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Modular Focused Proof Systems for Intuitionistic Modal Logics

Authors Kaustuv Chaudhuri, Sonia Marin, Lutz Straßburger

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Keywords
  • intuitionistic modal logic
  • focusing
  • proof search
  • cut elimination
  • nested sequents

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Abstract

Focusing is a general technique for syntactically compartmentalizing
the non-deterministic choices in a proof system, which not only
improves proof search but also has the representational benefit of
distilling sequent proofs into synthetic normal forms.  However, since
focusing is usually specified as a restriction of the sequent
calculus, the technique has not been transferred to logics that lack a
(shallow) sequent presentation, as is the case for some of the logics
of the modal cube.  We have recently extended the focusing technique
to classical nested sequents, a generalization of ordinary sequents.
In this work we further extend focusing to intuitionistic nested
sequents, which can capture all the logics of the intuitionistic S5
cube in a modular fashion.  We present an internal cut-elimination
procedure for the focused system which in turn is used to show its
completeness.

Cite As Get BibTex

Kaustuv Chaudhuri, Sonia Marin, and Lutz Straßburger. Modular Focused Proof Systems for Intuitionistic Modal Logics. In 1st International Conference on Formal Structures for Computation and Deduction (FSCD 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 52, pp. 16:1-16:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016) https://doi.org/10.4230/LIPIcs.FSCD.2016.16

Author Details

Kaustuv Chaudhuri
Sonia Marin
Lutz Straßburger

References

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