Two variable fragment of Term Modal Logic

Authors Anantha Padmanabha , R. Ramanujam

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Author Details

Anantha Padmanabha
  • Institute of Mathematical Sciences, HBNI, Chennai, India
R. Ramanujam
  • Institute of Mathematical Sciences, HBNI, Chennai, India


We thank Kamal Lodaya, Sreejith and Yanjing Wang for the insightful discussions. We also thank the anonymous referees for their comments and suggestions that helped better present the paper.

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Anantha Padmanabha and R. Ramanujam. Two variable fragment of Term Modal Logic. In 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 138, pp. 30:1-30:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


Term modal logics (TML) are modal logics with unboundedly many modalities, with quantification over modal indices, so that we can have formulas of the form Exists y Forall x (Box_x P(x,y) implies Diamond_y P(y,x)). Like First order modal logic, TML is also "notoriously" undecidable, in the sense that even very simple fragments are undecidable. In this paper, we show the decidability of one interesting fragment, that of two variable TML. This is in contrast to two-variable First order modal logic, which is undecidable.

Subject Classification

ACM Subject Classification
  • Theory of computation → Modal and temporal logics
  • Term modal logic
  • satisfiability problem
  • two variable fragment
  • decidability


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