A Treatise on Many-Valued Logics (2001)
| Venue: | Studies in Logic and Computation |
| Citations: | 43 - 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}
}
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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
