Three-valued logics, uncertainty management and rough sets

This paper is a survey of the connections between three-valued logics and rough sets from the point of view of incomplete information management. Based on the fact that many three-valued logics can be put under a unique algebraic umbrella, we show how to translate three-valued conjunctions and implications into operations on ill-known sets such as rough sets. We then show that while such translations may provide mathematically elegant algebraic settings for rough sets, the interpretability of these connectives in terms of an original set approximated via an equivalence relation is very limited, thus casting doubts on the practical relevance of truth-functional logical renderings of rough sets

Three-way Decisions with Evaluative Linguistic Expressions

We propose a linguistic interpretation of three-way decisions, where the regions of acceptance, rejection, and non-commitment are constructed by using the so-called evaluative linguistic expressions, which are expressions of natural language such as small, medium, very short, quite roughly strong, extremely good, etc. Our results highlight new connections between two different research areas: three-way decisions and the theory of evaluative linguistic expressions

From paraconsistent three-valued logics to multiple-source epistemic logic

National audienceSeveral interpretations can be given to the third truth value in three-valued logics. Here, we consider the case when it refers to the epistemic notion of contradictory, or both true and false at the same time. We study several paraconsistent three-valued logics that carry this concern and show that they can be translated into a fragment of a simple epistemic logic where modalities can only appear in front of literals. This logic is unusual in the sense that necessity modalities distribute over disjunctions instead of conjunctions. An equivalent translation into a fragment of KD modal logic can be obtained by exchanging the role of possibility and necessity modalities, highlighting the perfect symmetry between three-valued logics of contradiction and three-valued logics of incomplete information

An Algebraic Approach to Shadowed Sets

Abstract After the introduction of shadowed sets and the investigation of their relation with fuzzy sets, we present BZMV dM algebras as an abstract environment for both shadowed and fuzzy sets. Then, we introduce the weaker notion of pre-BZMV dM algebra. This structure enables us to algebraically define a mapping from fuzzy sets to shadowed sets

Relazione scuola-famiglia: alleanza e corresponsabilità educativa

The school-family educational alliance is a relationship defined by two dimensions: the frequency of contacts between these two systems and the quality of the undertaken relationships. A good educational alliance promotes a concrete implementation of the school-family co-responsibility pact. In order to provide tools and empirical evidence on how this relationship can be built, this paper documents a participatory research carried out with teachers, parents and pupils in a network of schools. The result was the construction of a “Co-responsibility Pact” inspired by the principles of comparison, sharing, mediation and participation

Borderline vs. unknown: comparing three-valued representations of imperfect information

International audienceIn this paper we compare the expressive power of elementary representation formats for vague, incomplete or conflicting information. These include Boolean valuation pairs introduced by Lawry and González-Rodríguez, orthopairs of sets of variables, Boolean possibility and necessity measures, three-valued valuations, supervaluations. We make explicit their connections with strong Kleene logic and with Belnap logic of conflicting information. The formal similarities between 3-valued approaches to vagueness and formalisms that handle incomplete information often lead to a confusion between degrees of truth and degrees of uncertainty. Yet there are important differences that appear at the interpretive level: while truth-functional logics of vagueness are accepted by a part of the scientific community (even if questioned by supervaluationists), the truth-functionality assumption of three-valued calculi for handling incomplete information looks questionable, compared to the non-truth-functional approaches based on Boolean possibility–necessity pairs. This paper aims to clarify the similarities and differences between the two situations. We also study to what extent operations for comparing and merging information items in the form of orthopairs can be expressed by means of operations on valuation pairs, three-valued valuations and underlying possibility distributions

Data-Driven Induction of Shadowed Sets Based on Grade of Fuzziness

We propose a procedure devoted to the induction of a shadowed set through the post-processing of a fuzzy set, which in turn is learned from labeled data. More precisely, the fuzzy set is inferred using a modified support vector clustering algorithm, enriched in order to optimize the fuzziness grade. Finally, the fuzzy set is transformed into a shadowed set through application of an optimal alpha-cut. The procedure is tested on synthetic and real-world datasets

Logiques tri-valuées de l'information incomplète et logique épistémique

Journées organisées en conjonction avec les Journées Francophones de Programmation par Contraintes (JFPC 2012)International audienc

A capacity-based framework encompassing Belnap–Dunn logic for reasoning about multisource information

International audienceBelnap-Dunn four-valued logic is one of the best known logics for handling elementary information items coming from several sources. More recently, a conceptually simple framework, namely a two-tiered propositional logic augmented with classical modal axioms (here called BC logic), was suggested by the second author and colleagues, for the handling of multisource information. It is a fragment of the non-normal modal logic EMN, whose semantics is expressed in terms of two-valued monotonic set functions called Boolean capacities. We show BC logic is more expressive than Belnap-Dunn logic by proposing a consequence-preserving translation of Belnap-Dunn logic in this setting. As special cases, we can recover already studied translations of three-valued logics such as Kleene and Priest logics. Moreover, BC logic is compared with the source-processor logic of Avron, Ben Naim and Konikowska. Our translation bridges the gap between Belnap-Dunn logic, epistemic logic, and theories of uncertainty like possibility theory or belief functions, and paves the way to a unified approach to various methods for handling inconsistency due to several conflicting sources of information