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Henri Prade - One of the best experts on this subject based on the ideXlab platform.
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Possibility Theory and possibilistic logic tools for reasoning under and about incomplete information
International Conference on Intelligence Science, 2021Co-Authors: Didier Dubois, Henri PradeAbstract:This brief overview provides a quick survey of qualitative Possibility Theory and possibilistic logic along with their applications to various forms of epistemic reasoning under and about incomplete information. It is highlighted that this formalism has the potential of relating various independently introduced logics for epistemic reasoning.
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Thick sets, multiple-valued mappings, and Possibility Theory
Statistical and Fuzzy Approaches to Data Processing with Applications to Econometrics and Other Areas, 2020Co-Authors: Didier Dubois, Luc Jaulin, Henri PradeAbstract:Carrying uncertain information via a multivalued function can be found in different settings, ranging from the computation of the image of a set by an inverse function to the Dempsterian transfer of a probabilistic space by a multivalued function. We then get upper and lower images. In each case one handles so-called thick sets in the sense of Jaulin, i.e., lower and upper bounded ill-known sets. Such ill-known sets can be found under different names in the literature, e.g., interval sets after Y. Y. Yao, twofold fuzzy sets in the sense of Dubois and Prade, or interval-valued fuzzy sets, ... Various operations can then be defined on these sets, then understood in a disjunctive manner (epistemic uncertainty), rather than conjunctively. The intended purpose of this note is to propose a unified view of these formalisms in the setting of Possibility Theory, which should enable us to provide graded extensions to some of the considered calculi.
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A Possibility Theory-based approach to desire change
2020Co-Authors: Didier Dubois, Emiliano Lorini, Henri PradeAbstract:Abstract. Desire is quite different from belief. While the accumulation of beliefs tend to reduce the remaining possible worlds they point at, the accumulation of desires tend to increase the set of states of affairs tentatively considered as satisfactory. Indeed beliefs are expected to be closed under conjunctions, while one can argue that endorsing ϕ ∨ ψ as a desire means to desire both ϕ and ψ. Still desiring ϕ and ¬ϕ at the same time is not usually regarded as rational, since it does not make much sense to desire one thing and its contrary at the same time. Thus when a new desire is added to the set of desires of an agent, a revision process may be necessary. Just as belief revision relies on an epistemic entrenchment relation, desire relation is based on a hedonic entrenchment relation satisfying other properties, due to the different natures of belief and desire. Epistemic entrenchment relations are known to be qualitative necessity relations. In this paper it is shown that a well-behaved desire revision operation obeying a set of reasonable postulates is underlied by a qualitative guaranteed Possibility relation in the sense of Possibility Theory. Then the general framework of possibilistic logic provides a syntactic setting for encoding desire change
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handling uncertainty in relational databases with Possibility Theory a survey of different modelings
Scalable Uncertainty Management, 2018Co-Authors: Olivier Pivert, Henri PradeAbstract:Mainstream approaches to uncertainty modeling in relational databases are probabilistic. Still some researchers persist in proposing representations based on Possibility Theory. They are motivated by the ability of this latter setting for modeling epistemic uncertainty and by its qualitative nature. Interestingly enough, several possibilistic models have been proposed over time, and have been motivated by different application needs ranging from database querying, to database design and to data cleaning. Thus, one may distinguish between four different frameworks ordered here according to an increasing representation power: databases with (i) layered tuples; (ii) certainty-qualified attribute values; (iii) attribute values restricted by general Possibility distributions; (iv) possibilistic c-tables. In each case, we discuss the role of the Possibility-necessity duality, the limitations and the benefit of the representation settings, and their suitability with respect to different tasks.
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graded cubes of opposition and Possibility Theory with fuzzy events
International Journal of Approximate Reasoning, 2017Co-Authors: Didier Dubois, Henri Prade, Agnes RicoAbstract:The paper discusses graded extensions of the cube of opposition, a structure that naturally emerges from the square of opposition in philosophical logic. These extensions of the cube of opposition agree with Possibility Theory and its four set functions. This extended cube then provides a synthetic and unified view of Possibility Theory. This is an opportunity to revisit basic notions of Possibility Theory, in particular regarding the handling of fuzzy events. It turns out that in Possibility Theory, two extensions of the four basic set functions to fuzzy events exist, which are needed for serving different purposes. The expressions of these extensions involve many-valued conjunction and implication operators that are related either via semi-duality or via residuation.
Didier Dubois - One of the best experts on this subject based on the ideXlab platform.
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Possibility Theory and possibilistic logic tools for reasoning under and about incomplete information
International Conference on Intelligence Science, 2021Co-Authors: Didier Dubois, Henri PradeAbstract:This brief overview provides a quick survey of qualitative Possibility Theory and possibilistic logic along with their applications to various forms of epistemic reasoning under and about incomplete information. It is highlighted that this formalism has the potential of relating various independently introduced logics for epistemic reasoning.
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Thick sets, multiple-valued mappings, and Possibility Theory
Statistical and Fuzzy Approaches to Data Processing with Applications to Econometrics and Other Areas, 2020Co-Authors: Didier Dubois, Luc Jaulin, Henri PradeAbstract:Carrying uncertain information via a multivalued function can be found in different settings, ranging from the computation of the image of a set by an inverse function to the Dempsterian transfer of a probabilistic space by a multivalued function. We then get upper and lower images. In each case one handles so-called thick sets in the sense of Jaulin, i.e., lower and upper bounded ill-known sets. Such ill-known sets can be found under different names in the literature, e.g., interval sets after Y. Y. Yao, twofold fuzzy sets in the sense of Dubois and Prade, or interval-valued fuzzy sets, ... Various operations can then be defined on these sets, then understood in a disjunctive manner (epistemic uncertainty), rather than conjunctively. The intended purpose of this note is to propose a unified view of these formalisms in the setting of Possibility Theory, which should enable us to provide graded extensions to some of the considered calculi.
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A Possibility Theory-based approach to desire change
2020Co-Authors: Didier Dubois, Emiliano Lorini, Henri PradeAbstract:Abstract. Desire is quite different from belief. While the accumulation of beliefs tend to reduce the remaining possible worlds they point at, the accumulation of desires tend to increase the set of states of affairs tentatively considered as satisfactory. Indeed beliefs are expected to be closed under conjunctions, while one can argue that endorsing ϕ ∨ ψ as a desire means to desire both ϕ and ψ. Still desiring ϕ and ¬ϕ at the same time is not usually regarded as rational, since it does not make much sense to desire one thing and its contrary at the same time. Thus when a new desire is added to the set of desires of an agent, a revision process may be necessary. Just as belief revision relies on an epistemic entrenchment relation, desire relation is based on a hedonic entrenchment relation satisfying other properties, due to the different natures of belief and desire. Epistemic entrenchment relations are known to be qualitative necessity relations. In this paper it is shown that a well-behaved desire revision operation obeying a set of reasonable postulates is underlied by a qualitative guaranteed Possibility relation in the sense of Possibility Theory. Then the general framework of possibilistic logic provides a syntactic setting for encoding desire change
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graded cubes of opposition and Possibility Theory with fuzzy events
International Journal of Approximate Reasoning, 2017Co-Authors: Didier Dubois, Henri Prade, Agnes RicoAbstract:The paper discusses graded extensions of the cube of opposition, a structure that naturally emerges from the square of opposition in philosophical logic. These extensions of the cube of opposition agree with Possibility Theory and its four set functions. This extended cube then provides a synthetic and unified view of Possibility Theory. This is an opportunity to revisit basic notions of Possibility Theory, in particular regarding the handling of fuzzy events. It turns out that in Possibility Theory, two extensions of the four basic set functions to fuzzy events exist, which are needed for serving different purposes. The expressions of these extensions involve many-valued conjunction and implication operators that are related either via semi-duality or via residuation.
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From a Possibility Theory View of Formal Concept Analysis to the Possibilistic Handling of Incomplete and Uncertain Contexts
2016Co-Authors: Zina Ait-yakoub, Yassine Djouadi, Didier Dubois, Henri PradeAbstract:The formal similarity between Possibility Theory and formal concept analysis, made ten years ago, has suggested the introduction in the latter setting of the counterpart of possibilistic operators, which were ignored before. These new operators can be related to the basic operator of formal concept analysis by a triple use of negations on the contexts, on the set-valued arguments and on the obtained results, and lead to consider new compositions worth of interest. They enable us to complete the Guigues-Duquenne basis with rules having disjunctive conclusions. Besides, the approach can be naturally generalized to incomplete contexts and then to uncertain context where uncertainty is graded.
Salem Benferhat - One of the best experts on this subject based on the ideXlab platform.
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uncertain lightweight ontologies in a product based Possibility Theory framework
International Journal of Approximate Reasoning, 2017Co-Authors: Salem Benferhat, Khaoula Boutouhami, Faiza Khellaf, Farid NouiouaAbstract:Abstract This paper investigates an extension of lightweight ontologies, encoded here in DL-Lite languages, to the product-based Possibility Theory framework. We first introduce the language (and its associated semantics) used for representing uncertainty in lightweight ontologies. We show that, contrarily to a min-based possibilistic DL-Lite, query answering in a product-based Possibility Theory is a hard task. We provide equivalent transformations between the problem of computing an inconsistency degree (the key notion in reasoning from a possibilistic DL-Lite knowledge base) and the weighted maximum 2-Horn SAT problem. The last part of the paper provides an encoding of the problem of computing inconsistency degree in product-based Possibility DL-Lite as a weighted set cover problem and the use of a greedy algorithm to compute an approximate value of the inconsistency degree. This encoding allows us to provide an approximate algorithm for answering instance checking queries in product-based possibilistic DL-Lite. Experimental studies show the quality of the approximate algorithms for both inconsistency degree computation and instance checking queries.
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representing lightweight ontologies in a product based Possibility Theory framework
Soft Methods in Probability and Statistics, 2016Co-Authors: Salem Benferhat, Khaoula Boutouhami, Faiza Khellaf, Farid NouiouaAbstract:This paper investigates an extension of lightweight ontologies, encoded here in DL-Lite languages , to the product-based Possibility Theory framework. We first introduce the language (and its associated semantics) used for representing uncertainty in lightweight ontologies. We show that, contrarily to a min-based possibilistic DL-Lite, query answering in a product-based Possibility Theory is a hard task. We provide equivalent transformations between the problem of computing an inconsistency degree (the key notion in reasoning from a possibilistic DL-Lite knowledge base) and the weighted maximum 2-Horn SAT problem.
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modeling positive and negative information in Possibility Theory
International Journal of Intelligent Systems, 2008Co-Authors: Salem Benferhat, Didier Dubois, Souhila Kaci, Henri PradeAbstract:From a knowledge representation point of view, it may be interesting to distinguish between (i) what is potentially possible because it is not inconsistent with the available knowledge on the one hand, and (ii) what is actually possible because it is reported from observations on the other hand. Such a distinction also makes sense when expressing preferences, to point out positively desired choices among merely tolerated ones. Possibility Theory provides a representation framework where this distinction can be made in a graded way. The two types of information can be encoded by two types of constraints expressed in terms of necessity measures and in terms of so-called guaranteed Possibility functions. These two set-functions are min-decomposable with respect to conjunction and disjunction, respectively. This gives birth to two forms of possibilistic logic bases, where clauses (resp., phrases) are weighted in terms of a necessity measure (resp., a guaranteed Possibility function). By application of a minimal commitment principle, the two bases induce a pair of Possibility distributions at the semantic level, for which a consistency condition should hold to ensure that what is claimed to be actually possible is indeed not impossible. The paper provides a survey of this bipolar representation framework, including the use of conditional measures, or the handling of comparative context-dependent constraints. The interest of the framework is stressed for expressing preferences, as well as in the representation of “if–then” rules in terms of examples and counterexamples. © 2008 Wiley Periodicals, Inc. A preliminary version of this work was presented by the last author at the Machine Intelligence 19 Workshop, held at Withersdane Conference Centre, Imperial College at Wye on September 18–20, 2002 (still accessible at ). A revised version should have appeared in the Electronic Transactions on Artificial Intelligence (ETAI; ) among selected articles from the Machine Intelligence 19 Workshop. It has been announced for many years as Volume 6 of ETAI, but never made accessible since then. The present version is a fully revised (again) and updated version of the previous one.
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bipolar Possibility Theory in preference modeling representation fusion and optimal solutions
Information Fusion, 2006Co-Authors: Salem Benferhat, Didier Dubois, Souhila Kaci, Henri PradeAbstract:The bipolar view in preference modeling distinguishes between negative and positive preferences. Negative preferences correspond to what is rejected, considered unacceptable, while positive preferences correspond to what is desired. But what is tolerated (i.e., not rejected) is not necessarily desired. Both negative and positive preferences can be a matter of degree. Bipolar preferences can be represented in possibilistic logic by two separate sets of formulas: prioritized constraints, which describe what is more or less tolerated, and weighted positive preferences, expressing what is particularly desirable. The problem of merging multiple-agent preferences in this bipolar framework is then discussed. Negative and positive preferences are handled separately and are combined in distinct ways. Since negative and positive preferences are stated separately, they may be inconsistent, especially in this context of preference fusion. Consistency can be enforced by restricting what is desirable to what is tolerated. After merging, and once the bipolar consistency is restored, the set of preferred solutions can be logically characterized. Preferred solutions should have the highest possible degree of feasibility, and only constraints with low priority may have to be discarded in case of inconsistency inside negative preferences. Moreover, preferred solutions should satisfy important positive preferences when feasible (positive preferences may be also inconsistent). Two types of preferred solutions can be characterized, either in terms of a disjunctive combination of the weighted positive preferences, or in terms of a cardinality-based evaluation.
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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.
Khaoula Boutouhami - One of the best experts on this subject based on the ideXlab platform.
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uncertain lightweight ontologies in a product based Possibility Theory framework
International Journal of Approximate Reasoning, 2017Co-Authors: Salem Benferhat, Khaoula Boutouhami, Faiza Khellaf, Farid NouiouaAbstract:Abstract This paper investigates an extension of lightweight ontologies, encoded here in DL-Lite languages, to the product-based Possibility Theory framework. We first introduce the language (and its associated semantics) used for representing uncertainty in lightweight ontologies. We show that, contrarily to a min-based possibilistic DL-Lite, query answering in a product-based Possibility Theory is a hard task. We provide equivalent transformations between the problem of computing an inconsistency degree (the key notion in reasoning from a possibilistic DL-Lite knowledge base) and the weighted maximum 2-Horn SAT problem. The last part of the paper provides an encoding of the problem of computing inconsistency degree in product-based Possibility DL-Lite as a weighted set cover problem and the use of a greedy algorithm to compute an approximate value of the inconsistency degree. This encoding allows us to provide an approximate algorithm for answering instance checking queries in product-based possibilistic DL-Lite. Experimental studies show the quality of the approximate algorithms for both inconsistency degree computation and instance checking queries.
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representing lightweight ontologies in a product based Possibility Theory framework
Soft Methods in Probability and Statistics, 2016Co-Authors: Salem Benferhat, Khaoula Boutouhami, Faiza Khellaf, Farid NouiouaAbstract:This paper investigates an extension of lightweight ontologies, encoded here in DL-Lite languages , to the product-based Possibility Theory framework. We first introduce the language (and its associated semantics) used for representing uncertainty in lightweight ontologies. We show that, contrarily to a min-based possibilistic DL-Lite, query answering in a product-based Possibility Theory is a hard task. We provide equivalent transformations between the problem of computing an inconsistency degree (the key notion in reasoning from a possibilistic DL-Lite knowledge base) and the weighted maximum 2-Horn SAT problem.
Farid Nouioua - One of the best experts on this subject based on the ideXlab platform.
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uncertain lightweight ontologies in a product based Possibility Theory framework
International Journal of Approximate Reasoning, 2017Co-Authors: Salem Benferhat, Khaoula Boutouhami, Faiza Khellaf, Farid NouiouaAbstract:Abstract This paper investigates an extension of lightweight ontologies, encoded here in DL-Lite languages, to the product-based Possibility Theory framework. We first introduce the language (and its associated semantics) used for representing uncertainty in lightweight ontologies. We show that, contrarily to a min-based possibilistic DL-Lite, query answering in a product-based Possibility Theory is a hard task. We provide equivalent transformations between the problem of computing an inconsistency degree (the key notion in reasoning from a possibilistic DL-Lite knowledge base) and the weighted maximum 2-Horn SAT problem. The last part of the paper provides an encoding of the problem of computing inconsistency degree in product-based Possibility DL-Lite as a weighted set cover problem and the use of a greedy algorithm to compute an approximate value of the inconsistency degree. This encoding allows us to provide an approximate algorithm for answering instance checking queries in product-based possibilistic DL-Lite. Experimental studies show the quality of the approximate algorithms for both inconsistency degree computation and instance checking queries.
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representing lightweight ontologies in a product based Possibility Theory framework
Soft Methods in Probability and Statistics, 2016Co-Authors: Salem Benferhat, Khaoula Boutouhami, Faiza Khellaf, Farid NouiouaAbstract:This paper investigates an extension of lightweight ontologies, encoded here in DL-Lite languages , to the product-based Possibility Theory framework. We first introduce the language (and its associated semantics) used for representing uncertainty in lightweight ontologies. We show that, contrarily to a min-based possibilistic DL-Lite, query answering in a product-based Possibility Theory is a hard task. We provide equivalent transformations between the problem of computing an inconsistency degree (the key notion in reasoning from a possibilistic DL-Lite knowledge base) and the weighted maximum 2-Horn SAT problem.
