Final Report Summary - NCLFITA (Non-Classical Logics and Fuzzy Inferences – Theory and Applications)
The aims of the research of the MC ERG grant 267589 were twofold. First, to contribute to the mathematical foundations of fuzzy inferences, second, to find characterizations of subclasses of left-continuous t-norms and, if possible, even classes of residuated lattices in general; thus strengthening then role of algebraic methods in (non-classical) logics. All project objectives have been successfully treated:
In [Jenei 2012, STUDIA LOGICA] Dr. Sándor Jenei could clarify foundational aspects of fuzzy inferences by establishing an axiomatization of some subclasses of substructural logics based on equivalences. The achieved results can even be generalized to the non-commutative case [Jenei & Korodi, 2013, ARCHIVE FOR MATHEMATICAL LOGIC]. By the characterization of strongly involutive uninorm algebras (see also [Jenei & Montagna, 2013, JOURNAL OF LOGIC AND COMPUTATION]) and the axiomatization of the related substructural fuzzy logic, namely the strongly involutive uninorm logic, an new fuzzy logic is now also available for fuzzy inference mechanisms. By the achieved results also an important contribution to the computational part of the theory of substructural logics has been given. Finally, in [Jenei & Montagna, 2014, SYNTHESE], even a classification of a subclass of residuated lattices under unexpectedly weak conditions could be achieved.
Summarizing, the objectives of the project have been treated successfully. Significant and interesting results have been obtained. They are published in international peer reviewed journals and have been communicated to colleagues and the scientific community at several conferences and meetings.
In [Jenei 2012, STUDIA LOGICA] Dr. Sándor Jenei could clarify foundational aspects of fuzzy inferences by establishing an axiomatization of some subclasses of substructural logics based on equivalences. The achieved results can even be generalized to the non-commutative case [Jenei & Korodi, 2013, ARCHIVE FOR MATHEMATICAL LOGIC]. By the characterization of strongly involutive uninorm algebras (see also [Jenei & Montagna, 2013, JOURNAL OF LOGIC AND COMPUTATION]) and the axiomatization of the related substructural fuzzy logic, namely the strongly involutive uninorm logic, an new fuzzy logic is now also available for fuzzy inference mechanisms. By the achieved results also an important contribution to the computational part of the theory of substructural logics has been given. Finally, in [Jenei & Montagna, 2014, SYNTHESE], even a classification of a subclass of residuated lattices under unexpectedly weak conditions could be achieved.
Summarizing, the objectives of the project have been treated successfully. Significant and interesting results have been obtained. They are published in international peer reviewed journals and have been communicated to colleagues and the scientific community at several conferences and meetings.