{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,29]],"date-time":"2022-03-29T09:54:47Z","timestamp":1648547687037},"reference-count":24,"publisher":"Cambridge University Press (CUP)","issue":"4-5","license":[{"start":{"date-parts":[[2012,9,5]],"date-time":"2012-09-05T00:00:00Z","timestamp":1346803200000},"content-version":"unspecified","delay-in-days":66,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Theory and Practice of Logic Programming"],"published-print":{"date-parts":[[2012,7]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Our broader goal is to automatically translate English sentences into formulas in appropriate knowledge representation languages as a step towards understanding and thus answering questions with respect to English text. Our focus in this paper is on the language of Answer Set Programming (ASP). Our approach to translate sentences to ASP rules is inspired by Montague's use of lambda calculus formulas as meaning of words and phrases. With ASP as the target language the meaning of words and phrases are ASP-lambda formulas. In an earlier work we illustrated our approach by manually developing a dictionary of words and their ASP-lambda formulas. However such an approach is not scalable. In this paper our focus is on two algorithms that allow one to construct ASP-lambda formulas in an inverse manner. In particular the two algorithms take as input two lambda-calculus expressions G and H and compute a lambda-calculus expression F such that F with input as G, denoted by F@G, is equal to H; and similarly G@F = H. We present correctness and complexity results about these algorithms. To do that we develop the notion of typed ASP-lambda calculus theories and their orders and use it in developing the completeness results.<\/jats:p>","DOI":"10.1017\/s1471068412000282","type":"journal-article","created":{"date-parts":[[2012,9,5]],"date-time":"2012-09-05T11:28:45Z","timestamp":1346844525000},"page":"775-791","source":"Crossref","is-referenced-by-count":1,"title":["Typed answer set programming lambda calculus theories and correctness of inverse lambda algorithms with respect to them"],"prefix":"10.1017","volume":"12","author":[{"given":"CHITTA","family":"BARAL","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"JURAJ","family":"DZIFCAK","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"MARCOS A.","family":"GONZALEZ","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"AARON","family":"GOTTESMAN","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2012,9,5]]},"reference":[{"key":"S1471068412000282_ref21","volume-title":"Formal Philosophy. Selected Papers of Richard Montague","author":"Montague","year":"1974"},{"key":"S1471068412000282_ref16","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511608865"},{"key":"S1471068412000282_ref15","volume-title":"Introduction to Combinators and Lambda-Calculus","author":"Hindley","year":"1986"},{"key":"S1471068412000282_ref14","unstructured":"Gonzalez M. A. 2010. An Inverse Lambda Calculus Algorithm For Natural Language Processing. MS Thesis, Arizona State University."},{"key":"S1471068412000282_ref12","doi-asserted-by":"crossref","unstructured":"Dzifcak J. , Scheutz M. , Baral C. and Schermerhorn P. 2009. What to do and how to do it: Translating natural language directives into temporal and dynamic logic representation for goal management and action execution. In Robotics and Automation, 2009. ICRA '09. 4163\u20134168.","DOI":"10.1109\/ROBOT.2009.5152776"},{"key":"S1471068412000282_ref4","volume-title":"Logic-based Artificial Intellgence","author":"Baral","year":"2012"},{"key":"S1471068412000282_ref23","first-page":"3","article-title":"Decidability of higher-order matching","volume":"5","author":"Stirling","year":"2009","journal-title":"To appear Logical Methods in Computer Science"},{"key":"S1471068412000282_ref22","volume-title":"The syntactic process","author":"Steedman","year":"2000"},{"key":"S1471068412000282_ref1","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511543357"},{"key":"S1471068412000282_ref8","doi-asserted-by":"publisher","DOI":"10.2307\/2266170"},{"key":"S1471068412000282_ref9","doi-asserted-by":"crossref","unstructured":"Clark S. and Curran J. R. 2007. Wide-coverage efficient statistical parsing with ccg and log-linear models. Computational Linguistics 33.","DOI":"10.1162\/coli.2007.33.4.493"},{"key":"S1471068412000282_ref6","volume-title":"Lambda Calculi with Types, Handbook of Logic in Computer Science","author":"Barendregt","year":"1992"},{"key":"S1471068412000282_ref2","unstructured":"Baral C. and Dzifcak J. 2012. Solving puzzles described in english by automated translation to answer set programming and learning how to do that translation. In KR (to appear)."},{"key":"S1471068412000282_ref3","unstructured":"Baral C. , Dzifcak J. and Son T. C. 2008. Using answer set programming and lambda calculus to characterize natural language sentences with normatives and exceptions. In AAAI'08: Proceedings of the 23rd national conference on Artificial intelligence. 818\u2013823."},{"key":"S1471068412000282_ref19","unstructured":"Kwiatkowski T. , Zettlemoyer L. , Goldwater S. and Steedman M. 2010. Inducing probabilistic CCG grammars from logical form with higher-order unification. In Proceedings of the Conference on Empirical Methods in Natural Language Processing (EMNLP). 1223\u20131233."},{"key":"S1471068412000282_ref20","doi-asserted-by":"publisher","DOI":"10.1093\/jigpal\/11.1.51"},{"key":"S1471068412000282_ref24","unstructured":"Zettlemoyer L. and Collins M. 2005. Learning to map sentences to logical form: Structured classification with probabilistic categorial grammars. In Proceedings of the 21th Annual Conference on Uncertainty in Artificial Intelligence. 658\u2013666."},{"key":"S1471068412000282_ref13","unstructured":"Gelfond M. and Lifschitz V. 1988. The stable model semantics for logic programming. In Logic Programming: Proceedings of the Fifth International Conference and Symposium. 1070\u20131080."},{"key":"S1471068412000282_ref17","doi-asserted-by":"publisher","DOI":"10.1016\/S0019-9958(73)90301-X"},{"key":"S1471068412000282_ref18","doi-asserted-by":"publisher","DOI":"10.1016\/0304-3975(75)90011-0"},{"key":"S1471068412000282_ref5","volume-title":"Mathematical Methods in Linguistics","author":"Barbara","year":"1990"},{"key":"S1471068412000282_ref10","unstructured":"Costantini S. and Paolucci A. 2010. Towards translating natural language sentences into asp. In Proceedings of the Intl. Workshop on Answer Set Programming and Other Computing Paradigms (ASPOCP)."},{"key":"S1471068412000282_ref7","volume-title":"Representation and Inference for Natural Language: A First Course in Computational Semantics","author":"Blackburn","year":"2005"},{"key":"S1471068412000282_ref11","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(94)90083-3"}],"container-title":["Theory and Practice of Logic Programming"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S1471068412000282","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,25]],"date-time":"2019-04-25T20:27:05Z","timestamp":1556224025000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S1471068412000282\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,7]]},"references-count":24,"journal-issue":{"issue":"4-5","published-print":{"date-parts":[[2012,7]]}},"alternative-id":["S1471068412000282"],"URL":"https:\/\/doi.org\/10.1017\/s1471068412000282","relation":{},"ISSN":["1471-0684","1475-3081"],"issn-type":[{"value":"1471-0684","type":"print"},{"value":"1475-3081","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,7]]}}}