Seminář: Non-classical logics: theory and applications

In this reviewing talk we consider some generalized logics, their theoretical basis and applications in real life problems. These logics belong to the realm of applied logics. More precisely, we focus on (1) Many-valued inference, theory and applications. The starting point is Pavelka-style fuzzy logic, an extension of the famous Lukasiewicz infinite valued logic. First we show how fuzzy IF-THEN inference systems are related to Pavelka logic and then we demonstrate several real-life applications utilizing this connection. The presented real-life applications vary from traffic signal control to a sports medical classification tasks. (2) Paraconsistent fuzzy logic and its connection to GUHA method in data mining. Most logic systems have a feature that, from contradictory premises, anything can be inferred. The major motivation behind paraconsistent logic is to challenge this orthodoxy. Thus, in paraconsistent, then even if we are in certain circumstances where the available information is inconsistent, the inference relation does not explode into triviality. Thus, paraconsistent logic accommodates inconsistency in a sensible manner that treats inconsistent information as informative. Paraconsistent logics is applied e.g. in decision making problems. (3) Bayesian approach and its connection to GUHA method in data mining. We show how four-fold contingency tables data mined by LISpMiner and, thus some GUHA quantifiers can be interpreted in Bayesian framework.