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Non Monotonic Reasoning
, 1997
"... These are the proceedings of the 11th Nonmonotonic Reasoning Workshop. The aim of this series ..."
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These are the proceedings of the 11th Nonmonotonic Reasoning Workshop. The aim of this series
H.: Towards an axiom system for default logic
 In: Proceedings of the AAAI Conference. (2006
"... Recently, Lakemeyer and Levesque proposed a logic of onlyknowing which precisely captures three forms of nonmonotonic reasoning: Moore’s Autoepistemic Logic, Konolige’s variant based on moderately grounded expansions, and Reiter’s default logic. Defaults have a uniform representation under all three ..."
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Recently, Lakemeyer and Levesque proposed a logic of onlyknowing which precisely captures three forms of nonmonotonic reasoning: Moore’s Autoepistemic Logic, Konolige’s variant based on moderately grounded expansions, and Reiter’s default logic. Defaults have a uniform representation under all three interpretations in the new logic. Moreover, the logic itself is monotonic, that is, nonmonotonic reasoning is cast in terms of validity in the classical sense. While Lakemeyer and Levesque gave a modeltheoretic account of their logic, a prooftheoretic characterization remained open. This paper fills that gap for the propositional subset: a sound and complete axiom system in the new logic for all three varieties of default reasoning. We also present formal derivations for some examples of default reasoning. Finally we present evidence that it is unlikely that a complete axiom system exists in the firstorder case, even when restricted to the simplest forms of default reasoning.
Alternative foundations for Reiter's default logic
 Artificial Intelligence
, 2000
"... We introduce an alternative conceptual basis for default reasoning in Reiter's default logic. In fact, most formal or computational treatments of default logic suffer from the necessity of exhaustive consistency checks with respect to the finally resulting set of conclusions; often this socall ..."
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We introduce an alternative conceptual basis for default reasoning in Reiter's default logic. In fact, most formal or computational treatments of default logic suffer from the necessity of exhaustive consistency checks with respect to the finally resulting set of conclusions; often this socalled extension is just about being constructed. On the theoretical side, this exhaustive approach is reflected by the usual fixedpoint characterizations of extensions. Our goal is to reduce such global considerations to local and strictly necessary ones. For this purpose, we develop various techniques and instruments that draw on an analysis of interaction patterns between default rules, embodied by their mutual blocking behavior. These formal tools provide us with alternative means for addressing a variety of questions in default logic. We demonstrate the utility of our approach by applying it to three traditional problems. First, we obtain a range of criteria guaranteeing the existence and nonexistence of extensions. Second, we get alternative characterizations of extensions that avoid fixedpoint conditions. Finally, we furnish a formal account of default proofs that was up to now neglected in the literature. 1
A Sequent Calculus for Circumscription
, 1997
"... . In this paper, we introduce a sequent calculus CIRC for propositional Circumscription. This work is part of a larger project, aiming at a uniform prooftheoretic reconstruction of the major families of nonmonotonic logics. Among the novelties of the calculus, we mention that CIRC is analytic ..."
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. In this paper, we introduce a sequent calculus CIRC for propositional Circumscription. This work is part of a larger project, aiming at a uniform prooftheoretic reconstruction of the major families of nonmonotonic logics. Among the novelties of the calculus, we mention that CIRC is analytic and comprises an axiomatic rejection method, which allows for a fully detailed formalization of the nonmonotonic aspects of inference. 1 Introduction Nonmonotonic logics play a fundamental role in knowledge representation and commonsense reasoning, as well as in the theory of programming languages. The semantic and algorithmic aspects of nonmonotonic reasoning have been extensively investigated (e.g. see [21, 25, 12, 16, 17, 8, 28, 33, 24] and [29, 26, 2, 5, 35, 1]). On the other hand, the prooftheoretic aspects are not yet completely understood. The fundamental papers by Gabbay [13] , Makinson [23] and Kraus, Lehmann and Magidor [18] , focus their attention on general properties of ...
A Sequent Calculus for Intuitionistic Default Logic
, 1997
"... Current research on nonmonotonic reasoning shows growing interest on implementation details, so the need for concrete calculi formalizing nonmonotonic logics is clearly recognized. On the other hand, there is also an increased number of works combining intuitionistic logic with various kinds of no ..."
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Current research on nonmonotonic reasoning shows growing interest on implementation details, so the need for concrete calculi formalizing nonmonotonic logics is clearly recognized. On the other hand, there is also an increased number of works combining intuitionistic logic with various kinds of nonmonotonic formalisms. As a case in point, intuitionistic versions of both default and autoepistemic logics have been proposed, and tight connections between intuitionistic logic and logic programs (or deductive databases) using hypothetical inferences have been established. In this paper, we present a sequent calculus for default reasoning in the style of Bonatti with intuitionistic logic as the underlying logical structure. In contrast to other proposals, Bonatti's technique allows a very simple and intuitive specification of the calculus, making it an ideal tool for implementation purposes. 1 Introduction Nonmonotonic reasoning techniques are an important cornerstone towards formalizin...
Rule calculus: Semantics, axioms and applications
 In Logics in Artificial Intelligence – JELIA, Lecture Notes in Computer Science
, 2008
"... Abstract. We consider the problem of how a default rule can be deduced from a default theory. For this purpose, we propose an axiom system which precisely captures the deductive reasoning about default rules. We show that our axiomatic system is sound and complete under the semantics of the logic of ..."
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Abstract. We consider the problem of how a default rule can be deduced from a default theory. For this purpose, we propose an axiom system which precisely captures the deductive reasoning about default rules. We show that our axiomatic system is sound and complete under the semantics of the logic of hereandthere. We also study other important properties such as substitution and monotonicity of our system and prove the essential decision problem complexity. Finally, we discuss applications of our default rule calculus to various problems. 1
A Sequent Calculus for a Paraconsistent Default Logic
, 1999
"... In spite of sequent calculus being one of the most elegant and convenient way of presenting logical systems, its use along nonmonotonic logic has almost entirely been neglected, but for very few and recent attempts. The reasons for this lack of interest in exploring sequent calculus presentations fo ..."
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In spite of sequent calculus being one of the most elegant and convenient way of presenting logical systems, its use along nonmonotonic logic has almost entirely been neglected, but for very few and recent attempts. The reasons for this lack of interest in exploring sequent calculus presentations for nonmonotonic logics may certainly be found in the context sensitiveness that is required for nonmonotonic inference, which seems to be in direct opposition to the local character of sequent calculus rules. So, they just look mutually incompatible. Nevertheless, it is the aim of this paper to show how it is possible to circumvent this incompatibility by adopting a special generalization of sequent calculus formalism, able to treat nonmonotonicity. The challenge here is that it has to be done without deforming too much the original characteristics of the sequent calculus method, in order of not throwing away its main beneficial outcomes. Of course, a precondition for this treatment is to have a definite notion of logical consequence to be expressed. It will be shown that, even working with credulous default reasoning, this can be accomplished in connection to IDL default logic, a paraconsistent logic of defaults that, by being tolerant to contradictions is able to combine divergent views in a single extension.
about only knowing and knowing
"... sound and complete tableau calculus for reasoning ..."
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