Connecting paraconsistent and many-valued logic in decision making task

Abstract: Paraconsistent logic refers to non-classical systems of logic, which reject the Principle of explosion; once a contradiction has been asserted, any proposition can be inferred. The primary motivation for paraconsistent logic is the conviction that it ought to be possible to reason with inconsistent information in a controlled and discriminating way. The principle of explosion precludes this, and so must be abandoned. The key note is evidence; if a statement is true, then there is also some evidence in favor of it, while the converse does not necessarily hold. If there is evidence in favor of a statement, it need not be true; there may also be evidence against it. Paraconsistent logics make it possible to reason with inconsistent information. Many-valued or fuzzy logics in turn are logic calculus in which there are more than two truth-values. Classical two-valued logic may be extended to infinite-valued Łukasiewicz logic and its extension, called Pavelka logic, has infinitely many truth-values and provability degrees. We show how paraconsistency and many-valuedness can be combined in Pavelka’s logic framework. Moreover, we show a real life application in decision-making how this logic system can be utilized.

Professor Esko Turunen earned his PhD in applied mathematics, entitled `A Mathematical Study of Fuzzy Logic: an Algebraic Approach´ in 1994 at Lappeenranta University of Technology, Finland. At present Turunen is the head of the Department of Mathematics at Tampere University of Technology, Finland. His scientific interests and research areas are in many-valued logics, fuzzy logic, paraconsistent logic, data mining and their real life applications. Turunen has published more than 50 scientific articles and conference papers with peer review process including three books. Turunen has wide international contacts to several universities all over the world; he has spent more than ten years in various universities and research institutes including Charles University and Prague University of Technology in Czech Republic, University of Naples, Salerno and Pisa in Italy and Technical University in Vienna, Austria. Turunen has supervised several doctoral theses and is a member of many editorial boards of scientific journals. Turunen has represented Finland in three COST Action research projects and is currently the representative of his country in COST Action IC1406. In addition to theoretical mathematical research, Turunen has worked as a mathematical expert in many industrial research projects, such as a developer of intelligent traffic systems, medical expert systems designer and creator of various other control systems.