{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,24]],"date-time":"2026-02-24T21:02:09Z","timestamp":1771966929197,"version":"3.50.1"},"reference-count":0,"publisher":"TechForum Publishing Group","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Bull. Comput. Data Sci."],"published-print":{"date-parts":[[2023,12,30]]},"abstract":"<jats:p>Dependence logic with generalized quantifiers is strictly more expressive than first-order logic with the same quantifiers, so completeness is typically obtained only for first-order consequences. For the special generalized quantifier \u201cthere exist uncountably many\u201d \\((Q^1)\\), earlier axiomatizations achieved \\(FO(Q^1)\\)-completeness by adding a Skolem rule that introduces new function symbols. In this paper we show that the Skolem step can be avoided. We present a natural deduction system for dependence logic with \\(Q^1\\) and its dual that stays in the original signature and prove that it is sound and complete for \\(FO(Q^1)\\)-consequences. The key idea is to replace Skolemization by a team-based uncountable choice rule that directly reflects the team-semantics clause for \\(Q^1\\).<\/jats:p>","DOI":"10.71448\/bcds2341-2","type":"journal-article","created":{"date-parts":[[2026,2,24]],"date-time":"2026-02-24T20:10:17Z","timestamp":1771963817000},"source":"Crossref","is-referenced-by-count":0,"title":["Skolem-Free Completeness for Dependence Logic with the Uncountability Quantifier"],"prefix":"10.71448","volume":"4","author":[{"name":"Department of Chemical and Material Engineering, University of alberta, Edmonton, Canada","sequence":"first","affiliation":[]},{"given":"Adnan","family":"Asghar","sequence":"first","affiliation":[]}],"member":"52394","published-online":{"date-parts":[[2023,12,30]]},"container-title":["Bulletin of Computer and Data Sciences"],"original-title":[],"deposited":{"date-parts":[[2026,2,24]],"date-time":"2026-02-24T20:10:18Z","timestamp":1771963818000},"score":1,"resource":{"primary":{"URL":"https:\/\/bcds.ch\/skolem-free-completeness-for-dependence-logic-with-the-uncountability-quantifier\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,12,30]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2023,12,30]]},"published-print":{"date-parts":[[2023,12,30]]}},"URL":"https:\/\/doi.org\/10.71448\/bcds2341-2","relation":{},"ISSN":["3072-2926"],"issn-type":[{"value":"3072-2926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,12,30]]}}}