Studia Logica 108 (2):163-198 (2020)

Every Berman’s variety \ which is the subvariety of Ockham algebras defined by the equation \ and \) determines a finitary substitution invariant consequence relation \. A sequent system \ is introduced as an axiomatization of the consequence relation \. The system \ is characterized by a single finite frame \ under the frame semantics given for the formal language. By the duality between frames and algebras, \ can be viewed as a \-valued logic as it is characterized by a distributive lattice of \ elements with a unary operator. Moreover, a structural-rule-free, cut-free and terminating sequent system \ is established for \. The Craig interpolation property of \ is shown proof-theoretically utilizing \.
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.1007/s11225-018-9840-6
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Translate to english
Revision history

Download options

PhilArchive copy

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 70,214
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

A Useful Four-Valued Logic.N. D. Belnap - 1977 - In J. M. Dunn & G. Epstein (eds.), Modern Uses of Multiple-Valued Logic. D. Reidel.
Partiality and its Dual.J. Michael Dunn - 2000 - Studia Logica 66 (1):5-40.
Equivalence of Consequence Operations.W. J. Blok & Bjarni Jónsson - 2006 - Studia Logica 83 (1-3):91-110.

View all 24 references / Add more references

Citations of this work BETA

A Paraconsistent Conditional Logic.Minghui Ma & Chun-Ting Wong - 2020 - Journal of Philosophical Logic 49 (5):883-903.

Add more citations

Similar books and articles

A Gentzen Calculus for Nothing but the Truth.Stefan Wintein & Reinhard Muskens - 2016 - Journal of Philosophical Logic 45 (4):451-465.
Characterizing Belnap's Logic Via De Morgan's Laws.Alexej P. Pynko - 1995 - Mathematical Logic Quarterly 41 (4):442-454.
The Power of Belnap: Sequent Systems for SIXTEEN ₃. [REVIEW]Heinrich Wansing - 2010 - Journal of Philosophical Logic 39 (4):369 - 393.
An Infinity of Super-Belnap Logics.Umberto Rivieccio - 2012 - Journal of Applied Non-Classical Logics 22 (4):319 - 335.
Four-Valued Logic.Katalin Bimbó & J. Michael Dunn - 2001 - Notre Dame Journal of Formal Logic 42 (3):171-192.


Added to PP index

Total views
31 ( #368,677 of 2,507,652 )

Recent downloads (6 months)
2 ( #277,140 of 2,507,652 )

How can I increase my downloads?


My notes