Disentangling FDE -Based Paraconsistent Modal Logics

Studia Logica 105 (6):1221-1254 (2017)
  Copy   BIBTEX

Abstract

The relationships between various modal logics based on Belnap and Dunn’s paraconsistent four-valued logic FDE are investigated. It is shown that the paraconsistent modal logic \, which lacks a primitive possibility operator \, is definitionally equivalent with the logic \, which has both \ and \ as primitive modalities. Next, a tableau calculus for the paraconsistent modal logic KN4 introduced by L. Goble is defined and used to show that KN4 is definitionally equivalent with \ without the absurdity constant. Moreover, a tableau calculus is defined for the modal bilattice logic MBL introduced and investigated by A. Jung, U. Rivieccio, and R. Jansana. MBL is a generalization of BK that in its Kripke semantics makes use of a four-valued accessibility relation. It is shown that MBL can be faithfully embedded into the bimodal logic \ over the non-modal vocabulary of MBL. On the way from \ to MBL, the Fischer Servi-style modal logic \ is defined as the set of all modal formulas valid under a modified standard translation into first-order FDE, and \ is shown to be characterized by the class of all models for \. Moreover, \ is axiomatized and this axiom system is proved to be strongly sound and complete with respect to the class of models for \. Moreover, the notion of definitional equivalence is suitably weakened, so as to show that \ and \ are weakly definitionally equivalent.

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 76,346

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

Nearly every normal modal logic is paranormal.Joao Marcos - 2005 - Logique Et Analyse 48 (189-192):279-300.
Some multi-conclusion modal paralogics.Casey McGinnis - 2007 - Logica Universalis 1 (2):335-353.
Modal logic S4 as a paraconsistent logic with a topological semantics.Marcelo E. Coniglio & Leonardo Prieto-Sanabria - 2017 - In Carlos Caleiro, Francisco Dionisio, Paula Gouveia, Paulo Mateus & João Rasga (eds.), Logic and Computation: Essays in Honour of Amilcar Sernadas. London, UK: College Publications. pp. 171-196.
Displaying the modal logic of consistency.Heinrich Wansing - 1999 - Journal of Symbolic Logic 64 (4):1573-1590.
Post Completeness in Congruential Modal Logics.Peter Fritz - 2016 - In Lev Beklemishev, Stéphane Demri & András Máté (eds.), Advances in Modal Logic, Volume 11. College Publications. pp. 288-301.
Classically complete modal relevant logics.Edwin D. Mares - 1993 - Mathematical Logic Quarterly 39 (1):165-177.
On Béziau’s logic Z.Hitoshi Omori & Toshiharu Waragai - 2008 - Logic and Logical Philosophy 17 (4):305-320.
Full Models for Positive Modal Logic.Ramon Jansana - 2002 - Mathematical Logic Quarterly 48 (3):427-445.

Analytics

Added to PP
2017-09-23

Downloads
28 (#418,835)

6 months
1 (#450,993)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Heinrich Wansing
Ruhr-Universität Bochum

References found in this work

Constructible falsity and inexact predicates.Ahmad Almukdad & David Nelson - 1984 - Journal of Symbolic Logic 49 (1):231-233.
Reasoning with logical bilattices.Ofer Arieli & Arnon Avron - 1996 - Journal of Logic, Language and Information 5 (1):25--63.
Modal logics with Belnapian truth values.Serge P. Odintsov & Heinrich Wansing - 2010 - Journal of Applied Non-Classical Logics 20 (3):279-304.

View all 16 references / Add more references