摘要 :
Measures of quantity of information have been studied extensively for more than fifty years. The seminal work on information theory is by Shannon. This work, based on probability theory, can be used in a logical setting when the w...
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Measures of quantity of information have been studied extensively for more than fifty years. The seminal work on information theory is by Shannon. This work, based on probability theory, can be used in a logical setting when the worlds are the possible events. This work is also the basis of Lozinskii's work for defining the quantity of information of a formula (or knowledgebase) in propositional logic. But this definition is not suitable when the knowledgebase is inconsistent. In this case, it has no classical model, so we have no "event" to count. This is a shortcoming since in practical applications (e.g. databases) it often happens that the knowledgebase is not consistent. And it is definitely not true that all inconsistent knowledgebases contain the same (null) amount of information, as given by the "classical information theory". As explored for several years in the paraconsistent logic community, two inconsistent knowledgebases can lead to very different conclusions, showing that they do not convey the same information. There has been some recent interest in this issue, with some interesting proposals. Though a general approach for information theory in (possibly inconsistent) logical knowledgebases is missing. Another related measure is the measure of contradiction. It is usual in classical logic to use a binary measure of contradiction: a knowledgebase is either consistent or inconsistent. This dichotomy is obvious when the only deductive tool is classical inference, since inconsistent knowledgebases are of no use. But there are now a number of logics developed to draw non-trivial conclusions from an inconsistent knowledgebase. So this dichotomy is not sufficient to describe the amount of contradiction of a knowledgebase, one needs more fine-grained measures. Some interesting proposals have been made for this. The main aim of this paper is to review the measures of information and contradiction, and to study some potential practical applications. This has significant potential in developing intelligent systems that can be tolerant to inconsistencies when reasoning with real-world knowledge.
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摘要 :
Belief revision has been studied for more than 30 years, and the theoretical properties of the belief revision operators are now well-known. Contrastingly, there are almost no practical applications of these operators. One of the ...
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Belief revision has been studied for more than 30 years, and the theoretical properties of the belief revision operators are now well-known. Contrastingly, there are almost no practical applications of these operators. One of the reasons is the computational complexity of the corresponding inference problem, which is typically NP-hard and coNP-hard. Especially, existing implementations of belief revision operators are capable to solve toy instances, but are still unable to cope with real-size problem instances. However, the improvements achieved by SAT solvers for the past few years have been very impressive and they allow to tackle the solving of instances of inference problems located beyond NP. In this paper we describe and evaluate SAT encodings for a large family of distance-based belief revision operators. The results obtained pave the way for the practical use of belief revision operators in large-scale applications.
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摘要 :
Belief revision has been studied for more than 30 years, and the theoretical properties of the belief revision operators are now well-known. Contrastingly, there are almost no practical applications of these operators. One of the ...
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Belief revision has been studied for more than 30 years, and the theoretical properties of the belief revision operators are now well-known. Contrastingly, there are almost no practical applications of these operators. One of the reasons is the computational complexity of the corresponding inference problem, which is typically NP-hard and coNP-hard. Especially, existing implementations of belief revision operators are capable to solve toy instances, but are still unable to cope with real-size problem instances. However, the improvements achieved by SAT solvers for the past few years have been very impressive and they allow to tackle the solving of instances of inference problems located beyond NP. In this paper we describe and evaluate SAT encodings for a large family of distance-based belief revision operators. The results obtained pave the way for the practical use of belief revision operators in large-scale applications.
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摘要 :
We study a generalisation of iterated belief revision in a setting where we keep track not only of the received information (in the form of messages) but also of the source of each message. We suppose that we have a special source...
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We study a generalisation of iterated belief revision in a setting where we keep track not only of the received information (in the form of messages) but also of the source of each message. We suppose that we have a special source, the oracle, which never fails. That is, all of the information provided by the oracle is assumed to be correct. We then evaluate the reliability of each source by confronting its messages with the facts given by the oracle. In this case it is natural to give higher priority to messages coming from more reliable sources. We therefore re-order (reconfigurate) the messages with respect to the reliability of the sources before performing iterated belief revision. We study how to compute this reliability, and the properties of the corresponding reconfiguration operators.
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In this paper we question the ability of the existant ranking semantics for argumentation to capture persuasion settings, emphasizing in particular the phenomena of protocatalepsis (the fact that it is often efficient to anticipat...
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In this paper we question the ability of the existant ranking semantics for argumentation to capture persuasion settings, emphasizing in particular the phenomena of protocatalepsis (the fact that it is often efficient to anticipate the counter-arguments of the audience), and of fading (the fact that long lines of argumentation become ineffective). It turns out that some widely accepted principles of ranking-based semantics are incompatible with a faithful treatment of these phenomena. We thus propose a parametrized semantics based on propagation of values, which allows to control the scope of arguments to be considered for evaluation. We investigate its properties (identifying in particular threshold values guaranteeing that some properties hold), and report experimental results showing that the family of rankings that may be returned have a high coherence rate.
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摘要 :
In this paper we question the ability of the existant ranking semantics for argumentation to capture persuasion settings, emphasizing in particular the phenomena of protocatalepsis (the fact that it is often efficient to anticipat...
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In this paper we question the ability of the existant ranking semantics for argumentation to capture persuasion settings, emphasizing in particular the phenomena of protocatalepsis (the fact that it is often efficient to anticipate the counter-arguments of the audience), and of fading (the fact that long lines of argumentation become ineffective). It turns out that some widely accepted principles of ranking-based semantics are incompatible with a faithful treatment of these phenomena. We thus propose a parametrized semantics based on propagation of values, which allows to control the scope of arguments to be considered for evaluation. We investigate its properties (identifying in particular threshold values guaranteeing that some properties hold), and report experimental results showing that the family of rankings that may be returned have a high coherence rate.
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In this paper we study iterated contraction in the epistemic state framework, offering a counterpart of the work of Darwiche and Pearl for iterated revision. We provide pure syntactical postulates for iterated contraction, that is...
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In this paper we study iterated contraction in the epistemic state framework, offering a counterpart of the work of Darwiche and Pearl for iterated revision. We provide pure syntactical postulates for iterated contraction, that is, the postulates are expressed only in terms of the contraction operator. We establish a representation theorem for these operators. Our results allow to highlight the relationships between iterated contraction and iterated revision. In particular we show that iterated revision operators form a larger class than that of iterated contraction operators. As a consequence of this, in the epistemic state framework, the Levi identity has limitations; namely, it doesn't allow to define all iterated revision operators.
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摘要 :
In this paper we study iterated contraction in the epistemic state framework, offering a counterpart of the work of Darwiche and Pearl for iterated revision. We provide pure syntactical postulates for iterated contraction, that is...
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In this paper we study iterated contraction in the epistemic state framework, offering a counterpart of the work of Darwiche and Pearl for iterated revision. We provide pure syntactical postulates for iterated contraction, that is, the postulates are expressed only in terms of the contraction operator. We establish a representation theorem for these operators. Our results allow to highlight the relationships between iterated contraction and iterated revision. In particular we show that iterated revision operators form a larger class than that of iterated contraction operators. As a consequence of this, in the epistemic state framework, the Levi identity has limitations; namely, it doesn't allow to define all iterated revision operators.
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In this paper, we investigate the revision issue for Dung argumentation frameworks. The main idea is that such frameworks can be translated into propositional formulae, allowing the use of propositional revision operators to perfo...
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In this paper, we investigate the revision issue for Dung argumentation frameworks. The main idea is that such frameworks can be translated into propositional formulae, allowing the use of propositional revision operators to perform a rational minimal change. Our translation-based approach to revising argumentation frameworks can take advantage of any propositional revision operator o. Via a translation, each propositional operator o can be associated with some revision operators * suited to argumentation frameworks. Some rationality postulates for the * operators are presented. If the revision formulae are restricted to formulae about acceptance statuses, some * operators satisfy these postulates provided that the corresponding o operator is AGM.
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摘要 :
In this paper, we investigate the revision issue for Dung argumentation frameworks. The main idea is that such frameworks can be translated into propositional formulae, allowing the use of propositional revision operators to perfo...
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In this paper, we investigate the revision issue for Dung argumentation frameworks. The main idea is that such frameworks can be translated into propositional formulae, allowing the use of propositional revision operators to perform a rational minimal change. Our translation-based approach to revising argumentation frameworks can take advantage of any propositional revision operator o. Via a translation, each propositional operator o can be associated with some revision operators ★ suited to argumentation frameworks. Some rationality postulates for the ★ operators are presented. If the revision formulae are restricted to formulae about acceptance statuses, some ★ operators satisfy these postulates provided that the corresponding o operator is AGM.
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