Algebraic study of substructural logics is rapidly growing and is one of most attracting research subjects of non-classical logics. The goal is to understand various non-classical logics, like many-valued logics, fuzzy logics, Lambek calculus, linear logic and relevant logics, within a unified view. Main technical tools are algebraic ones, used typically in the study of ordered algebraic structures, universal algebra and algebraic logic, and thus the study aims at developing a new, interdisciplinary field of non-classical logics and algebra. The goal of the proposed research covers the following topics: - Developing a study of interrelations between algebraic methods and proof-theoretic methods in non-classical logics, in order to obtain a deeper understanding of these two disciplines. - A study of mathematical fuzzy logics in relation to substructural logics, based on results and techniques developed recently in the study of substructural logics. - Conversely, extending geometrical approach, developed in mathematical fuzzy logics by the applicant, to substructural logics. The mathematical field to be investigated in this research lays down the foundation of several fields of Information Science, like artificial intelligence and software engineering. For example, the famous logic of Lukasiewicz is in strong connection with the famous Rényi-Ulam game with lies, which topic has turned out to be crucial in non-symmetric coding theory, and has been used to set up a coding protocol between the earth and a satellite. The forth goal of the research is - Application of results on non-classical logics to both game theory and information science, including Artificial Intelligence and Software Engineering.
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