{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,27]],"date-time":"2026-02-27T03:50:45Z","timestamp":1772164245672,"version":"3.50.1"},"reference-count":44,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2018,7,27]],"date-time":"2018-07-27T00:00:00Z","timestamp":1532649600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Appl Intell"],"published-print":{"date-parts":[[2019,1]]},"DOI":"10.1007\/s10489-018-1229-8","type":"journal-article","created":{"date-parts":[[2018,7,27]],"date-time":"2018-07-27T06:51:57Z","timestamp":1532674317000},"page":"79-102","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":32,"title":["Generalized logical operations among conditional events"],"prefix":"10.1007","volume":"49","author":[{"given":"Angelo","family":"Gilio","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0657-3833","authenticated-orcid":false,"given":"Giuseppe","family":"Sanfilippo","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2018,7,27]]},"reference":[{"key":"1229_CR1","doi-asserted-by":"publisher","first-page":"166","DOI":"10.1080\/00201746508601430","volume":"8","author":"EW Adams","year":"1965","unstructured":"Adams EW (1965) The logic of conditionals. Inquiry 8:166\u2013197","journal-title":"Inquiry"},{"key":"1229_CR2","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-015-7622-2","volume-title":"The logic of conditionals","author":"EW Adams","year":"1975","unstructured":"Adams EW (1975) The logic of conditionals. Reidel, Dordrecht"},{"key":"1229_CR3","doi-asserted-by":"publisher","first-page":"259","DOI":"10.1016\/S0004-3702(97)00012-X","volume":"92","author":"S Benferhat","year":"1997","unstructured":"Benferhat S, Dubois D, Prade H (1997) Nonmonotonic reasoning, conditional objects and possibility theory. Artif Intell 92:259\u2013276","journal-title":"Artif Intell"},{"issue":"2\u20133","key":"1229_CR4","doi-asserted-by":"publisher","first-page":"251","DOI":"10.1016\/S0888-613X(00)00038-4","volume":"24","author":"V Biazzo","year":"2000","unstructured":"Biazzo V, Gilio A (2000) A generalization of the fundamental theorem of de Finetti for imprecise conditional probability assessments. Int J Approx Reason 24(2\u20133):251\u2013272","journal-title":"Int J Approx Reason"},{"issue":"1\u20132","key":"1229_CR5","doi-asserted-by":"publisher","first-page":"35","DOI":"10.1007\/s10472-005-9005-y","volume":"45","author":"V Biazzo","year":"2005","unstructured":"Biazzo V, Gilio A, Lukasiewicz T, Sanfilippo G (2005) Probabilistic logic under coherence: complexity and algorithms. Ann Math Artif Intell 45(1\u20132):35\u201381","journal-title":"Ann Math Artif Intell"},{"key":"1229_CR6","unstructured":"Biazzo V, Gilio A, Sanfilippo G (2008) Generalized coherence and connection property of imprecise conditional previsions. In: Proceedings of the IPMU 2008, Malaga, Spain, June 22\u201327, pp 907\u2013914"},{"key":"1229_CR7","doi-asserted-by":"crossref","unstructured":"Biazzo V, Gilio A, Sanfilippo G (2012) Coherent conditional previsions and proper scoring rules. In: Advances in computational intelligence. IPMU 2012, volume 300 of CCIS. Springer, Berlin, pp 146\u2013156","DOI":"10.1007\/978-3-642-31724-8_16"},{"issue":"4","key":"1229_CR8","doi-asserted-by":"publisher","first-page":"597","DOI":"10.1017\/S0080456800032312","volume":"21","author":"G Boole","year":"1857","unstructured":"Boole G (1857) On the Application of the theory of probabilities to the question of the combination of testimonies or judgments. Trans R Soc Edinb 21(4):597\u2013653","journal-title":"Trans R Soc Edinb"},{"issue":"3","key":"1229_CR9","doi-asserted-by":"publisher","first-page":"187","DOI":"10.1016\/0020-0255(87)90023-5","volume":"42","author":"P Calabrese","year":"1987","unstructured":"Calabrese P (1987) An algebraic synthesis of the foundations of logic and probability. Inf Sci 42(3):187\u2013237","journal-title":"Inf Sci"},{"issue":"2","key":"1229_CR10","doi-asserted-by":"publisher","first-page":"132","DOI":"10.1198\/000313007X190943","volume":"61","author":"A Capotorti","year":"2007","unstructured":"Capotorti A, Lad F, Sanfilippo G (2007) Reassessing accuracy rates of median decisions. Am Stat 61 (2):132\u2013138","journal-title":"Am Stat"},{"key":"1229_CR11","doi-asserted-by":"crossref","unstructured":"Ciucci D, Dubois D (2012) Relationships between connectives in three-valued logics. In: Advances on computational intelligence, volume 297 of CCIS. Springer, Berlin, pp 633\u2013642","DOI":"10.1007\/978-3-642-31709-5_64"},{"issue":"3","key":"1229_CR12","doi-asserted-by":"publisher","first-page":"118","DOI":"10.1007\/s005000050060","volume":"3","author":"G Coletti","year":"1999","unstructured":"Coletti G, Scozzafava R (1999) Conditioning and inference in intelligent systems. Soft Comput 3(3):118\u2013130","journal-title":"Soft Comput"},{"key":"1229_CR13","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-010-0474-9","volume-title":"Probabilistic logic in a coherent setting","author":"G Coletti","year":"2002","unstructured":"Coletti G, Scozzafava R (2002) Probabilistic logic in a coherent setting. Kluwer, Dordrecht"},{"key":"1229_CR14","doi-asserted-by":"crossref","unstructured":"Coletti G, Scozzafava R, Vantaggi B (2013) Coherent conditional probability, fuzzy inclusion and default rules. In: Yager RR, Abbasov A M, Reformat M Z, Shahbazova S N (eds) Soft computing: state of the art theory and novel applications. Springer, Heidelberg, pp 193\u2013208","DOI":"10.1007\/978-3-642-34922-5_14"},{"issue":"4","key":"1229_CR15","doi-asserted-by":"publisher","first-page":"863","DOI":"10.1515\/ms-2015-0060","volume":"65","author":"G Coletti","year":"2015","unstructured":"Coletti G, Scozzafava R, Vantaggi B (2015) Possibilistic and probabilistic logic under coherence: default reasoning and System P. Math Slovaca 65(4):863\u2013890","journal-title":"Math Slovaca"},{"key":"1229_CR16","doi-asserted-by":"crossref","unstructured":"de Finetti B (1936) La logique de la probabilit\u00e9. In: Actes du Congr\u00e8s International de Philosophie Scientifique, Paris, 1935. Hermann et C.ie, Paris, pp IV 1\u2013IV 9","DOI":"10.5840\/icus11936454"},{"key":"1229_CR17","doi-asserted-by":"publisher","first-page":"235","DOI":"10.1093\/mind\/104.414.235","volume":"104","author":"D Edgington","year":"1995","unstructured":"Edgington D (1995) On conditionals. Mind 104:235\u2013329","journal-title":"Mind"},{"key":"1229_CR18","doi-asserted-by":"publisher","first-page":"5","DOI":"10.1023\/A:1014422615720","volume":"34","author":"A Gilio","year":"2002","unstructured":"Gilio A (2002) Probabilistic reasoning under coherence in System P. Ann Math Artif Intell 34:5\u201334","journal-title":"Ann Math Artif Intell"},{"issue":"3","key":"1229_CR19","doi-asserted-by":"publisher","first-page":"413","DOI":"10.1016\/j.ijar.2011.08.004","volume":"53","author":"A Gilio","year":"2012","unstructured":"Gilio A (2012) Generalizing inference rules in a coherence-based probabilistic default reasoning. Int J Approx Reason 53(3):413\u2013434","journal-title":"Int J Approx Reason"},{"key":"1229_CR20","doi-asserted-by":"crossref","unstructured":"Gilio A, Sanfilippo G (2010) Quasi conjunction and p-entailment in nonmonotonic reasoning. In: Combining soft computing and statistical methods in data analysis, volume 77 of Advances in intelligent and soft computing. Springer, Berlin, pp 321\u2013328","DOI":"10.1007\/978-3-642-14746-3_40"},{"key":"1229_CR21","unstructured":"Gilio A, Sanfilippo G (2011) Coherent conditional probabilities and proper scoring rules. In: Proceedings of ISIPTA\u201911. Innsbruck, pp 189\u2013198"},{"key":"#cr-split#-1229_CR22.1","doi-asserted-by":"crossref","unstructured":"Gilio A, Sanfilippo G (2013) Conditional random quantities and iterated conditioning in the setting of coherence. In: van der Gaag L C","DOI":"10.1007\/978-3-642-39091-3_19"},{"key":"#cr-split#-1229_CR22.2","unstructured":"(ed) Symbolic and Quantitative Approaches to Reasoning with Uncertainty, ECSQARU 2013, volume 7958 of LNCS. Springer, Berlin, pp 218-229"},{"key":"1229_CR23","doi-asserted-by":"crossref","unstructured":"Gilio A, Sanfilippo G (2013) Conjunction, disjunction and iterated conditioning of conditional events. In: Synergies of soft computing and statistics for intelligent data analysis, volume 190 of AISC. Springer, Berlin, pp 399\u2013407","DOI":"10.1007\/978-3-642-33042-1_43"},{"issue":"4","key":"1229_CR24","doi-asserted-by":"publisher","first-page":"513","DOI":"10.1016\/j.ijar.2012.11.001","volume":"54","author":"A Gilio","year":"2013","unstructured":"Gilio A, Sanfilippo G (2013) Probabilistic entailment in the setting of coherence: the role of quasi conjunction and inclusion relation. Int J Approx Reason 54(4):513\u2013525","journal-title":"Int J Approx Reason"},{"key":"1229_CR25","doi-asserted-by":"publisher","first-page":"146","DOI":"10.1016\/j.ins.2013.03.019","volume":"245","author":"A Gilio","year":"2013","unstructured":"Gilio A, Sanfilippo G (2013) Quasi conjunction, quasi disjunction, t-norms and t-conorms: probabilistic aspects. Inf Sci 245:146\u2013 167","journal-title":"Inf Sci"},{"issue":"4","key":"1229_CR26","doi-asserted-by":"publisher","first-page":"709","DOI":"10.1007\/s11225-013-9511-6","volume":"102","author":"A Gilio","year":"2014","unstructured":"Gilio A, Sanfilippo G (2014) Conditional random quantities and compounds of conditionals. Stud Log 102 (4):709\u2013729","journal-title":"Stud Log"},{"key":"1229_CR27","doi-asserted-by":"crossref","unstructured":"Gilio A, Sanfilippo G (2017) Conjunction and disjunction among conditional events. In: Benferhat S, Tabia K, Ali M (eds) IEA\/AIE 2017, Part II, volume 10351 of LNCS. Springer, Cham, pp 85\u201396","DOI":"10.1007\/978-3-319-60045-1_11"},{"key":"1229_CR28","doi-asserted-by":"publisher","first-page":"46","DOI":"10.1016\/j.jal.2015.09.012","volume":"14","author":"A Gilio","year":"2016","unstructured":"Gilio A, Pfeifer N, Sanfilippo G (2016) Transitivity in coherence-based probability logic. J Appl Log 14:46\u201364","journal-title":"J Appl Log"},{"key":"1229_CR29","doi-asserted-by":"crossref","unstructured":"Gilio A, Over D, Pfeifer N, Sanfilippo G (2017) Centering and compound conditionals under coherence. In: Soft methods for data science, volume 456 of AISC. Springer, Berlin, pp 253\u2013260","DOI":"10.1007\/978-3-319-42972-4_32"},{"key":"1229_CR30","unstructured":"Gilio A, Pfeifer N, Sanfilippo G Probabilistic entailment and iterated conditionals, submitted. Available on arXiv: 1804.06187v1"},{"key":"1229_CR31","unstructured":"Goodman IR, Nguyen HT (1988) Conditional objects and the modeling of uncertainties. In: Gupta M M, Yamakawa T (eds) Fuzzy computing. North-Holland, pp 119\u2013138"},{"key":"1229_CR32","doi-asserted-by":"publisher","DOI":"10.21236\/ADA241568","volume-title":"Conditional inference and logic for intelligent systems: a theory of measure-free conditioning","author":"IR Goodman","year":"1991","unstructured":"Goodman IR, Nguyen HT, Walker EA (1991) Conditional inference and logic for intelligent systems: a theory of measure-free conditioning. North-Holland, Amsterdam"},{"key":"1229_CR33","volume-title":"Sentential probability logic. Origins, development, current status, and technical applications","author":"T Hailperin","year":"1996","unstructured":"Hailperin T (1996) Sentential probability logic. Origins, development, current status, and technical applications. Lehigh University Press, Bethlehem"},{"key":"1229_CR34","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s10992-008-9088-0","volume":"38","author":"S Kaufmann","year":"2009","unstructured":"Kaufmann S (2009) Conditionals right and left: probabilities for the whole family. J Philos Log 38:1\u201353","journal-title":"J Philos Log"},{"key":"1229_CR35","volume-title":"Operational subjective statistical methods: a mathematical, philosophical, and historical introduction","author":"F Lad","year":"1996","unstructured":"Lad F (1996) Operational subjective statistical methods: a mathematical, philosophical, and historical introduction. Wiley, New York"},{"issue":"1","key":"1229_CR36","doi-asserted-by":"publisher","first-page":"13","DOI":"10.1063\/1.4759585","volume":"1490","author":"F Lad","year":"2012","unstructured":"Lad F, Sanfilippo G, Agr\u00f3 G (2012) Completing the logarithmic scoring rule for assessing probability distributions. AIP Conf Proc 1490(1):13\u201330","journal-title":"AIP Conf Proc"},{"issue":"1","key":"1229_CR37","doi-asserted-by":"publisher","first-page":"40","DOI":"10.1214\/14-STS430","volume":"30","author":"F Lad","year":"2015","unstructured":"Lad F, Sanfilippo G, Agr\u00f3 G (2015) Extropy: complementary dual of entropy. Stat Sci 30(1):40\u201358","journal-title":"Stat Sci"},{"issue":"4","key":"1229_CR38","doi-asserted-by":"publisher","first-page":"485","DOI":"10.2307\/2185116","volume":"98","author":"V McGee","year":"1989","unstructured":"McGee V (1989) Conditional probabilities and compounds of conditionals. Philos Rev 98(4):485\u2013541","journal-title":"Philos Rev"},{"issue":"2","key":"1229_CR39","doi-asserted-by":"publisher","first-page":"195","DOI":"10.1093\/bjps\/48.2.195","volume":"48","author":"P Milne","year":"1997","unstructured":"Milne P (1997) Bruno de Finetti and the logic of conditional events. Br J Philos Sci 48(2):195\u2013232","journal-title":"Br J Philos Sci"},{"key":"1229_CR40","doi-asserted-by":"publisher","first-page":"160","DOI":"10.1016\/j.ijar.2016.11.014","volume":"81","author":"D Petturiti","year":"2017","unstructured":"Petturiti D, Vantaggi B (2017) Envelopes of conditional probabilities extending a strategy and a prior probability. Int J Approx Reason 81:160\u2013182","journal-title":"Int J Approx Reason"},{"key":"1229_CR41","doi-asserted-by":"crossref","unstructured":"Sanfilippo G, Pfeifer N, Gilio A (2017) Generalized probabilistic modus ponens. In: Antonucci A, Cholvy L, Papini O (eds) Symbolic and Quantitative Approaches to Reasoning with Uncertainty, ECSQARU 2017, volume 10369 of LNCS. Springer, Berlin, pp 480\u2013490","DOI":"10.1007\/978-3-319-61581-3_43"},{"issue":"Supplement C","key":"1229_CR42","doi-asserted-by":"publisher","first-page":"103","DOI":"10.1016\/j.ijar.2017.10.027","volume":"93","author":"G Sanfilippo","year":"2018","unstructured":"Sanfilippo G, Pfeifer N, Over DE, Gilio A (2018) Probabilistic inferences from conjoined to iterated conditionals. Int J Approx Reason 93(Supplement C):103\u2013118","journal-title":"Int J Approx Reason"},{"issue":"1","key":"1229_CR43","doi-asserted-by":"publisher","first-page":"127","DOI":"10.1007\/s10506-017-9199-4","volume":"25","author":"B Verheij","year":"2017","unstructured":"Verheij B (2017) Proof with and without probabilities. Artif Intell Law 25(1):127\u2013154","journal-title":"Artif Intell Law"}],"container-title":["Applied Intelligence"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10489-018-1229-8\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10489-018-1229-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10489-018-1229-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,7,6]],"date-time":"2025-07-06T02:11:21Z","timestamp":1751767881000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10489-018-1229-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,7,27]]},"references-count":44,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2019,1]]}},"alternative-id":["1229"],"URL":"https:\/\/doi.org\/10.1007\/s10489-018-1229-8","relation":{},"ISSN":["0924-669X","1573-7497"],"issn-type":[{"value":"0924-669X","type":"print"},{"value":"1573-7497","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,7,27]]},"assertion":[{"value":"27 July 2018","order":1,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}