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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 54 (35 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.
Computing Preferred Answer Sets by MetaInterpretation in Answer Set Programming
 UNDER CONSIDERATION FOR PUBLICATION IN THEORY AND PRACTICE OF LOGIC PROGRAMMING
, 2001
"... Most recently, Answer Set Programming (ASP) has been attracting interest as a new paradigm for problem solving. An important aspect, for which several approaches have been presented, is the handling of preferences between rules. In this paper, we consider the problem of implementing preference handl ..."
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Cited by 25 (7 self)
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Most recently, Answer Set Programming (ASP) has been attracting interest as a new paradigm for problem solving. An important aspect, for which several approaches have been presented, is the handling of preferences between rules. In this paper, we consider the problem of implementing preference handling approaches by means of metainterpreters in Answer Set Programming. In particular, we consider the preferred answer set approaches by Brewka and Eiter, by Delgrande, Schaub and Tompits, and by Wang, Zhou and Lin. We present suitable metainterpreters for these semantics using DLV, which is an efficient engine for ASP. Moreover, we also present a metainterpreter for the weakly preferred answer set approach by Brewka and Eiter, which uses the weak constraint feature of DLV as a tool for expressing and solving an underlying optimization problem. We also consider advanced metainterpreters, which make use of graphbased characterizations and often allow for more efficient computations. Our approach shows the suitability of ASP in general and of DLV in particular for fast prototyping. This can be fruitfully exploited for experimenting with new languages and knowledgerepresentation formalisms.
The Role of Default Logic in Knowledge Representation
 LogicBased Artificial Intelligence
, 2001
"... . Various researchers in Artificial Intelligence have advocated formal logic as an analytical tool and as a formalism for the representation of knowledge. Our thesis in this paper is that commonsense reasoning frequently has a nonmonotonic aspect, either explicit or implicit, and that to this end De ..."
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Cited by 12 (8 self)
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. Various researchers in Artificial Intelligence have advocated formal logic as an analytical tool and as a formalism for the representation of knowledge. Our thesis in this paper is that commonsense reasoning frequently has a nonmonotonic aspect, either explicit or implicit, and that to this end Default Logic (DL) provides an appropriate elaboration of classical logic for the modelling of such phenomena. That is, DL is a very general, flexible, and powerful approach to nonmonotonic reasoning, and its very generality and power makes it suitable as a tool for modelling a wide variety of applications. We propose a general methodology for using Default Logic, involving the naming of default rules and the introduction of specialpurpose predicates, for detecting conditions for default rule applicability and controlling a rule's application. This allows the encoding of specific strategies and policies governing the set of default rules. Here we show that DL can be used to formalise preferences among properties and the inheritance of default properties, and so we essentially use DL to axiomatise such phenomena. 1.
An ArgumentBased Approach to Reasoning with Specificity
, 2001
"... We present a new prioritybased approach to reasoning with specificity which subsumes inheritance reasoning. The new approach differs from other prioritybased approaches in the literature in the way priority between defaults is handled. Here, it is conditional rather than unconditional as in other ..."
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Cited by 11 (0 self)
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We present a new prioritybased approach to reasoning with specificity which subsumes inheritance reasoning. The new approach differs from other prioritybased approaches in the literature in the way priority between defaults is handled. Here, it is conditional rather than unconditional as in other approaches. We show that
MetaInterpretation in Answer Set Programming
"... Most recently, Answer Set Programming (ASP) has been attracting interest as a new paradigm for problem solving. An important aspect, for which several approaches have been presented, is the handling of preferences between rules. In this paper, we consider the problem of implementing preference handl ..."
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Cited by 11 (3 self)
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Most recently, Answer Set Programming (ASP) has been attracting interest as a new paradigm for problem solving. An important aspect, for which several approaches have been presented, is the handling of preferences between rules. In this paper, we consider the problem of implementing preference handling approaches by means of metainterpreters in Answer Set Programming. In particular, we consider the preferred answer set approaches by Brewka and Eiter, by Delgrande, Schaub and Tompits, and by Wang, Zhou and Lin. We present suitable metainterpreters for these semantics using DLV, which is an efficient engine for ASP. Moreover, we also present a metainterpreter for the weakly preferred answer set approach by Brewka and Eiter, which uses the weak constraint feature of DLV as a tool for expressing and solving an underlying optimization problem. We also consider advanced metainterpreters, which make use of graphbased characterizations and often allow for more efficient computations. Our approach shows the suitability of ASP in general and of DLV in particular for fast prototyping. This can be fruitfully exploited for experimenting with new languages and knowledgerepresentation formalisms.
Nonmonotonic Reasoning as Prioritized Argumentation
 IEEE Transactions on Knowledge and Data Engineering
, 2001
"... This paper proposes a formalism for nonmonotonic reasoning based on prioritized argumentation. We argue that nonmonotonic reasoning in general can be viewed as selecting monotonic inferences by a simple notion of priority among inference rules. More importantly, these types of constrained inferen ..."
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Cited by 9 (0 self)
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This paper proposes a formalism for nonmonotonic reasoning based on prioritized argumentation. We argue that nonmonotonic reasoning in general can be viewed as selecting monotonic inferences by a simple notion of priority among inference rules. More importantly, these types of constrained inferences can be specified in a knowledge representation language where a theory consists of a collection of rules of first order formulas and a priority among these rules. We recast default reasoning as a form of prioritized argumentation, and illustrate how the parameterized formulation of priority may be used to allow various extensions and modifications to default reasoning. We also show that it is possible, but more difficult, to express prioritized argumentation by default logic: even some particular forms of prioritized argumentation cannot be represented modularly by defaults under the same language. Keywords: Nonmonotonic reasoning, argumentation; priority, default logic, represen...