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This note corrects a claim made in the above-mentioned paper about the exact representation of a conditional preference network by means of a possibilistic logic base with partially ordered symbolic weights. We provide a counter-example that shows that the possibilistic logic representation is indeed not always exact. This is the basis of a short discussion on the difficulty of obtaining an exact representation.

© Copyright 2015, for this paper by its authors. Answer set programming (ASP) is a form of logic programming in which negation-as-failure is defined in a purely declarative way, based on the notion of a stable model. This short paper briefly explains how a recent generalization of possibilistic logic (GPL) can be used to characterize the semantics of answer set programming. This characterization has several advantages over existing characterizations of the stable model semantics. First, unlike reduct-based approaches, it does not rely on a syntactic procedure: we can directly characterize answer sets based on the minimally specific models of a GPL theory. Second, GPL enables us to study extensions of ASP in an intuitive way: unlike in existing generalizations of ASP such as equilibrium logic and autoepistemic logic, all formulas in GPL have a meaning which is intuitively clear. Finally, being based on possibilistic logic, GPL offers a natural way of dealing with uncertainty in answer set programs.

© 2015 IEEE. This article was commissioned by the 22nd IEEE International Conference of Fuzzy Systems (FUZZ-IEEE) to celebrate the 50th Anniversary of Lotfi Zadeh's seminal 1965 paper on fuzzy sets. In addition to Lotfi's original paper, this note itemizes 100 citations of books and papers deemed 'important (significant, seminal, etc.)' by 20 of the 21 living IEEE CIS Fuzzy Systems pioneers. Each of the 20 contributors supplied 5 citations, and Lotfi's paper makes the overall list a tidy 101, as in 'Fuzzy Sets 101'. This note is not a survey in any real sense of the word, but the contributors did offer short remarks to indicate the reason for inclusion (e.g., historical, topical, seminal, etc.) of each citation. Citation statistics are easy to find and notoriously erroneous, so we refrain from reporting them-almost. The exception is that according to Google scholar on April 9, 2015, Lotfi's 1965 paper has been cited 55,479 times.

© 2015 Elsevier Ltd. Multiuser museum interactives are computer systems installed in museums or galleries which allow several visitors to interact together with digital representations of artefacts and information from the museum's collection. In this paper, we describe WeCurate, a socio-technical system that supports co-browsing across multiple devices and enables groups of users to collaboratively curate a collection of images, through negotiation, collective decision making and voting. The engineering of such a system is challenging since it requires to address several problems such as: distributed workflow control, collective decision making and multiuser synchronous interactions. The system uses a peer-to-peer Electronic Institution (EI) to manage and execute a distributed curation workflow and models community interactions into scenes, where users engage in different social activities. Social interactions are enacted by intelligent agents that interface the users participating in the curation workflow with the EI infrastructure. The multiagent system supports collective decision making, representing the actions of the users within the EI, where the agents advocate and support the desires of their users e.g. aggregating opinions for deciding which images are interesting enough to be discussed, and proposing interactions and resolutions between disagreeing group members. Throughout the paper, we describe the enabling technologies of WeCurate, the peer-to-peer EI infrastructure, the agent collective decision making capabilities and the multi-modal interface. We present a system evaluation based on data collected from cultural exhibitions in which WeCurate was used as supporting multiuser interactive.

© Springer International Publishing Switzerland 2015. Recommender systems aim at providing suggestions of interest for end-users. Two main types of approach underlie existing recommender systems: content-based methods and collaborative filtering. In this paper, encouraged by good results obtained in classification by analogical proportion-based techniques, we investigate the possibility of using analogy as the main underlying principle for implementing a prediction algorithm of the collaborative filtering type. The quality of a recommender system can be estimated along diverse dimensions. The accuracy to predict user’s rating for unseen items is clearly an important matter. Still other dimensions like coverage and surprise are also of great interest. In this paper, we describe our implementation and we compare the proposed approach with well-known recommender systems.

© 2015 Elsevier B.V. All rights reserved. This note provides a brief overview of the main ideas and notions underlying fifty years of research in fuzzy set and possibility theory, two important settings introduced by L.A. Zadeh for representing sets with unsharp boundaries and uncertainty induced by granules of information expressed with words. The discussion is organized on the basis of three potential understanding of the grades of membership to a fuzzy set, depending on what the fuzzy set intends to represent: a group of elements with borderline members, a plausibility distribution, or a preference profile. It also questions the motivations for some existing generalized fuzzy sets. This note clearly reflects the shared personal views of its authors.

© Springer International Publishing Switzerland 2015. In this paper, we consider the situation where a database may contain suspect values, i.e. precise values whose validity is not certain. We propose a database model based on the notion of possibilistic certainty to deal with such values. The operators of relational algebra are extended in this framework. A very interesting aspect is that queries have the same data complexity as in a classical database context.

© 2015 Elsevier B.V. All rights reserved. Modern applications require advanced techniques and tools to process large volumes of uncertain data. For that purpose we introduce cardinality constraints as a principled tool to control the occurrences of uncertain data. Uncertainty is modeled qualitatively by assigning to each object a degree of possibility by which the object occurs in an uncertain instance. Cardinality constraints are assigned a degree of certainty that stipulates on which objects they hold. Our framework empowers users to model uncertainty in an intuitive way, without the requirement to put a precise value on it. Our class of cardinality constraints enjoys a natural possible world semantics, which is exploited to establish several tools to reason about them. We characterize the associated implication problem axiomatically and algorithmically in linear input time. Furthermore, we show how to visualize any given set of our cardinality constraints in the form of an Armstrong sketch. Even though the problem of finding an Armstrong sketch is precisely exponential, our algorithm computes a sketch with conservative use of time and space. Data engineers may therefore compute Armstrong sketches that they can jointly inspect with domain experts in order to consolidate the set of cardinality constraints meaningful for a given application domain.

© 2014 The Authors and IOS Press. Introduced a few years ago, analogy-based classification methods are a noticeable addition to the set of lazy learning techniques. They provide amazing results (in terms of accuracy) on many classical datasets. They look for all triples of examples in the training set that are in analogical proportion with the item to be classified on a maximal number of attributes and for which the corresponding analogical proportion equation on the class has a solution. In this paper when classifying a new item, we demonstrate a new approach where we focus on a small part of the triples available. To restrict the scope of the search, we first look for examples that are as similar as possible to the new item to be classified. We then only consider the pairs of examples presenting the same dissimilarity as between the new item and one of its closest neighbors. Thus we implicitly build triples that are in analogical proportion on all attributes with the new item. Then the classification is made on the basis of a majority vote on the pairs leading to a solvable class equation. This new algorithm provides results as good as other analogical classifiers with a lower average complexity.

This research note revisits an important issue with respect to the representation of preference queries, namely the modeling of "if possible" in requirements of the form " and if possible ". We mainly distinguish between two types of understanding: either (i) and are requirements of the same nature and are viewed as constraints with different levels of priority, or (ii) theyare of different nature (only induces constraint(s) and is only used for breaking ties among items that are equally satisfying). We indicate that the two views are related to different types of bipolarity, and discuss them in relation with possibilistic logic. The disjunctive dual of the first view (" or at least ") is thenpresented in this logical setting. We also briefly mention the idea of an extension of the second view where may refer both to bonus conditions or malus conditions that may increase or decrease respectively the interest in an item satisfying. © 2014 Springer International Publishing Switzerland.

Sugeno integrals are a well-known family of qualitative multiple criteria aggregation operators. The paper investigates how the behavior of these operators can be described in a prioritized propositional logic language, namely possibilistic logic. The case of binary-valued criteria, which amounts to providing a logical description of the fuzzy measure underlying the integral, is first considered. The general case of a Sugeno integral when criteria are valued on a discrete scale is then studied. © 2014 Elsevier B.V.

In real-world problems, input data may be pervaded with uncertainty. In this paper, we investigate the behavior of naive possibilistic classifiers, as a counterpart to naive Bayesian ones, for dealing with classification tasks in the presence of uncertainty. For this purpose, we extend possibilistic classifiers, which have been recently adapted to numerical data, in order to cope with uncertainty in data representation. Here the possibility distributions that are used are supposed to encode the family of Gaussian probabilistic distributions that are compatible with the considered dataset. We consider two types of uncertainty: (i) the uncertainty associated with the class in the training set, which is modeled by a possibility distribution over class labels, and (ii) the imprecision pervading attribute values in the testing set represented under the form of intervals for continuous data. Moreover, the approach takes into account the uncertainty about the estimation of the Gaussian distribution parameters due to the limited amount of data available. We first adapt the possibilistic classification model, previously proposed for the certain case, in order to accommodate the uncertainty about class labels. Then, we propose an algorithm based on the extension principle to deal with imprecise attribute values. The experiments reported show the interest of possibilistic classifiers for handling uncertainty in data. In particular, the probability-to-possibility transform-based classifier shows a robust behavior when dealing with imperfect data. © 2013 Elsevier B.V. Published by Elsevier B.V. All rights reserved.

Rough set theory (RST) and formal concept analysis (FCA) are two formal settings in information management, which have found applications in learning and in data mining. Both rely on a binary relation. FCA starts with a formal context, which is a relation linking a set of objects with their properties. Besides, a rough set is a pair of lower and upper approximations of a set of objects induced by an indistinguishability relation; in the simplest case, this relation expresses that two objects are indistinguishable because their known properties are exactly the same. It has been recently noticed, with different concerns, that any binary relation on a Cartesian product of two possibly equal sets induces a cube of oppositions, which extends the classical Aristotelian square of oppositions structure, and has remarkable properties. Indeed, a relation applied to a given subset gives birth to four subsets, and to their complements, that can be organized into a cube. These four subsets are nothing but the usual image of the subset by the relation, together with similar expressions where the subset and / or the relation are replaced by their complements. The eight subsets corresponding to the vertices of the cube can receive remarkable interpretations, both in the RST and the FCA settings. One facet of the cube corresponds to the core of RST, while basic FCA operators are found on another facet. The proposed approach both provides an extended view of RST and FCA, and suggests a unified view of both of them. © 2014 Springer International Publishing.

© Springer Japan 2014. Classical deduction is limited as a tool for reasoning about logical domain theories, in its ability to make sense of situations that are not explicitly covered. Humans on the other hand are remarkably adept at speculation about new situations, by drawing analogies or by relying on knowledge of similar situations. In this chapter, we are interested in formalising this process to develop a form of commonsense reasoning about incomplete rule bases. More precisely, we discuss two methods which can be used to derive plausible rules from a given set of propositional rules and a set of analogical proportions. The first method is based on the view that whenever the antecedents of four rules are in an analogical proportion, their consequences are likely to be in an analogical proportion as well. It often produces useful results, although it may be too adventurous for some applications. The second method is more cautious and makes explicit the assumptions under which it produces sound conclusions. Finally, we show how the second method may be further refined, in such a way that we recover the first method as a special case.

This chapter presents several modes of reasoning based on analogy and similarity. The case-based reasoning, presented in Section 8.2, consists of look for cases (problem solving episodes) similar to the problem to be solved and adapt them to solve this problem. Section 8.3 presents developments recent analogy and analog proportion. Interpolative reasoning describes in section 8.4 in the formal framework of blurring representations is another form of reasoning based on similarity.

© 2014 The Authors and IOS Press. Artificial intelligence (AI) was not born ex nihilo in the mid-fifties of the XXth century. Beyond its immediate roots in cybernetics and in computer science that started about two decades before, its emergence is the result of a long and slow process in the history of humanity. This can be articulated around two main questions: the formalization of reasoning and the design of machines having autonomous capabilities in terms of computation and action. The aim of this paper is to gather some insufficiently known elements about the prehistory of AI in the last 350 years that precede the official birth of AI, a time period where only a few very well-known names, such as Thomas Bayes and Georges Boole, are usually mentioned in relation with AI.

A qualitative approach to decision making under uncertainty has been proposed in the setting of possibility theory, which is based on the assumption that levels of certainty and levels of priority (for expressing preferences) are commensurate. In this setting, pessimistic and optimistic decision criteria have been formally justified. This approach has been transposed into possibilistic logic in which the available knowledge is described by formulas which are more or less certainly true and the goals are described in a separate prioritized base. This paper adapts the possibilistic logic handling of qualitative decision making under uncertainty in the Answer Set Programming (ASP) setting. We show how weighted beliefs and prioritized preferences belonging to two separate knowledge bases can be handled in ASP by modeling qualitative decision making in terms of abductive logic programming where (uncertain) knowledge about the world and prioritized preferences are encoded as possibilistic definite logic programs and possibilistic literals respectively. We provide ASP-based and possibilistic ASP-based algorithms for calculating optimal decisions and utility values according to the possibilistic decision criteria. We describe a prototype implementing the algorithms proposed on top of different ASP solvers and we discuss the complexity of the different implementations. © 2013 Elsevier Inc. All rights reserved.

© Springer International Publishing Switzerland 2014. The formal modeling of analogical proportions (i.e., statements of the form “a is to b as c is to d”) has led in the last past years to different proposals for classification algorithms, which have been quite successful on benchmarks where data are described by binary or nominal features. As far as we know and up to one exception, numerical data have never been considered. We propose here a new algorithm for handling numerical data. Starting from multiple-valued logical modelings of analogical proportions, more or less strongly encoding the idea that the change from a to b is the same as the change from c to d, we investigate different implementations leading to very good results on classical benchmarks.

© Springer-Verlag Berlin Heidelberg 2014. Analogies play an important role in many reasoning tasks. This chapter surveys a series of recent works developing a logical view of the notion of analogical proportion, and its applications. Analogical proportions are statements of the form “A is to B as C is to D”. The logical representation used for encoding such proportions takes both into account what the four situations A, B,C,D have in common and how they differ. Thanks to the use of a Boolean modeling extended with suitable fuzzy logic connectives, the approach can deal with situations described by features that may be binary or multiple-valued. It is shown that an analogical proportion is a particular case of a more general concept, namely the one of logical proportion. Among the 120 existing logical proportions, we single out two groups of 4 proportions for their remarkable properties: the homogeneous proportions (including the analogical proportion) which are symmetrical, and the heterogeneous proportions which are not. These eight proportions are the only logical proportions to satisfy a remarkable code-independency property. We emphasize the interest of these two groups of proportions for dealing with a variety of reasoning tasks, ranging from the solving of IQ tests, to transductive reasoning for classification, to interpolative and extrapolative reasoning, and also to the handling of quizzes of the “find the odd one out” type. The approach does not just rely on the exploitation of similarities between pairs of cases (as in case-based reasoning), but rather takes advantage of the parallel made between a situation to be evaluated or to be completed, with triples of other situations.

© 2014 Elsevier Inc. Before presenting the contents of the special issue, we propose a structured introductory overview of a landscape of the weighted logics (in a general sense) that can be found in the Artificial Intelligence literature, highlighting their fundamental differences and their application areas.