{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,8]],"date-time":"2026-06-08T22:16:09Z","timestamp":1780956969215,"version":"3.54.1"},"reference-count":43,"publisher":"Oxford University Press (OUP)","issue":"1","license":[{"start":{"date-parts":[[2026,1,1]],"date-time":"2026-01-01T00:00:00Z","timestamp":1767225600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"funder":[{"name":"National Board for Higher Mathematics (NBHM) India","award":["02011\/13\/2023 NBHM (R.P)\/R&D II\/5863"],"award-info":[{"award-number":["02011\/13\/2023 NBHM (R.P)\/R&D II\/5863"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2026,1,8]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>The study of rough set theory in multi-agent\/multi-source contexts, and its extension to attribute-relative approximations, constitutes a significant line of research in the rough set literature. Motivated by these, we propose a unified modal framework based on multiple-source information structures, where accessibility relations are indexed by sources and parameterized by attribute sets. We introduce two semantics, W-semantics and S-semantics, interpreting modal formulas via weak and strong approximation operators from multi-granulation rough set models. These provide a formal system for reasoning about uncertainty that is both attribute-relative and source-sensitive. We establish sound and complete axiomatizations for the corresponding logics over classes of models satisfying structural properties like reflexivity, symmetry and transitivity. Our completeness proofs use a step-by-step construction adapted to the semantics, avoiding reliance on copying techniques. This work deepens the modal foundations of rough set theory and contributes to the logic of complex approximation systems.<\/jats:p>","DOI":"10.1093\/logcom\/exaf057","type":"journal-article","created":{"date-parts":[[2025,10,14]],"date-time":"2025-10-14T13:00:38Z","timestamp":1760446838000},"source":"Crossref","is-referenced-by-count":1,"title":["Reasoning about attribute-relative approximations in multi-source environments: a modal framework with axiomatization"],"prefix":"10.1093","volume":"36","author":[{"given":"Md Aquil","family":"Khan","sequence":"first","affiliation":[{"name":"Department of Mathematics, Indian Institute of Technology Indore , Indore 453552,","place":["India"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Amal","family":"Talukdar","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Indian Institute of Technology Indore , Indore 453552,","place":["India"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2026,1,8]]},"reference":[{"key":"2026010808240719400_ref1","doi-asserted-by":"crossref","first-page":"553","DOI":"10.1007\/978-3-7908-1888-8_17","article-title":"Axiomatization of logics based on Kripke models with relative accessibility relations","volume-title":"Incomplete Information: Rough Set Analysis","author":"Balbiani","year":"1998"},{"key":"2026010808240719400_ref2","doi-asserted-by":"crossref","first-page":"1021","DOI":"10.1002\/int.20305","article-title":"Logical approaches to deontic reasoning: from basic questions to dynamic solutions","volume":"23","author":"Balbiani","year":"2008","journal-title":"International Journal of Intelligent Systems"},{"key":"2026010808240719400_ref3","doi-asserted-by":"crossref","first-page":"303","DOI":"10.1080\/11663081.1999.10510969","article-title":"A hierarchy of modal logics with relative accessibility 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