On involutive FL e -monoids

Archive for Mathematical Logic 51 (7-8):719-738 (2012)

Authors
Hiroakira Ono
Japan Advanced Institute of Science and Technology
Abstract
The paper deals with involutive FL e -monoids, that is, commutative residuated, partially-ordered monoids with an involutive negation. Involutive FL e -monoids over lattices are exactly involutive FL e -algebras, the algebraic counterparts of the substructural logic IUL. A cone representation is given for conic involutive FL e -monoids, along with a new construction method, called twin-rotation. Some classes of finite involutive FL e -chains are classified by using the notion of rank of involutive FL e -chains, and a kind of duality is developed between positive and non-positive rank algebras. As a side effect, it is shown that the substructural logic IUL plus t ↔ f does not have the finite model property
Keywords FL e -algebra  Cone representation  Twin-rotation  Structural description  Classification
Categories (categorize this paper)
DOI 10.1007/s00153-012-0295-6
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

Our Archive


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 40,131
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

Substructural Fuzzy Logics.George Metcalfe & Franco Montagna - 2007 - Journal of Symbolic Logic 72 (3):834 - 864.
On the Structure of Rotation-Invariant Semigroups.Sándor Jenei - 2003 - Archive for Mathematical Logic 42 (5):489-514.
On the Reflection Invariance of Residuated Chains.Sándor Jenei - 2009 - Annals of Pure and Applied Logic 161 (2):220-227.

Add more references

Citations of this work BETA

Add more citations

Similar books and articles

Undecidability of Representability as Binary Relations.Robin Hirsch & Marcel Jackson - 2012 - Journal of Symbolic Logic 77 (4):1211-1244.
Logics for Classes of Boolean Monoids.Gerard Allwein, Hilmi Demir & Lee Pike - 2004 - Journal of Logic, Language and Information 13 (3):241-266.
Quasi-Varieties: A Special Access.Hans-Jürgen Hoehnke - 2004 - Studia Logica 78 (1-2):249 - 260.
Glivenko Theorems for Substructural Logics Over FL.Nikolaos Galatos & Hiroakira Ono - 2006 - Journal of Symbolic Logic 71 (4):1353 - 1384.
Topological Groupoid Quantales.A. Palmigiano & R. Re - 2010 - Studia Logica 95 (1-2):125 - 137.
3088 Varieties a Solution to the Ackermann Constant Problem.John K. Slaney - 1985 - Journal of Symbolic Logic 50 (2):487-501.
Failure of Interpolation in Relevant Logics.Alasdair Urquhart - 1993 - Journal of Philosophical Logic 22 (5):449 - 479.

Analytics

Added to PP index
2013-10-27

Total views
22 ( #366,383 of 2,237,168 )

Recent downloads (6 months)
6 ( #303,263 of 2,237,168 )

How can I increase my downloads?

Downloads

My notes

Sign in to use this feature