Implicational logics II: additional connectives and characterizations of semilinearity

Archive for Mathematical Logic 55 (3-4):353-372 (2016)
  Copy   BIBTEX

Abstract

This is the continuation of the paper :417–446, 2010). We continue the abstract study of non-classical logics based on the kind of generalized implication connectives they possess and we focus on semilinear logics, i.e. those that are complete with respect to the class of models where the implication defines a linear order. We obtain general characterizations of semilinearity in terms of the intersection-prime extension property, the syntactical semilinearity metarule and the class of finitely subdirectly irreducible models. Moreover, we consider extensions of the language with lattice connectives and generalized disjunctions, study their interplay with implication and obtain axiomatizations and further descriptions of semilinear logics in terms of disjunctions and the proof by cases property.

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 91,252

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

The shortest possible length of the longest implicational axiom.Dolph Ulrich - 1996 - Journal of Philosophical Logic 25 (1):101 - 108.
Deduction theorems for weak implicational logics.M. W. Bunder - 1982 - Studia Logica 41 (2-3):95 - 108.
Implicational f-structures and implicational relevance logics.A. Avron - 2000 - Journal of Symbolic Logic 65 (2):788-802.
On Combined Connectives.A. Sernadas, C. Sernadas & J. Rasga - 2011 - Logica Universalis 5 (2):205-224.
Completeness of implicational relevant logics.R. Kashima - 2000 - Logic Journal of the IGPL 8 (6):761-785.
BCI-algebras from the point of view of logic.Jacek K. Kabzinski - 1983 - Bulletin of the Section of Logic 12 (3):126-128.
The D-Completeness of T→.R. K. Meyer & M. W. Bunder - 2011 - Australasian Journal of Logic 8:1-8.
An algebraic approach to intuitionistic connectives.Xavier Caicedo & Roberto Cignoli - 2001 - Journal of Symbolic Logic 66 (4):1620-1636.
Noisy vs. Merely Equivocal Logics.Patrick Allo - 2013 - In Francesco Berto, Edwin Mares, Koji Tanaka & Francesco Paoli (eds.), Paraconsistency: Logic and Applications. Springer. pp. 57--79.
Advances in the ŁΠ and logics.Petr Cintula - 2003 - Archive for Mathematical Logic 42 (5):449-468.

Analytics

Added to PP
2015-12-02

Downloads
26 (#580,768)

6 months
5 (#565,734)

Historical graph of downloads
How can I increase my downloads?

Author's Profile