Name
Abstract | ||
|---|---|---|
This paper presents a new abstract framework to deal in a uniform way with the increasing variety of fuzzy logics studied in the literature. By means of notions and techniques from Abstract Algebraic Logic, we perform a study of non-classical logics based on the kind of generalized implication connectives they possess. It yields the new hierarchy of implicational logics. In this framework the notion of implicational semilinear logic can be naturally introduced as a property of the implication, namely a logic L is an implicational semilinear logic iff it has an implication such that L is complete w.r.t. the matrices where the implication induces a linear order, a property which is typically satisfied by well-known systems of fuzzy logic. The hierarchy of implicational logics is then restricted to the semilinear case obtaining a classification of implicational semilinear logics that encompasses almost all the known examples of fuzzy logics and suggests new directions for research in the field. |
Year | Venue | Keywords |
|---|---|---|
2009 | PROCEEDINGS OF THE JOINT 2009 INTERNATIONAL FUZZY SYSTEMS ASSOCIATION WORLD CONGRESS AND 2009 EUROPEAN SOCIETY OF FUZZY LOGIC AND TECHNOLOGY CONFERENCE | Abstract Algebraic Logic, Implicative logics, Leibniz Hierarchy, Mathematical Fuzzy Logic, Semilinear logics |
Field | DocType | Citations |
T-norm fuzzy logics,Discrete mathematics,Łukasiewicz logic,Algebra,Substructural logic,Classical logic,Monoidal t-norm logic,Many-valued logic,Relevance logic,Intermediate logic,Mathematics | Conference | 1 |
PageRank | References | Authors |
0.38 | 9 | 2 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Petr Cintula | 1 | 601 | 50.37 |
| Carles Noguera | 2 | 462 | 33.93 |