{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,4]],"date-time":"2022-04-04T13:34:12Z","timestamp":1649079252533},"reference-count":0,"publisher":"World Scientific Pub Co Pte Lt","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Patt. Recogn. Artif. Intell."],"published-print":{"date-parts":[[1989,3]]},"abstract":"<jats:p> In propositional logic (zero order) a system of logical rules may be put under the form of a conjunction of disjunction, i.e. a \u201csatisfiability\u201d or SAT-problem. SAT is central to NP-complete problems. Any result obtained on SAT would have consequences for a lot of problems important in artificial intelligence. We deal with the question of the number N of solutions of SAT. Firstly, any system of SAT clauses may be transformed in a system of independent clauses by an exponential process; N may be computed exactly. Secondly, by a statistical approach, results are obtained showing that for a given SAT-instance, it should be possible to find an estimate of N with a margin of confidence in polynomial time. Thirdly, we demonstrate the usefulness of these ideas on large knowledge bases. <\/jats:p>","DOI":"10.1142\/s0218001489000061","type":"journal-article","created":{"date-parts":[[2004,11,29]],"date-time":"2004-11-29T02:14:37Z","timestamp":1101694477000},"page":"53-65","source":"Crossref","is-referenced-by-count":2,"title":["NUMBER OF SOLUTIONS OF SATISFIABILITY INSTANCES\u2014APPLICATIONS TO KNOWLEDGE BASES"],"prefix":"10.1142","volume":"03","author":[{"given":"J.C.","family":"SIMON","sequence":"first","affiliation":[{"name":"Universit\u00e9 Pierre et Marie Curie, LAFORIA 4, Place Jussieu 75230 Paris Cedex 05, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"O.","family":"DUBOIS","sequence":"additional","affiliation":[{"name":"Universit\u00e9 Pierre et Marie Curie, LAFORIA 4, Place Jussieu 75230 Paris Cedex 05, France"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,21]]},"container-title":["International Journal of Pattern Recognition and Artificial Intelligence"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218001489000061","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T02:14:14Z","timestamp":1565144054000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218001489000061"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1989,3]]},"references-count":0,"journal-issue":{"issue":"01","published-online":{"date-parts":[[2011,11,21]]},"published-print":{"date-parts":[[1989,3]]}},"alternative-id":["10.1142\/S0218001489000061"],"URL":"https:\/\/doi.org\/10.1142\/s0218001489000061","relation":{},"ISSN":["0218-0014","1793-6381"],"issn-type":[{"value":"0218-0014","type":"print"},{"value":"1793-6381","type":"electronic"}],"subject":[],"published":{"date-parts":[[1989,3]]}}}