{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,29]],"date-time":"2022-03-29T18:28:54Z","timestamp":1648578534322},"reference-count":0,"publisher":"World Scientific Pub Co Pte Lt","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Unc. Fuzz. Knowl. Based Syst."],"published-print":{"date-parts":[[1995,9]]},"abstract":"<jats:p> This paper addresses the mathematical modeling of information as originally expressed in natural language in conditional form. A number of different conditional event algebras\u2014all avoiding the Lewis triviality result\u2014are briefly surveyed, including the main body of those proposed previously, classified as Type I, and the newly expanded Type II product space approach (PS) originally independently offered by Van Fraasen. The issue of higher order conditionals and triviality is also discussed. <\/jats:p><jats:p> In addition, this work considers two basic results of McGee: Firstly, this paper provides a new general procedure (M) which specializes to that result of McGee, where in effect, the probability evaluations of logical compounds of conditionals in the PS approach are independently derived from a fair standard betting scheme, though McGee does not obtain any explicit conditional event algebra underpinning for these evaluations. The new procedure, which can act upon any Type I conditional event algebra, is based, in part, upon decision theory principles, and in part, upon a fine-tuned evaluation of the third or indeterminate values of the three-valued logic form of Type I conditionals. It is shown that McGee\u2019s derivation is equivalent to M acting upon the Type I conditional event algebra called GNW in the literature\u2014or equivalently the min, max, 1-() conjunctive, disjunctive, negation fragment of Lukasiewicz\u2019 three-valued logic. On the other hand, it is shown that the action of M upon another Type I conditional event algebra called SAC in the literature\u2014equivalent to a corresponding fragment of a three-valued logic originally proposed by Sobocinski\u2014leads back to the same conditional event algebra. Secondly, this paper provides a new characterization of PS , corresponding to McGee\u2019s second result, and which, unlike McGee, does not assume\u2014nor is compatible, in general, with\u2014the import-export rule. Among other topics discussed, are conditional random variables, deduction and non-monotonic logic applications. <\/jats:p>","DOI":"10.1142\/s0218488595000165","type":"journal-article","created":{"date-parts":[[2004,11,10]],"date-time":"2004-11-10T11:14:37Z","timestamp":1100085277000},"page":"247-339","source":"Crossref","is-referenced-by-count":25,"title":["MATHEMATICAL FOUNDATIONS OF CONDITIONALS AND THEIR PROBABILISTIC ASSIGNMENTS"],"prefix":"10.1142","volume":"03","author":[{"given":"I.R.","family":"GOODMAN","sequence":"first","affiliation":[{"name":"Code 4221, NCCOSC RDTE DIV (NRaD) San Diego, CA 92152\u20137463, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"H.T.","family":"NGUYEN","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, New Mexico State University, Las Cruces, NM 88003\u20138001, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,21]]},"container-title":["International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218488595000165","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T02:53:34Z","timestamp":1565146414000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218488595000165"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1995,9]]},"references-count":0,"journal-issue":{"issue":"03","published-online":{"date-parts":[[2011,11,21]]},"published-print":{"date-parts":[[1995,9]]}},"alternative-id":["10.1142\/S0218488595000165"],"URL":"https:\/\/doi.org\/10.1142\/s0218488595000165","relation":{},"ISSN":["0218-4885","1793-6411"],"issn-type":[{"value":"0218-4885","type":"print"},{"value":"1793-6411","type":"electronic"}],"subject":[],"published":{"date-parts":[[1995,9]]}}}