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Algorithmic correspondence for intuitionistic modal mu-calculus, Part 2

4 pagesPublished: July 28, 2014

Abstract

Sahlqvist-style correspondence results remain a perennial theme and an active topic of research within modal logic. Recently there has been interest in extending classical results in this area to the modal mu-calculus. We show how the `calculus of correspondence' and the ALBA algorithm (Conradie and Palmigiano, 2012) can be extended to the intuitionistic mu-calculus, and be used to derive FO+LFP frame correspondents for formulas of that logic. We define the class of recursive mu-inequalities, which we compare it with related classes in the literature including the Sahlqvist mu-formulas of van Benthem, Bezhanishvili and Hodkinson. We show that the ALBA algorithm succeeds in reducing every recursive mu-inequality, and hence that every recursive mu-inequality has a frame correspondent in FO+LFP.

Keyphrases: correspondence theory, Heyting algebras, intuitionistic logic, modal logic, modal mu-calculus, Sahlvist theory

In: Nikolaos Galatos, Alexander Kurz and Constantine Tsinakis (editors). TACL 2013. Sixth International Conference on Topology, Algebra and Categories in Logic, vol 25, pages 57--60

Links:
BibTeX entry
@inproceedings{TACL2013:Algorithmic_correspondence_for_intuitionistic,
  author    = {Willem Conradie and Yves Fomatati and Alessandra Palmigiano and Sumit Sourabh},
  title     = {Algorithmic correspondence for intuitionistic modal mu-calculus, Part 2},
  booktitle = {TACL 2013. Sixth International Conference on Topology, Algebra and Categories in Logic},
  editor    = {Nikolaos Galatos and Alexander Kurz and Constantine Tsinakis},
  series    = {EPiC Series in Computing},
  volume    = {25},
  pages     = {57--60},
  year      = {2014},
  publisher = {EasyChair},
  bibsource = {EasyChair, https://easychair.org},
  issn      = {2398-7340},
  url       = {https://easychair.org/publications/paper/86Gl},
  doi       = {10.29007/r68t}}
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