## A logic for reasoning about relative similarity

B. Konikowska. A logic for reasoning about relative similarity. *Studia Logica*, 58:185–226, 1997.

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#### Abstract:

This paper deals with the problem of similarity of objects. The basic framework for these considerations is Pawlak's rough set methodology. A multi-modal logical language for relative similarities is presented. The language together with its complete Gentzen calculus system is shown to be useful for reasoning about any family of similarity relations defined by subsets of a given set of attributes. The logic supports the operations of lower and upper approximations with respect to similarity relations. Since such approximations are of interest in many AI problems, this gives a wide range of potential applications of the proposed system. To achieve completeness of the system two technical tools are used: the mechanism DRS (a deductive system in Rasiowa-Sikorski style), and a representation of the set of properties selected. It is shown that the system presented can be easily generalized to the case of indiscernibility relations. Similarly, the logical language given in the paper can be extended to a first-order language. Some other possible extensions of the system are also briefly discussed.

#### BibTeX: (download)

@ARTICLE{konikowska97, author = {B. Konikowska}, title = {A logic for reasoning about relative similarity}, journal = {Studia Logica}, year = {1997}, volume = {58}, pages = {185--226}, abstract = { This paper deals with the problem of similarity of objects. The basic framework for these considerations is Pawlak's rough set methodology. A multi-modal logical language for relative similarities is presented. The language together with its complete Gentzen calculus system is shown to be useful for reasoning about any family of similarity relations defined by subsets of a given set of attributes. The logic supports the operations of lower and upper approximations with respect to similarity relations. Since such approximations are of interest in many AI problems, this gives a wide range of potential applications of the proposed system. To achieve completeness of the system two technical tools are used: the mechanism DRS (a deductive system in Rasiowa-Sikorski style), and a representation of the set of properties selected. It is shown that the system presented can be easily generalized to the case of indiscernibility relations. Similarly, the logical language given in the paper can be extended to a first-order language. Some other possible extensions of the system are also briefly discussed.} }

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