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Ilkka Niemelä - One of the best experts on this subject based on the ideXlab platform.
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Nonmonotonic Reasoning, Answer Set Programming and Constraints - 05171 Abstracts Collection -- Nonmonotonic Reasoning, Answer Set Programming and Constraints
2020Co-Authors: Gerhard Brewka, Ilkka Niemelä, Miroslaw Truszczynski, Torsten Schaub, Joost VennekensAbstract:From 24.04.05 to 29.04.05, the Dagstuhl Seminar 05171 ``Nonmonotonic Reasoning, Answer Set Programming and Constraints'' was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available.
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Cumulativity Tailored for Nonmonotonic Reasoning
Advances in Knowledge Representation Logic Programming and Abstract Argumentation, 2014Co-Authors: Tomi Janhunen, Ilkka NiemeläAbstract:In Nonmonotonic Reasoning, conclusions can be retracted when new pieces of information are incorporated into premises. This contrasts with classical Reasoning which is monotonic, i.e., new premises can only increase the set of conclusions that can be drawn. Slightly weaker properties, such as cumulativity and rationality, seem reasonable counterparts of such a monotonicity property for Nonmonotonic Reasoning but intriguingly it turned out that some major Nonmonotonic logics failed to be cumulative. These observations led to the study of variants in hope of restoring cumulativity but not losing other essential properties. In this paper, we take a fresh view on cumulativity by starting from a notion of rule entailment in the context of answer set programs. It turns out that cumulativity can be revived if the expressive precision of rules subject to answer set semantics is fully exploited when new premises are being incorporated. Even stronger properties can be established and we illustrate how the approach can be generalized for major Nonmonotonic logics.
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des a challenge problem for Nonmonotonic Reasoning systems
arXiv: Artificial Intelligence, 2000Co-Authors: Maarit Hietalahti, Fabio Massacci, Ilkka NiemeläAbstract:The US Data Encryption Standard, DES for short, is put forward as an interesting benchmark problem for Nonmonotonic Reasoning systems because (i) it provides a set of test cases of industrial relevance which shares features of randomly generated problems and real-world problems, (ii) the representation of DES using normal logic programs with the stable model semantics is simple and easy to understand, and (iii) this subclass of logic programs can be seen as an interesting special case for many other formalizations of Nonmonotonic Reasoning. In this paper we present two encodings of DES as logic programs: a direct one out of the standard specifications and an optimized one extending the work of Massacci and Marraro. The computational properties of the encodings are studied by using them for DES key search with the Smodels system as the implementation of the stable model semantics. Results indicate that the encodings and Smodels are quite competitive: they outperform state-of-the-art SAT-checkers working with an optimized encoding of DES into SAT and are comparable with a SAT-checker that is customized and tuned for the optimized SAT encoding.
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Report on the Seventh International Workshop on Nonmonotonic Reasoning
Ai Magazine, 1998Co-Authors: Gerhard Brewka, Ilkka NiemeläAbstract:The Seventh International Workshop on Nonmonotonic Reasoning was held in Trento, Italy, on 30 May to 1 June 1998 in conjunction with the Sixth International Conference on the Principles of Knowledge Representation and Reasoning (KR-98). The workshop was sponsored by the Association for the Advancement of Artificial Intelligence, Compulog, Associazione Italiana per l'Intelligenza Artificiale, and the Prolog Development Center.
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A decision method for Nonmonotonic Reasoning based on autoepistemic Reasoning
Journal of Automated Reasoning, 1995Co-Authors: Ilkka NiemeläAbstract:A novel decision method for autoepistemic Reasoning is developed and proved correct. The method is applicable in a general setting, i.e., for an autoepistemic logic based on a given classical logic. It provides a decision procedure for a tightly grounded from of autoepistemic Reasoning based on L-hierarchic expansions as well as for autoepistemic Reasoning based on Moorestyle expansions and N-expansions. Prominent formalizations of Nonmonotonic Reasoning, such as default logic and circumscription, can be embedded into autoepistemic logic based on L-hierarchic expansions using simple local translations. Hence, the method can serve as a unified Reasoning tool for a wide range of forms of Nonmonotonic Reasoning. The method is conceptually simple, and the inherent sources of complexity and targets for optimization are clearly identifiable. As an example of exploiting optimization possibilities, a new decision method for Reiter's default logic is developed where ideas from autoepistemic Reasoning are used to prune the search space for applicable default rules when constructing extensions of a default theory.
Gian Luca Pozzato - One of the best experts on this subject based on the ideXlab platform.
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a minimal model semantics for Nonmonotonic Reasoning
European Conference on Logics in Artificial Intelligence, 2012Co-Authors: Laura Giordano, Valentina Gliozzi, Nicola Olivetti, Gian Luca PozzatoAbstract:This paper provides a general semantic framework for Nonmonotonic Reasoning, based on a minimal models semantics on the top of KLM systems for Nonmonotonic Reasoning. This general framework can be instantiated in order to provide a semantic reconstruction within modal logic of the notion of rational closure, introduced by Lehmann and Magidor. We give two characterizations of rational closure: the first one in terms of minimal models where propositional interpretations associated to worlds are fixed along minimization, the second one where they are allowed to vary. In both cases a knowledge base must be expanded with a suitable set of consistency assumptions, represented by negated conditionals. The correspondence between rational closure and minimal model semantics suggests the possibility of defining variants of rational closure by changing either the underlying modal logic or the comparison relation on models.
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JELIA - A minimal model semantics for Nonmonotonic Reasoning
Logics in Artificial Intelligence, 2012Co-Authors: Laura Giordano, Valentina Gliozzi, Nicola Olivetti, Gian Luca PozzatoAbstract:This paper provides a general semantic framework for Nonmonotonic Reasoning, based on a minimal models semantics on the top of KLM systems for Nonmonotonic Reasoning. This general framework can be instantiated in order to provide a semantic reconstruction within modal logic of the notion of rational closure, introduced by Lehmann and Magidor. We give two characterizations of rational closure: the first one in terms of minimal models where propositional interpretations associated to worlds are fixed along minimization, the second one where they are allowed to vary. In both cases a knowledge base must be expanded with a suitable set of consistency assumptions, represented by negated conditionals. The correspondence between rational closure and minimal model semantics suggests the possibility of defining variants of rational closure by changing either the underlying modal logic or the comparison relation on models.
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TABLEAUX - KLMLean 2.0: A Theorem Prover for KLM Logics of Nonmonotonic Reasoning
Lecture Notes in Computer Science, 2007Co-Authors: Laura Giordano, Valentina Gliozzi, Gian Luca PozzatoAbstract:We present KLMLean 2.0, a theorem prover for propositional KLM logics of Nonmonotonic Reasoning. KLMLean 2.0 implements some analytic tableaux calculi for these logics recently introduced. KLMLean 2.0 is inspired by the "lean" methodology, it is implemented in SICStus Prolog and it also contains a graphical interface written in Java.
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analytic tableaux calculi for klm logics of Nonmonotonic Reasoning
arXiv: Logic in Computer Science, 2006Co-Authors: Laura Giordano, Valentina Gliozzi, Nicola Olivetti, Gian Luca PozzatoAbstract:We present tableau calculi for some logics of Nonmonotonic Reasoning, as defined by Kraus, Lehmann and Magidor. We give a tableau proof procedure for all KLM logics, namely preferential, loop-cumulative, cumulative and rational logics. Our calculi are obtained by introducing suitable modalities to interpret conditional assertions. We provide a decision procedure for the logics considered, and we study their complexity.
Henri Prade - One of the best experts on this subject based on the ideXlab platform.
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decision Nonmonotonic Reasoning and possibilistic logic
Logic-based artificial intelligence, 2000Co-Authors: Salem Bernferhat, Didier Dubois, Helene Fragier, Henri Prade, Regis SabbadinAbstract:The paper survey recent AI-oriented works in qualitative decision developed by the authors in the framework of possibility theory. Lottery-based and act-based axiomatics underlying pessimistic and optimistic criteria for decision under uncertainty are first briefly restated, when uncertainty and preferences are encoded with an ordinal scale. A logical machinery capable of computing optimal decisions in the sense of these criteria is presented. Then an approach to qualitative decision under uncertainty which does not require a commensurateness hypothesis between the uncertainty and the preference scales is proposed; this approach is closely related to Nonmonotonic Reasoning, but turns our to be ineffective for practical decision. Lastly, the modeling of preference as prioritized sets of goals, as sets of solutions reaching some given level of satisfaction, or in terms of possibilistic constraints is discussed briefly.
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an overview of possibilistic logic and its application to Nonmonotonic Reasoning and data fusion
Computational Intelligence and Data Mining, 2000Co-Authors: Salem Benferhat, Didier Dubois, Henri PradeAbstract:This paper provides a brief survey of possibilistic logic as a simple and efficient tool for handling Nonmonotonic Reasoning and data fusion. In Nonmonotonic Reasoning, Lehmann’s preferential System P is known to provide reasonable but very cautious conclusions, and in particular, preferential inference is blocked by the presence of “irrelevant” properties. When using Lehmann’s rational closure, the inference machinery, which is then more productive, may still remain too cautious. These two types of inference can be represented using a possibility theory-based semantics. The paper proposes several safe ways to overcome the cautiousness of these systems. One of these ways takes advantage of (contextual) independence assumptions of the form: the fact that δ is true (or is false) does not affect the validity of the rule “normally if α then β”. The modelling of such independence assumptions is discussed in the possibilistic framework. This paper presents a general approach for fusing several ordered belief bases provided by different sources according to various modes. More precisely, the paper provides the syntactic counterparts of different ways of aggregating possibility distributions, well-known at the semantic level.
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Nonmonotonic Reasoning conditional objects and possibility theory
Artificial Intelligence, 1997Co-Authors: Salem Benferhat, Didier Dubois, Henri PradeAbstract:Abstract This short paper relates the conditional object-based and possibility theory-based approaches for Reasoning with conditional statements pervaded with exceptions, to other methods in Nonmonotonic Reasoning which have been independently proposed: namely, Lehmann's preferential and rational closure entailments which obey normative postulates, the infinitesimal probability approach, and the conditional (modal) logics-based approach. All these methods are shown to be equivalent with respect to their capabilities for Reasoning with conditional knowledge although they are based on different modeling frameworks. It thus provides a unified understanding of Nonmonotonic consequence relations. More particularly, conditional objects, a purely qualitative counterpart to conditional probabilities, offer a very simple semantics, based on a 3-valued calculus, for the preferential entailment, while in the purely ordinal setting of possibility theory both the preferential and the rational closure entailments can be represented.
Gerhard Brewka - One of the best experts on this subject based on the ideXlab platform.
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Nonmonotonic Reasoning, Answer Set Programming and Constraints - 05171 Abstracts Collection -- Nonmonotonic Reasoning, Answer Set Programming and Constraints
2020Co-Authors: Gerhard Brewka, Ilkka Niemelä, Miroslaw Truszczynski, Torsten Schaub, Joost VennekensAbstract:From 24.04.05 to 29.04.05, the Dagstuhl Seminar 05171 ``Nonmonotonic Reasoning, Answer Set Programming and Constraints'' was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available.
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Handling Exceptions in Knowledge Representation: A Brief Introduction to Nonmonotonic Reasoning
2020Co-Authors: Gerhard BrewkaAbstract:Argumentation Arguments are “atomic”, their structure irrelevant. All that matters are attacks among arguments. Argumentation frameworks (AFs) represent attack relations. Semantics formalize different intuitions about how to solve conflicts and how to pick acceptable arguments. Semantics map an AF to subsets of its arguments (extensions). Nonmonotonic: new argument may throw out what was accepted. Brewka/Woltran () Nonmonotonic Reasoning March 2013 2 / 23
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IJCAI - Strong Inconsistency in Nonmonotonic Reasoning
Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence, 2017Co-Authors: Gerhard Brewka, Matthias Thimm, Markus UlbrichtAbstract:Minimal inconsistent subsets of knowledge bases play an important role in classical logics, most notably for repair and inconsistency measurement. It turns out that for Nonmonotonic Reasoning a stronger notion is needed. In this paper we develop such a notion, called strong inconsistency. We show that—in an arbitrary logic, monotonic or not—minimal strongly inconsistent subsets play the same role as minimal inconsistent subsets in classical Reasoning. In particular, we show that the well-known classical duality between hitting sets of minimal inconsistent subsets and maximal consistent subsets generalizes to arbitrary logics if the strong notion of inconsistency is used. We investigate the complexity of various related Reasoning problems and present a generic algorithm for computing minimal strongly inconsistent subsets of a knowledge base. We also demonstrate the potential of our new notion for applications, focusing on repair and inconsistency measurement.
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Report on the Seventh International Workshop on Nonmonotonic Reasoning
Ai Magazine, 1998Co-Authors: Gerhard Brewka, Ilkka NiemeläAbstract:The Seventh International Workshop on Nonmonotonic Reasoning was held in Trento, Italy, on 30 May to 1 June 1998 in conjunction with the Sixth International Conference on the Principles of Knowledge Representation and Reasoning (KR-98). The workshop was sponsored by the Association for the Advancement of Artificial Intelligence, Compulog, Associazione Italiana per l'Intelligenza Artificiale, and the Prolog Development Center.
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Nonmonotonic and Inductive Logic - A Tutorial on Nonmonotonic Reasoning
Nonmonotonic and Inductive Logic, 1993Co-Authors: Gerhard Brewka, Kurt KonoligeAbstract:Nonmonotonic Reasoning, in its broadest sense, is Reasoning to conclusions on the basis of incomplete information. Given more information, we are prepared to retract previously drawn inferences. To exhibit the classic example: if all we know about Tweety is that he is bird, then we plausibly conclude that he can fly; on learning that Tweety is a penguin, we withdraw that conclusion. We call this Reasoning Nonmonotonic because the set of plausible conclusions does not grow monotonically with increasing information.
Laura Giordano - One of the best experts on this subject based on the ideXlab platform.
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a minimal model semantics for Nonmonotonic Reasoning
European Conference on Logics in Artificial Intelligence, 2012Co-Authors: Laura Giordano, Valentina Gliozzi, Nicola Olivetti, Gian Luca PozzatoAbstract:This paper provides a general semantic framework for Nonmonotonic Reasoning, based on a minimal models semantics on the top of KLM systems for Nonmonotonic Reasoning. This general framework can be instantiated in order to provide a semantic reconstruction within modal logic of the notion of rational closure, introduced by Lehmann and Magidor. We give two characterizations of rational closure: the first one in terms of minimal models where propositional interpretations associated to worlds are fixed along minimization, the second one where they are allowed to vary. In both cases a knowledge base must be expanded with a suitable set of consistency assumptions, represented by negated conditionals. The correspondence between rational closure and minimal model semantics suggests the possibility of defining variants of rational closure by changing either the underlying modal logic or the comparison relation on models.
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JELIA - A minimal model semantics for Nonmonotonic Reasoning
Logics in Artificial Intelligence, 2012Co-Authors: Laura Giordano, Valentina Gliozzi, Nicola Olivetti, Gian Luca PozzatoAbstract:This paper provides a general semantic framework for Nonmonotonic Reasoning, based on a minimal models semantics on the top of KLM systems for Nonmonotonic Reasoning. This general framework can be instantiated in order to provide a semantic reconstruction within modal logic of the notion of rational closure, introduced by Lehmann and Magidor. We give two characterizations of rational closure: the first one in terms of minimal models where propositional interpretations associated to worlds are fixed along minimization, the second one where they are allowed to vary. In both cases a knowledge base must be expanded with a suitable set of consistency assumptions, represented by negated conditionals. The correspondence between rational closure and minimal model semantics suggests the possibility of defining variants of rational closure by changing either the underlying modal logic or the comparison relation on models.
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TABLEAUX - KLMLean 2.0: A Theorem Prover for KLM Logics of Nonmonotonic Reasoning
Lecture Notes in Computer Science, 2007Co-Authors: Laura Giordano, Valentina Gliozzi, Gian Luca PozzatoAbstract:We present KLMLean 2.0, a theorem prover for propositional KLM logics of Nonmonotonic Reasoning. KLMLean 2.0 implements some analytic tableaux calculi for these logics recently introduced. KLMLean 2.0 is inspired by the "lean" methodology, it is implemented in SICStus Prolog and it also contains a graphical interface written in Java.
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analytic tableaux calculi for klm logics of Nonmonotonic Reasoning
arXiv: Logic in Computer Science, 2006Co-Authors: Laura Giordano, Valentina Gliozzi, Nicola Olivetti, Gian Luca PozzatoAbstract:We present tableau calculi for some logics of Nonmonotonic Reasoning, as defined by Kraus, Lehmann and Magidor. We give a tableau proof procedure for all KLM logics, namely preferential, loop-cumulative, cumulative and rational logics. Our calculi are obtained by introducing suitable modalities to interpret conditional assertions. We provide a decision procedure for the logics considered, and we study their complexity.
