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Generalized Bundled Fragments for First-Order Modal Logic

Authors Mo Liu , Anantha Padmanabha , R. Ramanujam, Yanjing Wang

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Author Details

Mo Liu
  • LORIA, Unviersity of Lorraine, Nancy, France
Anantha Padmanabha
  • DI ENS, École Normale Supérieure, Université PSL, CNRS, Inria, Paris, France
R. Ramanujam
  • Institute of Mathematical Sciences, HBNI, Chennai, India (Retired)
  • Azim Premji University, Bengaluru (Visiting)
Yanjing Wang
  • Department of Philosophy, Peking University, Beijing, China


The authors thank the anonymous reviewers of MFCS2022 for their comments that improved the presentation of the paper.

Cite AsGet BibTex

Mo Liu, Anantha Padmanabha, R. Ramanujam, and Yanjing Wang. Generalized Bundled Fragments for First-Order Modal Logic. In 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 241, pp. 70:1-70:14, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)


When we bundle quantifiers and modalities together (as in ∃x□, ◇∀x etc.) in first-order modal logic (FOML), we get new logical operators whose combinations produce interesting bundled fragments of FOML. It is well-known that finding decidable fragments of FOML is hard, but existing work shows that certain bundled fragments are decidable [Anantha Padmanabha et al., 2018], without any restriction on the arity of predicates, the number of variables, or the modal scope. In this paper, we explore generalized bundles such as ∀x∀y□, ∀x∃y◇ etc., and map the terrain with regard to decidability, presenting both decidability and undecidability results. In particular, we propose the loosely bundled fragment, which is decidable over increasing domains and encompasses all known decidable bundled fragments.

Subject Classification

ACM Subject Classification
  • Theory of computation → Modal and temporal logics
  • Theory of computation → Logic and verification
  • bundled fragments
  • first-order modal logic
  • decidability
  • tableaux


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