NCLFITA · Non-Classical Logics and Fuzzy Inferences – Theory and Applications
FP7 — People (Marie Curie Actions)
- Duration
- 2010-12-01 → 2013-11-30
- EU contribution
- €45,000
- Participants
- 1
- Scheme
- MC-ERG
Lines connect the coordinator with its partners.
Results in brief
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.
Data: CORDIS, © European Union
Project objective
The goal of the proposed research covers the following two topics:1. Theoretical foundation and investigation of different fuzzy inferences: There is a tremendous number of applications in daily life and industry where fuzzy theory is successfully applied. Those methods usually are based on a fuzzy inference. Therefore the mathematical foundation of fuzzy inferences as well as the finding of new methods which are superior to the ones applied today is an important task. Thus, this research supports the theoretical foundation of several fields of Artificial Intelligence and Software Engineering such as fuzzy control, knowledge-based systems, search engines on the web, and leads to industrial applications too.2. A study of mathematical fuzzy logics in relation to substructural logics, based on results and techniques developed recently in the study of substructural logics: Finding algebraic characterizations of different subclasses of left-continuous t-norms and residuated lattices. Further extending the geometric approach, developed in mathematical fuzzy logics by the applicant, to substructural logics. New findings at this line of the research could be very beneficial in supporting the research goals of point 1 too. A final aim is to develop a study of interrelations between algebraic methods and proof-theoretic methods in non-classical logics, in particular, in substructural logics, and in mathematical fuzzy logics in order to obtain a deeper understanding of these two disciplines.
Original text from CORDIS.
Participants
- UNIVERSITAT LINZ · LinzCoordinatorAustria
Links
Data: CORDIS, © European Union