Name
Abstract | ||
|---|---|---|
In abstract algebraic logic, the general study of propositional non-classical logics has been traditionally based on the abstraction
of the Lindenbaum-Tarski process. In this process one considers the Leibniz relation of indiscernible formulae. Such approach
has resulted in a classification of logics partly based on generalizations of equivalence connectives: the Leibniz hierarchy. This paper performs an analogous abstract study of non-classical logics based on the kind of generalized implication connectives
they possess. It yields a new classification of logics expanding Leibniz hierarchy: the 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 | DOI | Venue |
|---|---|---|
2010 | 10.1007/s00153-010-0178-7 | Arch. Math. Log. |
Keywords | Field | DocType |
linear order,non classical logic,abstract algebraic logic,fuzzy logic,satisfiability | T-norm fuzzy logics,Discrete mathematics,Łukasiewicz logic,Algebraic logic,Substructural logic,Classical logic,Monoidal t-norm logic,Many-valued logic,Intermediate logic,Mathematics | Journal |
Volume | Issue | ISSN |
49 | 4 | 1432-0665 |
Citations | PageRank | References |
21 | 1.13 | 13 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Petr Cintula | 1 | 601 | 50.37 |
| Carles Noguera | 2 | 462 | 33.93 |