic program with aggregates we consider the problem of computing the length of the shortest path between two nodes in a direc
A logic of nonmonotone inductive definitions
 ACM transactions on computational logic
, 2007
"... Wellknown principles of induction include monotone induction and different sorts of nonmonotone induction such as inflationary induction, induction over wellfounded sets and iterated induction. In this work, we define a logic formalizing induction over wellfounded sets and monotone and iterated i ..."
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Cited by 28 (16 self)
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Wellknown principles of induction include monotone induction and different sorts of nonmonotone induction such as inflationary induction, induction over wellfounded sets and iterated induction. In this work, we define a logic formalizing induction over wellfounded sets and monotone and iterated induction. Just as the principle of positive induction has been formalized in FO(LFP), and the principle of inflationary induction has been formalized in FO(IFP), this paper formalizes the principle of iterated induction in a new logic for NonMonotone Inductive Definitions (IDlogic). The semantics of the logic is strongly influenced by the wellfounded semantics of logic programming. This paper discusses the formalisation of different forms of (non)monotone induction by the wellfounded semantics and illustrates the use of the logic for formalizing mathematical and commonsense knowledge. To model different types of induction found in mathematics, we define several subclasses of definitions, and show that they are correctly formalized by the wellfounded semantics. We also present translations into classical first or second order logic. We develop modularity and totality results and demonstrate their use to analyze and simplify complex definitions. We illustrate the use of the logic for temporal reasoning. The logic formally extends Logic Programming, Abductive Logic Programming and Datalog, and thus formalizes the view on these formalisms as logics of (generalized) inductive definitions. Categories and Subject Descriptors:... [...]:... 1.
Abstract dialectical frameworks
 In Proc. KR2010
, 2010
"... In this paper we introduce dialectical frameworks, a powerful generalization of Dungstyle argumentation frameworks where each node comes with an associated acceptance condition. This allows us to model different types of dependencies, e.g. support and attack, as well as different types of nodes wit ..."
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Cited by 11 (3 self)
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In this paper we introduce dialectical frameworks, a powerful generalization of Dungstyle argumentation frameworks where each node comes with an associated acceptance condition. This allows us to model different types of dependencies, e.g. support and attack, as well as different types of nodes within a single framework. We show that Dung’s standard semantics can be generalized to dialectical frameworks, in case of stable and preferred semantics to a slightly restricted class which we call bipolar frameworks. We show how acceptance conditions can be conveniently represented using weights respectively priorities on the links and demonstrate how some of the legal proof standards can be modeled based on this idea.
Rough Sets and Approximation Schemes
"... Abstract. Approximate reasoning is used in a variety of reasoning tasks in Logicbased Artificial Intelligence. In this abstract we compare a number of such reasoning schemes and show how they relate and differ from the approach of Pawlak’s Rough Sets. 1 ..."
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Abstract. Approximate reasoning is used in a variety of reasoning tasks in Logicbased Artificial Intelligence. In this abstract we compare a number of such reasoning schemes and show how they relate and differ from the approach of Pawlak’s Rough Sets. 1
Towards a Unified Theory of Logic Programming
, 2005
"... Currently, the variety of expressive extensions and di#erent semantics created for logic programs with negation is diverse and heterogeneous, and there is a lack of comprehensive comparative studies which map out the multitude of perspectives in a uniform way. Most recently, however, new methodo ..."
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Currently, the variety of expressive extensions and di#erent semantics created for logic programs with negation is diverse and heterogeneous, and there is a lack of comprehensive comparative studies which map out the multitude of perspectives in a uniform way. Most recently, however, new methodologies have been proposed which allow one to derive uniform characterizations of di#erent declarative semantics for logic programs with negation. In this paper, we study the relationship between two of these approaches, namely the level mapping characterizations due to [17], and the selector generated models due to [24]. We will show that the latter can be captured by means of the former, thereby supporting the claim that level mappings provide a very flexible framework which is applicable to very diversely defined semantics.
Nonmonotonic logics and their algebraic foundations
"... Abstract. The goal of this note is to provide a background and references for the invited lecture presented at Computer Science Logic 2006. We briefly discuss motivations that led to the emergence of nonmonotonic logics and introduce two major nonmonotonic formalisms, default and autoepistemic logic ..."
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Abstract. The goal of this note is to provide a background and references for the invited lecture presented at Computer Science Logic 2006. We briefly discuss motivations that led to the emergence of nonmonotonic logics and introduce two major nonmonotonic formalisms, default and autoepistemic logics. We then point out to algebraic principles behind the two logics and present an abstract algebraic theory that unifies them and provides an effective framework to study properties of nonmonotonic reasoning. We conclude with comments on other major research directions in nonmonotonic logics. 1 Why nonmonotonic logics In the late 1970s, research on languages for knowledge representation, and considerations of basic patterns of commonsense reasoning brought attention to rules of inference that admit exceptions and are used only under the assumption of normality of the world in which one functions or to put it differently, when things are as expected. For instance, a knowledge base concerning a university should support an inference that, given no information that might indicate otherwise, if Dr. Jones is a professor at
Reiter’s Default Logic Is a Logic of Autoepistemic Reasoning And a Good One, Too
"... Abstract: A fact apparently not observed earlier in the literature of nonmonotonic reasoning is that Reiter, in his default logic paper, did not directly formalize informal defaults. Instead, he translated a default into a certain natural language proposition and provided a formalization of the latt ..."
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Abstract: A fact apparently not observed earlier in the literature of nonmonotonic reasoning is that Reiter, in his default logic paper, did not directly formalize informal defaults. Instead, he translated a default into a certain natural language proposition and provided a formalization of the latter. A few years later, Moore noted that propositions like the one used by Reiter are fundamentally different than defaults and exhibit a certain autoepistemic nature. Thus, Reiter had developed his default logic as a formalization of autoepistemic propositions rather than of defaults. The first goal of this paper is to show that some problems of Reiter’s default logic as a formal way to reason about informal defaults are directly attributable to the autoepistemic nature of default logic and to the mismatch between informal defaults and the Reiter’s formal defaults, the latter being a formal expression of the autoepistemic propositions Reiter used as a representation of informal defaults. The second goal of our paper is to compare the work of Reiter and Moore. While each of them attempted to formalize autoepistemic propositions, the modes of reasoning in their respective logics were different. We revisit Moore’s and Reiter’s intuitions and present them from the perspective of autotheoremhood, where theories can include propositions referring to the theory’s own theorems. We then discuss the formalization of this perspective in the logics of Moore and Reiter, respectively, using the unifying semantic framework for default and autoepistemic logics that we developed earlier. We argue that Reiter’s default logic is a better formalization of Moore’s intuitions about autoepistemic propositions than Moore’s own autoepistemic logic. 1
Advancing MultiContext Systems by Inconsistency Management ⋆
, 1107
"... Abstract. MultiContext Systems are an expressive formalism to model (possibly) nonmonotonic information exchange between heterogeneous knowledge bases. Such information exchange, however, often comeswith unforseen sideeffects leading to violation of constraints, making the system inconsistent, an ..."
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Abstract. MultiContext Systems are an expressive formalism to model (possibly) nonmonotonic information exchange between heterogeneous knowledge bases. Such information exchange, however, often comeswith unforseen sideeffects leading to violation of constraints, making the system inconsistent, and thus unusable. Although there are many approaches to assess and repair a single inconsistent knowledge base, the heterogeneous nature of MultiContext Systems poses problems which have not yet been addressed in a satisfying way: How to identify and explain a inconsistency that spreads over multiple knowledge bases with different logical formalisms (e.g., logic programs and ontologies)? What are the causes of inconsistency if inference/information exchange is nonmonotonic (e.g., absent information as cause)? How to deal with inconsistency if access to knowledge bases is restricted (e.g., companies exchange information, but do not allow arbitrary modifications to their knowledge bases)? Many traditional approaches solely aim for a consistent system, but automatic removal of inconsistency is not always desireable. Therefore a human operator has to be supported in finding the erroneous parts contributing to the inconsistency. In my thesis those issues will be adressed mainly from a foundational perspective, while our research project also provides algorithms and prototype implementations. 1
Reconciling WellFounded Semantics of DLPrograms and Aggregate Programs ∗
"... Logic programs with aggregates and description logic programs (dlprograms) are two recent extensions to logic programming. In this paper, we study the relationships between these two classes of logic programs, under the wellfounded semantics. The main result is that, under a satisfactionpreservin ..."
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Logic programs with aggregates and description logic programs (dlprograms) are two recent extensions to logic programming. In this paper, we study the relationships between these two classes of logic programs, under the wellfounded semantics. The main result is that, under a satisfactionpreserving mapping from dlatoms to aggregates, the wellfounded semantics of dlprograms by Eiter et al., coincides with the wellfounded semantics of aggregate programs, defined by Pelov et al. as the least fixpoint of a 3valued immediate consequence operator under the ultimate approximating aggregate. This result enables an alternative definition of the same wellfounded semantics for aggregate programs, in terms of the first principle of unfounded sets. Furthermore, the result can be applied, in a uniform manner, to define the wellfounded semantics for dlprograms with aggregates, which agrees with the existing semantics when either dlatoms or aggregates are absent.