Studia Logica 105 (6):1319-1347 (2017)

Stefan Wintein
Tilburg University
Reinhard Muskens
University of Amsterdam
The semantic valuations of classical logic, strong Kleene logic, the logic of paradox and the logic of first-degree entailment, all respect the Dunn conditions: we call them Dunn logics. In this paper, we study the interpolation properties of the Dunn logics and extensions of these logics to more expressive languages. We do so by relying on the \ calculus, a signed tableau calculus whose rules mirror the Dunn conditions syntactically and which characterizes the Dunn logics in a uniform way. In terms of the \ calculus, we first introduce two different interpolation methods, each of which uniformly shows that the Dunn logics have the interpolation property. One of the methods is closely related to Maehara’s method but the other method, which we call the pruned tableau method, is novel to this paper. We provide various reasons to prefer the pruned tableau method to the Maehara-style method. We then turn our attention to extensions of Dunn logics with so-called appropriate implication connectives. Although these logics have been considered at various places in the literature, a study of the interpolation properties of these logics is lacking. We use the pruned tableau method to uniformly show that these extended Dunn logics have the interpolation property and explain that the same result cannot be obtained via the Maehara-style method. Finally, we show how the pruned tableau method constructs interpolants for functionally complete extensions of the Dunn logics.
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.1007/s11225-017-9720-5
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: 51,639
Through your library

References found in this work BETA

The Logic of Paradox.Graham Priest - 1979 - Journal of Philosophical Logic 8 (1):219 - 241.
Proof Theory.Gaisi Takeuti - 1990 - Studia Logica 49 (1):160-161.
Reasoning with Logical Bilattices.Ofer Arieli & Arnon Avron - 1996 - Journal of Logic, Language and Information 5 (1):25--63.

View all 18 references / Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles

An Infinity of Super-Belnap Logics.Umberto Rivieccio - 2012 - Journal of Applied Non-Classical Logics 22 (4):319 - 335.
Leibniz Interpolation Properties.Leonardo Cabrer & José Gil-Férez - 2014 - Annals of Pure and Applied Logic 165 (4):933-962.
Interpolation in Fuzzy Logic.Matthias Baaz & Helmut Veith - 1999 - Archive for Mathematical Logic 38 (7):461-489.
Decision Procedures for Some Strong Hybrid Logics.Andrzej Indrzejczak & Michał Zawidzki - 2013 - Logic and Logical Philosophy 22 (4):389-409.


Added to PP index

Total views
21 ( #465,523 of 2,331,390 )

Recent downloads (6 months)
2 ( #396,513 of 2,331,390 )

How can I increase my downloads?


My notes