{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,3]],"date-time":"2026-07-03T03:18:17Z","timestamp":1783048697147,"version":"3.54.6"},"reference-count":49,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2020,11,9]],"date-time":"2020-11-09T00:00:00Z","timestamp":1604880000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2020,11,9]],"date-time":"2020-11-09T00:00:00Z","timestamp":1604880000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100001821","name":"Vienna Science and Technology Fund","doi-asserted-by":"publisher","award":["MA16-28"],"award-info":[{"award-number":["MA16-28"]}],"id":[{"id":"10.13039\/501100001821","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Artif Intell Law"],"published-print":{"date-parts":[[2021,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Over the course of more than two millennia the philosophical school of M\u012bm\u0101\u1e43s\u0101 has thoroughly analyzed normative statements. In this paper we approach a formalization of the deontic system which is applied but never explicitly discussed in M\u012bm\u0101\u1e43s\u0101 to resolve conflicts between deontic statements by giving preference to the more specific ones. We first extend with prohibitions and recommendations the non-normal deontic logic extracted in Ciabattoni et al. (in: TABLEAUX 2015, volume 9323 of LNCS, Springer, 2015) from M\u012bm\u0101\u1e43s\u0101 texts, obtaining a multimodal dyadic version of the deontic logic<jats:inline-formula><jats:alternatives><jats:tex-math>$$\\mathsf {MD}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>MD<\/mml:mi><\/mml:math><\/jats:alternatives><\/jats:inline-formula>. Sequent calculus is then used to close a set of prima-facie injunctions under a restricted form of monotonicity, using specificity to avoid conflicts. We establish decidability and complexity results, and investigate the potential use of the resulting system for M\u012bm\u0101\u1e43s\u0101 philosophy and, more generally, for the formal interpretation of normative statements.<\/jats:p>","DOI":"10.1007\/s10506-020-09278-w","type":"journal-article","created":{"date-parts":[[2020,11,9]],"date-time":"2020-11-09T07:05:49Z","timestamp":1604905549000},"page":"351-394","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["M\u012bm\u0101\u1e43s\u0101 deontic reasoning using specificity: a proof theoretic approach"],"prefix":"10.1007","volume":"29","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5335-1838","authenticated-orcid":false,"given":"Bj\u00f6rn","family":"Lellmann","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Francesca","family":"Gulisano","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6947-8772","authenticated-orcid":false,"given":"Agata","family":"Ciabattoni","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2020,11,9]]},"reference":[{"issue":"2\u20133","key":"9278_CR1","doi-asserted-by":"publisher","first-page":"117","DOI":"10.1007\/s10506-011-9109-0","volume":"19","author":"M Abraham","year":"2011","unstructured":"Abraham M, Gabbay DM, Schild U (2011) Obligations and prohibitions in Talmudic deontic logic. Artif Intell Law 19(2\u20133):117\u2013148","journal-title":"Artif Intell Law"},{"key":"9278_CR2","doi-asserted-by":"crossref","unstructured":"Bartolini C, Lenzini G, Santos C (2018) An agile approach to validate a formal representation of the GDPR. In: Kazuhiro K, Maki S, Koji M, Ken S (eds) New frontiers in artificial intelligence. JSAI-isAI\u00a02018, volume 11717 of LNCS. Springer, pp 160\u2013176","DOI":"10.1007\/978-3-030-31605-1_13"},{"key":"9278_CR3","volume-title":"Legal language and legal writing","author":"KL Bathia","year":"2010","unstructured":"Bathia KL (2010) Legal language and legal writing. Universal Law Publishing Co, New Delhi"},{"key":"9278_CR4","unstructured":"Batsakis S, Baryannis G, Governatori G, Tachmazidis I, Antoniou G (2018) Legal representation and reasoning in practice: a critical comparison. In: Legal knowledge and information\u2014JURIX\u00a02018. IOS Press, pp 31\u201340"},{"key":"9278_CR5","unstructured":"Boella G, van\u00a0der Torre LWN (2004) Regulative and constitutive norms in normative multiagent systems. In: Didier D, Christopher AW, Mary-Anne W (eds) Principles of knowledge representation and reasoning: proceedings of the ninth international conference (KR2004), June 2\u20135, 2004. AAAI Press, Whistler, Canada, pp 255\u2013266"},{"issue":"2","key":"9278_CR6","doi-asserted-by":"publisher","first-page":"226","DOI":"10.1145\/505372.505374","volume":"3","author":"PA Bonatti","year":"2002","unstructured":"Bonatti PA, Olivetti N (2002) Sequent calculi for propositional nonmonotonic logics. ACM Trans Comput Log 3(2):226\u2013278","journal-title":"ACM Trans Comput Log"},{"issue":"2","key":"9278_CR7","first-page":"203","volume":"130","author":"D Brick","year":"2010","unstructured":"Brick D (2010) The Dharma\u015b\u0101stric debate on widow-burning. J Am Orient Soc 130(2):203\u2013223","journal-title":"J Am Orient Soc"},{"key":"9278_CR8","unstructured":"Calegari R, Contissa G, Lagioia F, Omicini A, Sartor G (2019) Defeasible systems in legal reasoning: a comparative assessment. In: Legal knowledge and information systems. IOS Press, pp 169\u2013174"},{"issue":"1","key":"9278_CR9","doi-asserted-by":"publisher","first-page":"114","DOI":"10.1145\/322234.322243","volume":"28","author":"AK Chandra","year":"1981","unstructured":"Chandra AK, Kozen DC, Stockmeyer LJ (1981) Alternation. J Assoc Comput Mach 28(1):114\u2013133","journal-title":"J Assoc Comput Mach"},{"key":"9278_CR10","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511621192","volume-title":"Modal logic","author":"BF Chellas","year":"1980","unstructured":"Chellas BF (1980) Modal logic. Cambridge University Press, Cambridge"},{"key":"9278_CR11","doi-asserted-by":"crossref","unstructured":"Ciabattoni A, Freschi E, Genco FA, Lellmann B (2015) M\u012bm\u0101ms\u0101 deontic logic: proof theory and applications. In: TABLEAUX 2015, volume 9323 of LNCS. Springer, pp 323\u2013338","DOI":"10.1007\/978-3-319-24312-2_22"},{"key":"9278_CR12","first-page":"47","volume":"2","author":"A Ciabattoni","year":"2017","unstructured":"Ciabattoni A, Freschi E, Genco FA, Lellmann B (2017) Understanding prescriptive texts: rules and logic as elaborated by the M\u012bm\u0101ms\u0101 school. Online J World Philos 2:47\u201366","journal-title":"Online J World Philos"},{"key":"9278_CR13","unstructured":"Ciabattoni A, Gulisano F, Lellmann B (2018) Resolving conflicting obligations in M\u012bm\u0101ms\u0101: a sequent-based approach. In: Jan B, Cleo C, Shyam N, Gabriella P (eds) DEON\u00a02018 proceedings. College Publications, pp 91\u2013109"},{"issue":"1","key":"9278_CR14","doi-asserted-by":"publisher","first-page":"301","DOI":"10.1016\/S0004-3702(96)00045-8","volume":"90","author":"JP Delgrande","year":"1997","unstructured":"Delgrande JP, Schaub TH (1997) Compiling specificity into approaches to nonmonotonic reasoning. Artif Intell 90(1):301\u2013348","journal-title":"Artif Intell"},{"key":"9278_CR15","doi-asserted-by":"crossref","unstructured":"Freschi E (2012) Duty, language and exegesis in Pr\u0101bh\u0101kara M\u012bm\u0101ms\u0101: including an edition and translation of R\u0101m\u0101nuj\u0101c\u0101rya\u2019s Tantrarahasya, \u015a\u0101straprameyapariccheda. Number\u00a017 in Jerusalem studies in religion and culture. Brill, Leiden","DOI":"10.1163\/9789004230248"},{"key":"9278_CR16","doi-asserted-by":"publisher","first-page":"148","DOI":"10.4324\/9781315666792-15","volume-title":"History of Indian philosophy","author":"E Freschi","year":"2017","unstructured":"Freschi E (2017) M\u012bm\u0101ms\u0101. In: Bilimoria P (ed) History of Indian philosophy. Routledge, London, pp 148\u2013156"},{"key":"9278_CR17","doi-asserted-by":"publisher","first-page":"323","DOI":"10.1080\/01445340.2019.1615366","volume":"40","author":"E Freschi","year":"2019","unstructured":"Freschi E, Ollett A, Pascucci M (2019) Duty and sacrifice: a logical analysis of the M\u012bm\u0101ms\u0101 theory of vedic injunctions. Hist Philos Log 40:323\u2013354","journal-title":"Hist Philos Log"},{"key":"9278_CR18","doi-asserted-by":"crossref","unstructured":"Gabbay DM (1985) Theoretical foundations for non-monotonic reasoning in expert systems. In: Logics and models of concurrent systems. Springer, pp 439\u2013457","DOI":"10.1007\/978-3-642-82453-1_15"},{"key":"9278_CR19","unstructured":"Goble L (2013) Prima facie norms, normative conflicts, and dilemmas. In: Gabbay D, Horty J, Parent X, van der Meyden R, van der Torre L (eds) Handbook of deontic logic and normative systems. College Publications, pp 241\u2013351. http:\/\/www.collegepublications.co.uk\/handbooks\/?00001"},{"issue":"1","key":"9278_CR20","first-page":"13","volume":"6","author":"L Goble","year":"2019","unstructured":"Goble L (2019) Axioms for Hansson\u2019s dyadic deontic logics. Filosofiska Notiser 6(1):13\u201361","journal-title":"Filosofiska Notiser"},{"key":"9278_CR21","doi-asserted-by":"crossref","unstructured":"Governatori G, Rotolo A (2004) Defeasible logic: agency, intention and obligation. In: Alessio L, Donald N (eds) Deontic logic in computer science, volume 3065 of LNCS. Springer, pp 114\u2013128","DOI":"10.1007\/978-3-540-25927-5_8"},{"key":"9278_CR22","first-page":"193","volume":"4","author":"G Governatori","year":"2006","unstructured":"Governatori G, Rotolo A (2006) Logic of violations: a Gentzen system for reasoning with contrary-to-duty obligations. Australas J Log 4:193\u2013215","journal-title":"Australas J Log"},{"key":"9278_CR23","doi-asserted-by":"publisher","first-page":"221","DOI":"10.1023\/B:ARTI.0000046011.13621.08","volume":"11","author":"J Hage","year":"2003","unstructured":"Hage J (2003) Law and defeasibility. Artif Intell Law 11:221\u2013243","journal-title":"Artif Intell Law"},{"issue":"4","key":"9278_CR24","doi-asserted-by":"publisher","first-page":"373","DOI":"10.2307\/2214372","volume":"3","author":"B Hansson","year":"1969","unstructured":"Hansson B (1969) An analysis of some deontic logics. No\u00fbs 3(4):373\u2013398","journal-title":"No\u00fbs"},{"issue":"1\u20132","key":"9278_CR25","doi-asserted-by":"publisher","first-page":"69","DOI":"10.1007\/BF01531262","volume":"9","author":"JF Horty","year":"1993","unstructured":"Horty JF (1993) Deontic logic as founded on nonmonotonic logic. Ann Math Artif Intell 9(1\u20132):69\u201391","journal-title":"Ann Math Artif Intell"},{"key":"9278_CR26","doi-asserted-by":"publisher","DOI":"10.1093\/acprof:oso\/9780199744077.001.0001","volume-title":"Reasons as defaults","author":"JF Horty","year":"2012","unstructured":"Horty JF (2012) Reasons as defaults. Oxford University Press, Oxford"},{"key":"9278_CR27","unstructured":"Huisjes CH (1981) Norms and logic. Thesis. University of Groningen"},{"key":"9278_CR28","doi-asserted-by":"publisher","first-page":"45","DOI":"10.1007\/BF00118478","volume":"1","author":"AJI Jones","year":"1992","unstructured":"Jones AJI, Sergot M (1992) Deontic logic in the representation of law: towards a methodology. Artif Intell Law 1:45\u201364","journal-title":"Artif Intell Law"},{"key":"9278_CR29","first-page":"615","volume-title":"P\u016brvam\u012bm\u012bm\u0101ms\u0101 from an interdisciplinary point of view, volume II of history of science, philosophy, and culture in Indian civilization: life, thought, and culture in India","author":"M Katju","year":"2006","unstructured":"Katju M (2006) The m\u012bm\u0101ms\u0101 principles of interpretation. In: Krishnacharya TP (ed) P\u016brvam\u012bm\u012bm\u0101ms\u0101 from an interdisciplinary point of view, volume II of history of science, philosophy, and culture in Indian civilization: life, thought, and culture in India. Munshiram Manoharlal Publishers Pvt. Ltd., New Delhi, pp 615\u2013625"},{"key":"9278_CR30","doi-asserted-by":"crossref","unstructured":"Lellmann B, Pattinson D (2013) Constructing cut free sequent systems with context restrictions based on classical or intuitionistic logic. In: ICLA 2013, volume 7750 of LNCS. Springer, pp 148\u2013160","DOI":"10.1007\/978-3-642-36039-8_14"},{"key":"9278_CR31","doi-asserted-by":"publisher","unstructured":"Libal T, Norotn\u00e1 T (2020) Towards automating inconsistency checking of legal texts. In: Jusletter IT: IRIS\u00a02020. Editions Weblaw. https:\/\/doi.org\/10.38023\/336778dc-530a-48ac-95da-336a8bd40995","DOI":"10.38023\/336778dc-530a-48ac-95da-336a8bd40995"},{"key":"9278_CR32","doi-asserted-by":"crossref","unstructured":"Libal T, Pascucci M (2019) Automated reasoning in normative detachment structures with ideal conditions. In: ICAIL\u00a02019. ACM, pp 63\u201372","DOI":"10.1145\/3322640.3326707"},{"key":"9278_CR33","doi-asserted-by":"publisher","unstructured":"Libal T, Steen A (2020) NAI: towards transparent and usable semi-automated legal analysis. In: Jusletter IT: IRIS\u00a02020. Editions Weblaw, pp 265\u2013272. https:\/\/doi.org\/10.38023\/2eb63e02-f13e-45f5-9a7b-d7fe55e42c6c","DOI":"10.38023\/2eb63e02-f13e-45f5-9a7b-d7fe55e42c6c"},{"key":"9278_CR34","doi-asserted-by":"publisher","first-page":"199","DOI":"10.1016\/0004-3702(91)90061-N","volume":"48","author":"D Makinson","year":"1991","unstructured":"Makinson D, Schlechta K (1991) Floating conclusions and zombie paths: two deep difficulties in the \u2019directly skeptical\u2019 approach to inheritance nets. Artif Intell 48:199\u2013209","journal-title":"Artif Intell"},{"issue":"4","key":"9278_CR35","doi-asserted-by":"publisher","first-page":"383","DOI":"10.1023\/A:1004748624537","volume":"29","author":"D Makinson","year":"2000","unstructured":"Makinson D, van der Torre L (2000) Input\/output logics. J Philos Log 29(4):383\u2013408","journal-title":"J Philos Log"},{"key":"9278_CR36","doi-asserted-by":"publisher","first-page":"287","DOI":"10.1007\/978-94-015-8851-5_12","volume-title":"Defeasible deontic logic","author":"D Nute","year":"1997","unstructured":"Nute D (1997) Apparent obligation. In: Nute D (ed) Defeasible deontic logic. Springer, Dordrecht, pp 287\u2013315"},{"key":"9278_CR37","doi-asserted-by":"crossref","unstructured":"Nute D (2003) Defeasible logic. In: INAP\u00a02001, volume 2543 of LNCS. Springer, pp 151\u2013169","DOI":"10.1007\/3-540-36524-9_13"},{"key":"9278_CR38","doi-asserted-by":"crossref","unstructured":"Prakken H, Sartor G (1999) A system for defeasible argumentation, with defeasible priorities. In: Wooldridge MJ, Veloso MM (eds) Artificial intelligence today: recent trends and developments, volume 1600 of lecture notes in computer science. Springer, pp 365\u2013379","DOI":"10.1007\/3-540-48317-9_15"},{"key":"9278_CR39","doi-asserted-by":"publisher","first-page":"223","DOI":"10.1007\/978-94-015-8851-5_10","volume-title":"Defeasible deontic logic","author":"H Prakken","year":"1997","unstructured":"Prakken H, Sergot M (1997) Dyadic deontic logic and contrary-to-duty obligations. In: Nute D (ed) Defeasible deontic logic. Kluwer, Dordrecht, pp 223\u2013262"},{"key":"9278_CR40","doi-asserted-by":"crossref","unstructured":"Royakkers LMM (1998) Extending deontic logic for the formalisation of legal rules, volume\u00a036 of law and philosohpy library. Springer","DOI":"10.1007\/978-94-015-9099-0"},{"key":"#cr-split#-9278_CR41.1","unstructured":"Stra\u00dfer C, Antonelli GA (2016) Non-monotonic logic. In: Zalta EN"},{"key":"#cr-split#-9278_CR41.2","unstructured":"(ed) The Stanford encyclopedia of philosophy (Fall 2016 Edition). Stanford University, pp 1-62. https:\/\/plato.stanford.edu\/archives\/fall2016\/entries\/logic-nonmonotonic\/"},{"issue":"3","key":"9278_CR42","doi-asserted-by":"publisher","first-page":"381","DOI":"10.1093\/logcom\/exv050","volume":"29","author":"C Stra\u00dfer","year":"2019","unstructured":"Stra\u00dfer C, Arieli O (2019) Normative reasoning by sequent-based argumentation. J Log Comput 29(3):381\u2013415","journal-title":"J Log Comput"},{"key":"9278_CR43","doi-asserted-by":"publisher","first-page":"143","DOI":"10.1353\/pew.2004.0009","volume":"54","author":"J Taber","year":"2004","unstructured":"Taber J (2004) Is Indian logic nonmonotonic? Philos East West 54:143\u2013170","journal-title":"Philos East West"},{"key":"9278_CR44","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781139168717","volume-title":"Basic proof theory","author":"AS Troelstra","year":"2000","unstructured":"Troelstra AS, Schwichtenberg H (2000) Basic proof theory, 2nd edn. Cambridge University Press, Cambridge","edition":"2"},{"key":"9278_CR45","unstructured":"van\u00a0der Torre LWN (1994) Violated obligations in a defeasible deontic logic. In: ECAI\u00a094. Wiley, pp 371\u2013375"},{"issue":"3\u20134","key":"9278_CR46","doi-asserted-by":"publisher","first-page":"417","DOI":"10.1007\/BF00255570","volume":"1","author":"BC van Fraassen","year":"1972","unstructured":"van Fraassen BC (1972) The logic of conditional obligation. J Philos Log 1(3\u20134):417\u2013438","journal-title":"J Philos Log"},{"key":"9278_CR47","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1163\/24689300-00101017","volume":"1","author":"GH von Wright","year":"1964","unstructured":"von Wright GH (1964) A new system of deontic logic. Dan Yearb Philos 1:173\u2013182","journal-title":"Dan Yearb Philos"},{"key":"9278_CR48","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1163\/24689300-00201008","volume":"2","author":"GH von Wright","year":"1965","unstructured":"von Wright GH (1965) A correction to a new system of deontic logic. Dan Yearb Philos 2:103\u2013107","journal-title":"Dan Yearb Philos"}],"container-title":["Artificial Intelligence and Law"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10506-020-09278-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10506-020-09278-w\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10506-020-09278-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,11,27]],"date-time":"2022-11-27T08:37:15Z","timestamp":1669538235000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10506-020-09278-w"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,11,9]]},"references-count":49,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2021,9]]}},"alternative-id":["9278"],"URL":"https:\/\/doi.org\/10.1007\/s10506-020-09278-w","relation":{},"ISSN":["0924-8463","1572-8382"],"issn-type":[{"value":"0924-8463","type":"print"},{"value":"1572-8382","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,11,9]]},"assertion":[{"value":"13 October 2020","order":1,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"9 November 2020","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}