{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,18]],"date-time":"2026-03-18T02:50:54Z","timestamp":1773802254087,"version":"3.50.1"},"reference-count":0,"publisher":"Association for the Advancement of Artificial Intelligence (AAAI)","issue":"17","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["AAAI"],"abstract":"<jats:p>Several proof systems for model counting have been introduced in recent years, mainly in an attempt to model #SAT solving and to allow proof logging of solvers. We reexamine these different approaches and show that: \n(i) with moderate adaptations, the conceptually quite different proof models of the dynamic system MICE and the static system of annotated Decision-DNNFs are equivalent and \n(ii) they tightly characterise state-of-the-art #SAT solving. \nThus, these proof systems provide a precise and robust proof-theoretic underpinning of current model counting. We also propose new strengthenings of these proof systems that might lead to stronger model counters.<\/jats:p>","DOI":"10.1609\/aaai.v40i17.38431","type":"journal-article","created":{"date-parts":[[2026,3,18]],"date-time":"2026-03-18T00:31:40Z","timestamp":1773793900000},"page":"14184-14191","source":"Crossref","is-referenced-by-count":0,"title":["Proof Systems That Tightly Characterise Model Counting Algorithms"],"prefix":"10.1609","volume":"40","author":[{"given":"Olaf","family":"Beyersdorff","sequence":"first","affiliation":[]},{"given":"Tim","family":"Hoffmann","sequence":"additional","affiliation":[]},{"given":"Kaspar","family":"Kasche","sequence":"additional","affiliation":[]}],"member":"9382","published-online":{"date-parts":[[2026,3,14]]},"container-title":["Proceedings of the AAAI Conference on Artificial Intelligence"],"original-title":[],"link":[{"URL":"https:\/\/ojs.aaai.org\/index.php\/AAAI\/article\/download\/38431\/42393","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/ojs.aaai.org\/index.php\/AAAI\/article\/download\/38431\/42393","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,18]],"date-time":"2026-03-18T00:31:40Z","timestamp":1773793900000},"score":1,"resource":{"primary":{"URL":"https:\/\/ojs.aaai.org\/index.php\/AAAI\/article\/view\/38431"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,3,14]]},"references-count":0,"journal-issue":{"issue":"17","published-online":{"date-parts":[[2026,3,17]]}},"URL":"https:\/\/doi.org\/10.1609\/aaai.v40i17.38431","relation":{},"ISSN":["2374-3468","2159-5399"],"issn-type":[{"value":"2374-3468","type":"electronic"},{"value":"2159-5399","type":"print"}],"subject":[],"published":{"date-parts":[[2026,3,14]]}}}