{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:58:00Z","timestamp":1760245080955,"version":"3.41.0"},"reference-count":3,"publisher":"Association for Computing Machinery (ACM)","issue":"2","license":[{"start":{"date-parts":[[2006,4,1]],"date-time":"2006-04-01T00:00:00Z","timestamp":1143849600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Comput. Logic"],"published-print":{"date-parts":[[2006,4]]},"abstract":"<jats:p>\n            Computability logic is a formal theory of computational tasks and resources. Its formulas represent interactive computational problems, logical operators stand for operations on computational problems, and validity of a formula is understood as its being a scheme of problems that always have algorithmic solutions. The earlier article \u201cPropositional computability logic I\u201d proved soundness and completeness for the (in a sense) minimal nontrivial fragment\n            <jats:bold>CL1<\/jats:bold>\n            of computability logic. The present article extends that result to the significantly more expressive propositional system\n            <jats:bold>CL2<\/jats:bold>\n            . What makes\n            <jats:bold>CL2<\/jats:bold>\n            more expressive than\n            <jats:bold>CL1<\/jats:bold>\n            is the presence of two sorts of atoms in its language:\n            <jats:italic>elementary atoms<\/jats:italic>\n            , representing elementary computational problems (i.e. predicates), and\n            <jats:italic>general atoms<\/jats:italic>\n            , representing arbitrary computational problems.\n            <jats:bold>CL2<\/jats:bold>\n            conservatively extends\n            <jats:bold>CL1<\/jats:bold>\n            , with the latter being nothing but the general-atom-free fragment of the former.\n          <\/jats:p>","DOI":"10.1145\/1131313.1131319","type":"journal-article","created":{"date-parts":[[2006,7,25]],"date-time":"2006-07-25T14:14:26Z","timestamp":1153836866000},"page":"331-362","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":20,"title":["Propositional computability logic II"],"prefix":"10.1145","volume":"7","author":[{"given":"Giorgi","family":"Japaridze","sequence":"first","affiliation":[{"name":"Villanova University, Villanova, PA"}]}],"member":"320","published-online":{"date-parts":[[2006,4]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(92)90073-9"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0168-0072(03)00023-X"},{"key":"e_1_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.1145\/1131313.1131318"}],"container-title":["ACM Transactions on Computational Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1131313.1131319","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/1131313.1131319","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T15:06:16Z","timestamp":1750259176000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1131313.1131319"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,4]]},"references-count":3,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2006,4]]}},"alternative-id":["10.1145\/1131313.1131319"],"URL":"https:\/\/doi.org\/10.1145\/1131313.1131319","relation":{},"ISSN":["1529-3785","1557-945X"],"issn-type":[{"type":"print","value":"1529-3785"},{"type":"electronic","value":"1557-945X"}],"subject":[],"published":{"date-parts":[[2006,4]]},"assertion":[{"value":"2006-04-01","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}