NDLI: Interpolation and Definability over the Logic Gl

Content Provider	Springer Nature Link
Author	Maksimova, Larisa
Copyright Year	2011
Abstract	In a previous paper [21] all extensions of Johansson’s minimal logic J with the weak interpolation property WIP were described. It was proved that WIP is decidable over J. It turned out that the weak interpolation problem in extensions of J is reducible to the same problem over a logic Gl, which arises from J by adding tertium non datur.In this paper we consider extensions of the logic Gl. We prove that only finitely many logics over Gl have the Craig interpolation property CIP, the restricted interpolation property IPR or the projective Beth property PBP. The full list of Gl-logics with the mentioned properties is found, and their description is given. We note that IPR and PBP are equivalent over Gl. It is proved that CIP, IPR and PBP are decidable over the logic Gl.
Starting Page	249
Ending Page	267
Page Count	19
File Format	PDF
ISSN	00393215
Journal	Studia Logica
Volume Number	99
Issue Number	1-3
e-ISSN	15728730
Language	English
Publisher	Springer Netherlands
Publisher Date	2011-08-25
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Minimal logic interpolation definability amalgamation Mathematical Logic and Foundations Logic Computational Linguistics
Content Type	Text
Resource Type	Article
Subject	Logic History and Philosophy of Science

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Interpolation and Definability over the Logic Gl