{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,19]],"date-time":"2026-01-19T03:21:54Z","timestamp":1768792914798,"version":"3.49.0"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:p>We consider logics with truth values in the unit interval $[0,1]$. Such\nlogics are used to define queries and to define probability distributions. In\nthis context the notion of almost sure equivalence of formulas is generalized\nto the notion of asymptotic equivalence. We prove two new results about the\nasymptotic equivalence of formulas where each result has a convergence law as a\ncorollary. These results as well as several older results can be formulated as\nresults about the relative asymptotic expressivity of inference frameworks. An\ninference framework $\\mathbf{F}$ is a class of pairs $(\\mathbb{P}, L)$, where\n$\\mathbb{P} = (\\mathbb{P}_n : n = 1, 2, 3, \\ldots)$, $\\mathbb{P}_n$ are\nprobability distributions on the set $\\mathbf{W}_n$ of all $\\sigma$-structures\nwith domain $\\{1, \\ldots, n\\}$ (where $\\sigma$ is a first-order signature) and\n$L$ is a logic with truth values in the unit interval $[0, 1]$. An inference\nframework $\\mathbf{F}'$ is asymptotically at least as expressive as an\ninference framework $\\mathbf{F}$ if for every $(\\mathbb{P}, L) \\in \\mathbf{F}$\nthere is $(\\mathbb{P}', L') \\in \\mathbf{F}'$ such that $\\mathbb{P}$ is\nasymptotically total variation equivalent to $\\mathbb{P}'$ and for every\n$\\varphi(\\bar{x}) \\in L$ there is $\\varphi'(\\bar{x}) \\in L'$ such that\n$\\varphi'(\\bar{x})$ is asymptotically equivalent to $\\varphi(\\bar{x})$ with\nrespect to $\\mathbb{P}$. This relation is a preorder. If, in addition,\n$\\mathbf{F}$ is at least as expressive as $\\mathbf{F}'$ then we say that\n$\\mathbf{F}$ and $\\mathbf{F}'$ are asymptotically equally expressive. Our third\ncontribution is to systematize the new results of this paper and several\nprevious results in order to get a preorder on a number of inference systems\nthat are of relevance in the context of machine learning and artificial\nintelligence.<\/jats:p>","DOI":"10.46298\/lmcs-20(4:13)2024","type":"journal-article","created":{"date-parts":[[2024,11,12]],"date-time":"2024-11-12T10:15:09Z","timestamp":1731406509000},"source":"Crossref","is-referenced-by-count":1,"title":["On the relative asymptotic expressivity of inference frameworks"],"prefix":"10.46298","volume":"Volume 20, Issue 4","author":[{"given":"Vera","family":"Koponen","sequence":"first","affiliation":[]},{"given":"Felix","family":"Weitk\u00e4mper","sequence":"additional","affiliation":[]}],"member":"25203","published-online":{"date-parts":[[2024,11,12]]},"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/lmcs.episciences.org\/14725\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/lmcs.episciences.org\/14725\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,11,12]],"date-time":"2024-11-12T10:15:10Z","timestamp":1731406510000},"score":1,"resource":{"primary":{"URL":"https:\/\/lmcs.episciences.org\/9560"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,11,12]]},"references-count":0,"URL":"https:\/\/doi.org\/10.46298\/lmcs-20(4:13)2024","relation":{"has-preprint":[{"id-type":"arxiv","id":"2204.09457v6","asserted-by":"subject"},{"id-type":"arxiv","id":"2204.09457v5","asserted-by":"subject"},{"id-type":"arxiv","id":"2204.09457v3","asserted-by":"subject"}],"is-same-as":[{"id-type":"arxiv","id":"2204.09457","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.2204.09457","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"value":"1860-5974","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,11,12]]},"article-number":"9560"}}