The logic of knights, knaves, normals and mutes

R. M. Smullyan wrote in his book about islands, knights and knaves. The knights always tell the truth and the knaves axe always lying. Instead of say we shall examine the can say modal operator. W e show the soundness and the completeness of this logic

Correlation clustering: a parallel approach?

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Density of tautologies in logics with one variable

In the present paper we estimate the ratio of the number of tautologies and the number of formulae of length n by determining the asymptotic density of tautologies in different kinds of logics with one variable. The logics under consideration are the ones with a single connective (nand or nor); negation with a connective (disjunction or conjunction); and several connectives

On a correlational clustering of integers

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Finding the representative in a cluster using correlation clustering

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Finding the representative in a cluster using correlation clustering

Correlation clustering is a widely used technique in data mining. The clusters contain objects, which are typically similar to each other and different from objects from other groups. It can be an interesting task to find the member, which is the most similar to the others for each group. These objects can be called representatives. In this paper, a possible way to find these representatives are shown and software to test the method is also provided

Different types of search algorithms for rough sets

Based on the available information in many cases it can happen that two objects cannot be distinguished. If a set of data is given and in this set two objects have the same attribute values, then these two objects are called indiscernible. This indiscernibility has an effect on the membership relation, because in some cases it makes our judgment uncertain about a given object. The uncertainty appears because if something about an object is needed to be stated, then all the objects that are indiscernible from the given object must be taken into consideration. The indiscernibility relation is an equivalence relation which represents background knowledge embedded in an information system. In a Pawlakian system this relation is used in set approximation. Correlation clustering is a clustering technique which generates a partition using search algorithms. In the authors’ previous research the possible usage of the correlation clustering in rough set theory was investigated. In this paper the authors show how different types of search algorithms affect the set approximation