Studia Logica 81 (3):311-324 (2005)

Abstract
In this paper we characterize, classify and axiomatize all axiomatic extensions of the IMT3 logic. This logic is the axiomatic extension of the involutive monoidal t-norm logic given by ¬φ3 ∨ φ. For our purpose we study the lattice of all subvarieties of the class IMT3, which is the variety of IMTL-algebras given by the equation ¬(x 3) ∨ x ≈ ⊤, and it is the algebraic counterpart of IMT3 logic. Since every subvariety of IMT3 is generated by their totally ordered members, we study the structure of all IMT3-chains in order to determine the lattice of all subvarieties of IMT3. Given a family of IMT3-chains the number of elements of the largest odd finite subalgebra in the family and the number of elements of the largest even finite subalgebra in the family turns out to be a complete classifier of the variety generated. We obtain a canonical set of generators and a finite equational axiomatization for each subvariety and, for each corresponding logic, a finite set of characteristic matrices and a finite set of axioms.
Keywords Philosophy   Logic   Mathematical Logic and Foundations   Computational Linguistics
Categories (categorize this paper)
DOI 10.1007/s11225-005-4647-7
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 70,008
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

Add more references

Citations of this work BETA

On N -Contractive Fuzzy Logics.Rostislav Horčík, Carles Noguera & Milan Petrík - 2007 - Mathematical Logic Quarterly 53 (3):268-288.

Add more citations

Similar books and articles

Axiomatic Extensions of the Milpotent Minimum Logic.J. Braso - 2003 - Reports on Mathematical Logic:113-123.
Implicit Connectives of Algebraizable Logics.Xavier Caicedo - 2004 - Studia Logica 78 (1-2):155 - 170.
Generalized Ordinal Sums and Translations.Nikolaos Galatos - 2011 - Logic Journal of the IGPL 19 (3):455-466.
A Set of Axioms for Nonstandard Extensions.Abhijit Dasgupta - 2011 - Mathematical Logic Quarterly 57 (5):485-493.
An Algebraic Approach to Intuitionistic Connectives.Xavier Caicedo & Roberto Cignoli - 2001 - Journal of Symbolic Logic 66 (4):1620-1636.
A Splitting Logic in NExt(KTB).Yutaka Miyazaki - 2007 - Studia Logica 85 (3):381 - 394.

Analytics

Added to PP index
2009-01-28

Total views
27 ( #422,941 of 2,505,201 )

Recent downloads (6 months)
1 ( #416,705 of 2,505,201 )

How can I increase my downloads?

Downloads

My notes