n-Contractive BL-logics

Archive for Mathematical Logic 50 (3-4):257-285 (2011)
  Copy   BIBTEX


In the field of many-valued logics, Hájek’s Basic Logic BL was introduced in Hájek (Metamathematics of fuzzy logic, trends in logic. Kluwer Academic Publishers, Berlin, 1998). In this paper we will study four families of n-contractive (i.e. that satisfy the axiom \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\phi^n\rightarrow\phi^{n+1}}$$\end{document}, for some \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${n\in\mathbb{N}^+}$$\end{document}) axiomatic extensions of BL and their corresponding varieties: BLn, SBLn, BLn and SBLn. Concerning BLn we have that every BLn-chain is isomorphic to an ordinal sum of MV-chains of at most n + 1 elements, whilst every BLn-chain is isomorphic to an ordinal sum of MVn-chains (for SBLn and SBLn a similar property holds, with the difference that the first component must be the two elements boolean algebra); all these varieties are locally finite. Moving to the content of the paper, after a preliminary section, we will study generic and k-generic algebras, completeness and computational complexity results, amalgamation and interpolation properties. Finally, we will analyze the first-order versions of these logics, from the point of view of completeness and arithmetical complexity.



    Upload a copy of this work     Papers currently archived: 92,168

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

Naive Modus Ponens.Elia Zardini - 2013 - Journal of Philosophical Logic 42 (4):575-593.
A universal logic approach to adaptive logics.Diderik Batens - 2007 - Logica Universalis 1 (1):221-242.
Substructural Logics.Greg Restall - forthcoming - Stanford Encyclopedia of Philosophy.
Substructural Fuzzy Logics.George Metcalfe & Franco Montagna - 2007 - Journal of Symbolic Logic 72 (3):834 - 864.
An infinity of super-Belnap logics.Umberto Rivieccio - 2012 - Journal of Applied Non-Classical Logics 22 (4):319-335.
Normal monomodal logics can simulate all others.Marcus Kracht & Frank Wolter - 1999 - Journal of Symbolic Logic 64 (1):99-138.
Where gamma fails.Robert K. Meyer, Steve Giambrone & Ross T. Brady - 1984 - Studia Logica 43 (3):247 - 256.


Added to PP

62 (#261,076)

6 months
7 (#437,422)

Historical graph of downloads
How can I increase my downloads?