Open AccessQuasiorders, Tolerance Relations and Corresponding “Partitions”
Author(s) -
Marek Nowak
Publication year - 2016
Publication title -
bulletin of the section of logic
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.225
H-Index - 13
eISSN - 2449-836X
pISSN - 0138-0680
DOI - 10.18778/0138-0680.45.2.01
Subject(s) - generalization , partition (number theory) , equivalence relation , mathematics , binary relation , equivalence (formal languages) , binary number , class (philosophy) , simple (philosophy) , algebra over a field , discrete mathematics , pure mathematics , computer science , combinatorics , arithmetic , artificial intelligence , epistemology , mathematical analysis , philosophy
The paper deals with a generalization of the notion of partition for wider classes of binary relations than equivalences: for quasiorders and tolerance relations. The counterpart of partition for the quasiorders is based on a generalization of the notion of equivalence class while it is shown that such a generalization does not work in case of tolerances. Some results from [5] are proved in a much more simple way. The third kind of “partition” corresponding to tolerances, not occurring in [5], is introduced.