Completing rule bases in symbolic domains by analogy making

The paper considers the problem of completing a set of parallel if-then rules that provides a partial description of how a conclusion variable depends on the values of condition variables, where each variable takes its value among a finite ordered set of labels. The proposed approach does not require the use of fuzzy sets for the interpretation of these labels or for defining similarity measures, but rather relies on the extrapolation of missing rules on the basis of analogical proportions that hold for each variable between the labels of several parallel rules. The analogical proportions are evaluated for binary and multiple-valued variables on the basis of a logical expression involving lukasiewicz implication. The underlying assumption is that the mapping partially specified by the given rules is as regular as suggested by these rules. A comparative discussion with other approaches is presented. © 2011. The authors-Published by Atlantis Press

Incomplete conjunctive information

AbstractMany information systems capable of handling incomplete or fuzzy information manipulate objects with single-valued attributes. Information is then said to be disjunctive. Information is said to be conjunctive when pertaining to many-valued attributes. While a piece of incomplete disjunctive information is easily represented by means of a set of mutually exclusive possible values, modeling incomplete conjunctive information theoretically leads to consider families of sets, since attributes are then set-valued under complete information. Some proposals are made in order to efficiently and rigorously represent incomplete conjunctive information, and deal with query evaluation, especially in the case where only upper and/or lower bounds of the set of values of a many-valued attribute are known. Applications of this approach can be expected for the processing of time intervals, as well as spatial reasoning, among other topics, in knowledge base management

The structure of oppositions in rough set theory and formal concept analysis - Toward a new bridge between the two settings

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

Excretion of low molecular weight, folin-positive metabolites by the female receptor mycelium, in response to mating.

Excretion of low molecular weight, folin-positive metabolites by the female receptor mycelium, in response to mating

Reasoning about uncertainty and explicit ignorance in generalized possibilistic logic

© 2014 The Authors and IOS Press. Generalized possibilistic logic (GPL) is a logic for reasoning about the revealed beliefs of another agent. It is a two-tier propositional logic, in which propositional formulas are encapsulated by modal operators that are interpreted in terms of uncertainty measures from possibility theory. Models of a GPL theory represent weighted epistemic states and are encoded as possibility distributions. One of the main features of GPL is that it allows us to explicitly reason about the ignorance of another agent. In this paper, we study two types of approaches for reasoning about ignorance in GPL, based on the idea of minimal specificity and on the notion of guaranteed possibility, respectively. We show how these approaches naturally lead to different flavours of the language of GPL and a number of decision problems, whose complexity ranges from the first to the third level of the polynomial hierarchy

Workshop on X-rays from electron beams

Workshop on X-rays from electron beams with special emphasis on possible developments at ELB

Analogical Proportions and Multiple-Valued Logics

National audienceRecently, a propositional logic modeling of analogical proportions, i.e., statements of the form “A is to B as C is to D”, has been proposed, and has then led to introduce new related proportions in a general setting. This framework is well-suited for analogical reasoning and classification tasks about situations described by means of Boolean properties. There is a clear need for extending this approach to deal with the cases where i) properties are gradual ; ii) properties may not apply to some situations ; iii) the truth status of a property is unknown. The paper investigates the appropriate extension in each of these three cases

Imprecise data fusion

Possibility theory offers a natural setting for representing imprecise data and poor information. This theory turns out to be quite useful for the purpose of pooling pieces of information stemming from several sources (for instance, several experts, sensors, or databases) . Indeed it looks more flexible than probability theory for the representation of aggregation modes that do not express averaging processes . This paper tentatively explains why possibility theory is appealing for the fusion of imprecise data, and it describes several aggregation modes it allows, along with their underlying assumptions . The existence of adaptive combination rules are pointed out, that take into account the level of conflict between the sources . This approach sounds natural in the pooling of expert opinions . It is suggested here that, under some assumptions, it might also be useful in sensor data fusion .La théorie des possibilités offre un cadre formel naturel pour la représentation de données imprécises, d'informations pauvres. Cette théorie prend tout son intérêt quand il s'agit d'agréger des informations issues de plusieurs sources (par exemple un groupe d'experts, un ensemble hétérogène de capteurs, plusieurs bases de données). En effet elle s'avère être beaucoup plus souple que la théorie des probabilités pour décrire des modes d'agrégation qui ne correspondent pas à des moyennes. Dans cet article on tente d'expliquer pourquoi la théorie des possibilités est intéressante dans le problème de fusion d'informations imprécises, et on décrit les modes d'agrégation qu'elle permet de représenter, avec les hypothèses qui les sous-tendent. On indique notamment l'existence d'opérations de combinaison adaptatives qui prennent en compte le niveau de conflit entre les sources. Cette approche semble justifiée pour l'agrégation d'opinions d'experts. On suggère ici qu'elle peut, dans certaines conditions, être utilisée pour la fusion multi-capteur