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.
@InProceedings{padmanabha_et_al:LIPIcs.MFCS.2019.30, author = {Padmanabha, Anantha and Ramanujam, R.}, title = {{Two variable fragment of Term Modal Logic}}, booktitle = {44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)}, pages = {30:1--30:14}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-117-7}, ISSN = {1868-8969}, year = {2019}, volume = {138}, editor = {Rossmanith, Peter and Heggernes, Pinar and Katoen, Joost-Pieter}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2019.30}, URN = {urn:nbn:de:0030-drops-109741}, doi = {10.4230/LIPIcs.MFCS.2019.30}, annote = {Keywords: Term modal logic, satisfiability problem, two variable fragment, decidability} }
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