{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,30]],"date-time":"2026-03-30T13:03:24Z","timestamp":1774875804332,"version":"3.50.1"},"reference-count":14,"publisher":"Wiley","issue":"4","license":[{"start":{"date-parts":[[2003,5,13]],"date-time":"2003-05-13T00:00:00Z","timestamp":1052784000000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[2003,7]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We introduce a probabilistic extension of propositional intuitionistic logic. The logic allows making statements such as <jats:italic>P<\/jats:italic><jats:sub>\u2265<jats:italic>s<\/jats:italic><\/jats:sub>\u03b1, with the intended meaning \u201cthe probability of truthfulness of <jats:italic>\u03b1<\/jats:italic> is at least <jats:italic>s<\/jats:italic>\u201d. We describe the corresponding class of models, which are Kripke models with a naturally arising notion of probability, and give a sound and complete infinitary axiomatic system. We prove that the logic is decidable.<\/jats:p>","DOI":"10.1002\/malq.200310044","type":"journal-article","created":{"date-parts":[[2003,5,16]],"date-time":"2003-05-16T17:32:56Z","timestamp":1053106376000},"page":"415-424","source":"Crossref","is-referenced-by-count":25,"title":["A probabilistic extension of intuitionistic logic"],"prefix":"10.1002","volume":"49","author":[{"given":"Zoran","family":"Markovi\u0107","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zoran","family":"Ognjanovi\u0107","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Miodrag","family":"Ra\u0161kovi\u0107","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2003,5,13]]},"reference":[{"key":"e_1_2_1_2_2","unstructured":"K. P. S.Bhaskara Rao andM.Bhaskara Rao Theory of Charges (Academic Press New York 1983)."},{"key":"e_1_2_1_3_2","first-page":"365","article-title":"A probabilistic validity measure in intuitionistic propositional logic","volume":"10","author":"Bori\u010di\u0107 B.","year":"1996","journal-title":"Mathematica Balkanica, n. s."},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1002\/malq.19970430410"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1016\/0890-5401(90)90060-U"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.1145\/174652.174658"},{"key":"e_1_2_1_7_2","unstructured":"M.Fitting Intuitionistic Logic Model Theory and Forcing (North\u2010Holland Publ. Comp. Amsterdam 1969)."},{"key":"e_1_2_1_8_2","unstructured":"S. C.Kleene Introduction to Metamathematics (North\u2010Holland Publ. Comp. Amsterdam 1971)."},{"key":"e_1_2_1_9_2","doi-asserted-by":"crossref","unstructured":"S.Kripke Semantical analysis of intuitionistic logic I. In: Formal Systems and Recursive Functions pp. 93\u2013130 (North\u2010Holland Publ. Comp. Amsterdam 1965).","DOI":"10.1016\/S0049-237X(08)71685-9"},{"key":"e_1_2_1_10_2","doi-asserted-by":"publisher","DOI":"10.1093\/logcom\/9.2.181"},{"key":"e_1_2_1_11_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-3975(98)00341-7"},{"issue":"67","key":"e_1_2_1_12_2","first-page":"1","article-title":"Classical logic with some probability operators","volume":"53","author":"Ra\u0161kovi\u0107 M.","year":"1993","journal-title":"Publications de l'InstitutMath\u00e9matique, Nouvelle S\u00e9rie, Beograd"},{"key":"e_1_2_1_13_2","unstructured":"C. A.Smorynski Applications of Kripke models. In: [13]."},{"key":"e_1_2_1_14_2","doi-asserted-by":"crossref","unstructured":"A. S.Troelstra(ed.) Metamathematical Investigation of Intuitionistic Arithmetic and Analysis. Lecture Notes inMathematics 344 (Springer\u2010Verlag Berlin 1973).","DOI":"10.1007\/BFb0066739"},{"key":"e_1_2_1_15_2","unstructured":"A. S.Troelstra andD.vanDalen Constructivism in Mathematics (North\u2010Holland Publ. Comp. Amsterdam 1988)."}],"container-title":["Mathematical Logic Quarterly"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmalq.200310044","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.200310044","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,11,17]],"date-time":"2023-11-17T15:11:55Z","timestamp":1700233915000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/malq.200310044"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,5,13]]},"references-count":14,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2003,7]]}},"alternative-id":["10.1002\/malq.200310044"],"URL":"https:\/\/doi.org\/10.1002\/malq.200310044","archive":["Portico"],"relation":{},"ISSN":["0942-5616","1521-3870"],"issn-type":[{"value":"0942-5616","type":"print"},{"value":"1521-3870","type":"electronic"}],"subject":[],"published":{"date-parts":[[2003,5,13]]}}}