## A Treatise on Many-Valued Logics (2001)

Venue: | Studies in Logic and Computation |

Citations: | 52 - 3 self |

### BibTeX

@INPROCEEDINGS{Gottwald01atreatise,

author = {Siegfried Gottwald},

title = {A Treatise on Many-Valued Logics},

booktitle = {Studies in Logic and Computation},

year = {2001},

publisher = {Press}

}

### Years of Citing Articles

### OpenURL

### Abstract

The paper considers the fundamental notions of many- valued logic together with some of the main trends of the recent development of infinite valued systems, often called mathematical fuzzy logics. Besides this logical approach also a more algebraic approach is discussed. And the paper ends with some hints toward applications which are based upon actual theoretical considerations about infinite valued logics. Key words: mathematical fuzzy logic, algebraic semantics, continuous t-norms, left-continuous t-norms, Pavelka-style fuzzy logic, fuzzy set theory, non-monotonic fuzzy reasoning 1 Basic ideas 1.1 From classical to many-valued logic Logical systems in general are based on some formalized language which includes a notion of well formed formula, and then are determined either semantically or syntactically. That a logical system is semantically determined means that one has a notion of interpretation or model 1 in the sense that w.r.t. each such interpretation every well formed formula has some (truth) value or represents a function into