A cut-free sequent system for the smallest interpretability logic

Studia Logica 70 (3):353-372 (2002)
The idea of interpretability logics arose in Visser [Vis90]. He introduced the logics as extensions of the provability logic GLwith a binary modality. The arithmetic realization of A B in a theory T will be that T plus the realization of B is interpretable in T plus the realization of A. More precisely, there exists a function f on the formulas of the language of T such that T + B C implies T + A f.The interpretability logics were considered in several papers. An arithmetic completeness of the interpretability logic ILM, obtained by adding Montagna ''s axiom to the smallest interpretability logic IL, was proved in Berarducci [Ber90] and Shavrukov [Sha88]. [Vis90] proved that the interpretability logic ILP, an extension of IL, is also complete for another arithmetic interpretation. The completeness with respect to Kripke semantics due to Veltman was, for IL, ILMand ILP, proved in de Jongh and Veltman [JV90]. The fixed point theorem of GLcan be extended to ILand hence ILMand ILP. The unary pendant "T interprets T + A" is much less expressive and was studied in de Rijke [Rij92]. For an overview of interpretability logic, see Visser [Vis97], and Japaridze and de Jongh [JJ98].
Keywords Philosophy   Logic   Mathematical Logic and Foundations   Computational Linguistics
Categories (categorize this paper)
Reprint years 2004
DOI 10.1023/A:1015150314504
 Save to my reading list
Follow the author(s)
Edit this record
My bibliography
Export citation
Find it on Scholar
Mark as duplicate
Request removal from index
Revision history
Download options
Our Archive

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 30,122
Through your library
References found in this work BETA

No references found.

Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles
Added to PP index

Total downloads
15 ( #322,204 of 2,191,731 )

Recent downloads (6 months)
5 ( #42,087 of 2,191,731 )

How can I increase my downloads?

Monthly downloads
My notes
Sign in to use this feature