Integration of expert knowledge into a probabilistic expert system
Interval-valued linguistic summaries of databases
Knowledge revision in Markov networks.
A lot of research in graphical models has been devoted to developing correct and efficient evidence propagation methods, like join tree propagation or bucket elimination. With these methods it is possible to condition the represented probability distribution on given evidence, a reasoning process that is sometimes also called focusing. In practice, however, there is the additional need to revise the represented probability distribution in order to reflect some knowledge changes by satisfying new...
Knowledge sharing in organizational structures
The organizational structure is usually defined using the best experience and there is a minimum of formal approach involved. This paper shows the possibilities of the theory of concept analysis that can help to understand organizational structure based on solid mathematical foundations. This theory is extended by the concept of knowledge sharing and diversity that enables to evaluate the organizational structure. The alternative approach based on the hierarchical methods of cluster analysis is...
Knowledge vagueness and logic
The aim of the paper is to outline an idea of solving the problem of the vagueness of concepts. The starting point is a definition of the concept of vague knowledge. One of the primary goals is a formal justification of the classical viewpoint on the controversy about the truth and object reference of expressions including vague terms. It is proved that grasping the vagueness in the language aspect is possible through the extension of classical logic to the logic of sentences which may contain vague...
Kripke models with relative accessibility and their applications to inferences from incomplete information
Les schémas mentaux : représenter et maintenir une connaissance apprise
Nous nous intéressons à l'apprentissage à partir d'exemples et à la résolution de problème dans un univers évolutif représenté par une base de connaissances incomplète. Nous formalisons un cadre de représentation de connaissances susceptible d'être élaboré et critiqué par des humains comme par des machines. Cette représentation des connaissances est appelée théorie semi-empirique car cette forme de théorie n'est pas complètement axiomatique. Nous avons formalisé la gestion de la croissance incrémentale...
Local Boolean manifolds from knowledge representation systems.
We introduce a structure to represent observations on entities in order to obtain knowledge about some of their characteristic properties or attributes. This structure is based on the Pawlak's definition of information systems (also knowledge representation systems) and lead us to obtain algebraic structures of lattice depending from the choice of an observational context. The semantical algebraic structure so obtained is of local Boolean manifold whose global structure is an orthoposet which shows...
Marginalization like a projection.
This paper studies the problem of marginalizing convex polytopes of probabilities represented by a set of constraints. This marginalization is obtained as a special case of projection on a specific subspace. An algorithm that projects a convex polytope on any subspace has been built and the expression of the subspace, where the projection must be made for obtaining the marginalization, has been calculated.
Mixed integer programming, general concept inclusions and fuzzy description logics.
Modeling biased information seeking with second order probability distributions
Updating probabilities by information from only one hypothesis and thereby ignoring alternative hypotheses, is not only biased but leads to progressively imprecise conclusions. In psychology this phenomenon was studied in experiments with the “pseudodiagnosticity task”. In probability logic the phenomenon that additional premises increase the imprecision of a conclusion is known as “degradation”. The present contribution investigates degradation in the context of second order probability distributions....
Non additive ordinal relations representable by lower or upper probabilities
We characterize (in terms of necessary and sufficient conditions) binary relations representable by a lower probability. Such relations can be non- additive (as the relations representable by a probability) and also not “partially monotone” (as the relations representable by a belief function). Moreover we characterize relations representable by upper probabilities and those representable by plausibility. In fact the conditions characterizing these relations are not immediately deducible by means...
On a fuzzy querying and data mining interface
In the paper an interface is proposed that combines flexible (fuzzy) querying and data mining functionality. The point of departure is the fuzzy querying interface designed and implemented previously by the present authors. It makes it possible to formulate and execute, against a traditional (crisp) database, queries containing imprecisely specified conditions. Here we discuss possibilities to extend it with some data mining features. More specifically, linguistic summarization of data (databases),...
On computable formal concepts in computable formal contexts.
On computations with causal compositional models
The knowledge of causal relations provides a possibility to perform predictions and helps to decide about the most reasonable actions aiming at the desired objectives. Although the causal reasoning appears to be natural for the human thinking, most of the traditional statistical methods fail to address this issue. One of the well-known methodologies correctly representing the relations of cause and effect is Pearl's causality approach. The paper brings an alternative, purely algebraic methodology...
On contexts of direct products, ordinal sums and ordinal products
On effective presentations of formal concept lattices.
On factorization of probability distributions over directed graphs
Four notions of factorizability over arbitrary directed graphs are examined. For acyclic graphs they coincide and are identical with the usual factorization of probability distributions in Markov models. Relations between the factorizations over circuits are described in detail including nontrivial counterexamples. Restrictions on the cardinality of state spaces cause that a factorizability with respect to some special cyclic graphs implies the factorizability with respect to their, more simple,...
On fuzzy temporal constraint networks.
Temporal Constraint Networks are a well-defined, natural and efficient formalism for representing temporal knowledge based on metric temporal constraints. They support the representation of both metric and some qualitative temporal relations and are provided with efficient algorithms based on CSP techniques. Recently, a generalization based on fuzzy sets has been proposed in order to cope with vagueness in temporal relations. In this paper we generalize some earlier definitions for Fuzzy Temporal...
Ontologies and soft computing in flexible querying