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Discovering patterns in a sequence is an important aspect of data mining. One popular choice of such patterns are episodes, patterns in sequential data describing events that often occur in the vicinity of each other. Episodes also enforce in which order events are allowed to occur. In this work we introduce a technique for discovering closed episodes. Adopting existing approaches for discovering...
The notions and algorithms of generating basis for exactness rules and the proper basis for conditional rules of redescription database are presented using closure operator of Galois connection based on the operations of formal concept analysis (FCA). It is demonstrated that constructed rules of redescription database are minimal non-redundant. At the same time, a new algorithm, i.e. non-redundant...
This paper aims at developing the logic theories of intuitionistic fuzzy sets. Starting from the intuitionistic fuzzy set and a defined lattice L*, a residuated lattice induced by L* is proposed which shows the structure of truth values of IF logic based on the IF algebra. Some basic properties of logic operation are presented. In the last, we define four pairs of logic operators based on the intuitionistic...
We study the complexity of evaluating positive equality-free sentences of first-order (FO) logic over a fixed, finite structure B. This may be seen as a natural generalisation of the non-uniform quantified constraint satisfaction problem QCSP(B). We introduce subjective hyper-endomorphisms and use them in proving a Galois connection that characterises definability in positive equality-free FO. Through...
We investigate a positive primitive formula closure (formed by (exist,&,=)-formulas) in countable structures which establishes an algebraic framework for Constraint Satisfaction Problems on a countable set. The main question under consideration is the characterization of countable structures, called positive primitive, in which, similar to a finite case, such closure coincides with the Galois...
Interpretation, one of the most applied techniques for semantics based static analysis of software, is based on two main key-concepts: the correspondence between concrete and abstract semantics through Galois connections/insertions, and the feasibility of a fixed point computation of the abstract semantics, through the fast convergence of widening operators. The latter point is crucial to ensure the...
We study isotone fuzzy Galois connections and concept lattices parameterized by truth-stressing hedges. Isotone fuzzy Galois connections and concept lattices provide an alternative to antitone fuzzy Galois connections and concept lattices which are the foundational structures for formal concept analysis of data with fuzzy attributes. We demonstrate that hedges enable us to control the number of fixed...
This paper proposes a method to reduce the number of concepts still conserving their formal structure. Our main idea is first to gather objects into classes such that the members of the same class share some set of properties, and then define a kind of Galois connection via a concept of inclusion degree in order to cope, to a certain degree (denoted as alpha), with this partition. Thus, a complete...
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