Gentzen-type methods for bilattice negation

Studia Logica 80 (2-3):265 - 289 (2005)
A general Gentzen-style framework for handling both bilattice (or strong) negation and usual negation is introduced based on the characterization of negation by a modal-like operator. This framework is regarded as an extension, generalization or re- finement of not only bilattice logics and logics with strong negation, but also traditional logics including classical logic LK, classical modal logic S4 and classical linear logic CL. Cut-elimination theorems are proved for a variety of proposed sequent calculi including CLS (a conservative extension of CL) and CLScw (a conservative extension of some bilattice logics, LK and S4). Completeness theorems are given for these calculi with respect to phase semantics, for SLK (a conservative extension and fragment of LK and CLScw, respectively) with respect to a classical-like semantics, and for SS4 (a conservative extension and fragment of S4 and CLScw, respectively) with respect to a Kripke-type semantics. The proposed framework allows for an embedding of the proposed calculi into LK, S4 and CL.
Keywords Philosophy   Logic   Mathematical Logic and Foundations   Computational Linguistics
Categories (categorize this paper)
DOI 10.2307/20016718
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history Request removal from index
Download options
PhilPapers Archive

Upload a copy of this paper     Check publisher's policy on self-archival     Papers currently archived: 15,974
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
Ofer Arieli & Arnon Avron (1996). Reasoning with Logical Bilattices. Journal of Logic, Language and Information 5 (1):25--63.

View all 16 references / Add more references

Citations of this work BETA

Add more citations

Similar books and articles

Monthly downloads

Added to index


Total downloads

15 ( #172,086 of 1,725,862 )

Recent downloads (6 months)

7 ( #92,975 of 1,725,862 )

How can I increase my downloads?

My notes
Sign in to use this feature

Start a new thread
There  are no threads in this forum
Nothing in this forum yet.