{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T15:34:59Z","timestamp":1753889699682,"version":"3.41.2"},"reference-count":1,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","license":[{"start":{"date-parts":[[2015,7,28]],"date-time":"2015-07-28T00:00:00Z","timestamp":1438041600000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/arxiv.org\/licenses\/nonexclusive-distrib\/1.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:p>Computability logic (see http:\/\/www.csc.villanova.edu\/~japaridz\/CL\/) is a\nlong-term project for redeveloping logic on the basis of a constructive game\nsemantics, with games seen as abstract models of interactive computational\nproblems. Among the fragments of this logic successfully axiomatized so far is\nCL12 --- a conservative extension of classical first-order logic, whose\nlanguage augments that of classical logic with the so called choice sorts of\nquantifiers and connectives. This system has already found fruitful\napplications as a logical basis for constructive and complexity-oriented\nversions of Peano arithmetic, such as arithmetics for polynomial time\ncomputability, polynomial space computability, and beyond. The present paper\nintroduces a third, indispensable complexity measure for interactive\ncomputations termed amplitude complexity, and establishes the adequacy of CL12\nwith respect to A-amplitude, S-space and T-time computability under certain\nminimal conditions on the triples (A,S,T) of function classes. This result very\nsubstantially broadens the potential application areas of CL12. The paper is\nself-contained, and targets readers with no prior familiarity with the subject.<\/jats:p>","DOI":"10.2168\/lmcs-11(3:1)2015","type":"journal-article","created":{"date-parts":[[2016,11,21]],"date-time":"2016-11-21T13:46:02Z","timestamp":1479735962000},"source":"Crossref","is-referenced-by-count":0,"title":["On the system CL12 of computability logic"],"prefix":"10.46298","volume":"Volume 11, Issue 3","author":[{"given":"Giorgi","family":"Japaridze","sequence":"first","affiliation":[]}],"member":"25203","published-online":{"date-parts":[[2015,7,28]]},"reference":[{"key":"731:not-found"}],"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/lmcs.episciences.org\/1577\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/lmcs.episciences.org\/1577\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,4,11]],"date-time":"2023-04-11T20:06:57Z","timestamp":1681243617000},"score":1,"resource":{"primary":{"URL":"https:\/\/lmcs.episciences.org\/1577"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,7,28]]},"references-count":1,"URL":"https:\/\/doi.org\/10.2168\/lmcs-11(3:1)2015","relation":{"is-same-as":[{"id-type":"arxiv","id":"1203.0103","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.1203.0103","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"type":"electronic","value":"1860-5974"}],"subject":[],"published":{"date-parts":[[2015,7,28]]},"article-number":"1577"}}