2026-08-25T22:09:01Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:27375 2026-08-24T14:08:31Z ddc:004 open_access

Positional Properties in Temporal Logic Newman, Jessica Plummer, Benjamin Positionality Temporal Logic ATL Games on graphs We study positional properties in the context of game-based reactive synthesis. Our motivation stems from having a usable specification logic, for which tractable synthesis is guaranteed. We demonstrate that every ω-regular positional property (with respect to state- or edge-labelled game graphs), is expressible in linear-time temporal logic. Additionally, we provide some necessary and sufficient conditions for when an ω-regular property is positional, and identify well-behaved subclasses of ω-regular positional properties. Using varieties of languages, we prove that no class of ω-regular positional properties can simultaneously contain a prefix-independent property and be closed under Boolean operations. We conclude by discussing the implications on alternating-time temporal logic, where we isolate a few different fragments with tractable model checking, and compare the associated expressivity of such fragments. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Jessica Newman and Benjamin Plummer 2026 Is Part Of LIPIcs, Volume 391, 37th International Conference on Concurrency Theory (CONCUR 2026) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.CONCUR.2026.44 urn:nbn:de:0030-drops-273755 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2026.44 eng https://creativecommons.org/licenses/by/4.0/legalcode