{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,27]],"date-time":"2025-03-27T23:46:42Z","timestamp":1743119202841,"version":"3.40.3"},"publisher-location":"Cham","reference-count":33,"publisher":"Springer Nature Switzerland","isbn-type":[{"type":"print","value":"9783031436185"},{"type":"electronic","value":"9783031436192"}],"license":[{"start":{"date-parts":[[2023,1,1]],"date-time":"2023-01-01T00:00:00Z","timestamp":1672531200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,1,1]],"date-time":"2023-01-01T00:00:00Z","timestamp":1672531200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2023]]},"DOI":"10.1007\/978-3-031-43619-2_35","type":"book-chapter","created":{"date-parts":[[2023,9,23]],"date-time":"2023-09-23T15:02:40Z","timestamp":1695481360000},"page":"515-530","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Categorical Approximation Fixpoint Theory"],"prefix":"10.1007","author":[{"given":"Angelos","family":"Charalambidis","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Panos","family":"Rondogiannis","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2023,9,24]]},"reference":[{"key":"35_CR1","doi-asserted-by":"crossref","unstructured":"Abramsky, S., Jung, A.: Domain Theory, pp. 1\u2013168. Oxford University Press Inc. (1995)","DOI":"10.1093\/oso\/9780198537625.003.0001"},{"issue":"2","key":"35_CR2","doi-asserted-by":"publisher","first-page":"181","DOI":"10.1006\/inco.1995.1061","volume":"118","author":"J Ad\u00e1mek","year":"1995","unstructured":"Ad\u00e1mek, J.: Recursive data types in algebraically omega-complete categories. Inf. Comput. 118(2), 181\u2013190 (1995). https:\/\/doi.org\/10.1006\/inco.1995.1061","journal-title":"Inf. Comput."},{"key":"35_CR3","unstructured":"Ad\u00e1mek, J., Herrlich, H., Strecker, G.E.: Abstract and Concrete Categories - The Joy of Cats. Dover Publications (2009)"},{"issue":"2","key":"35_CR4","doi-asserted-by":"publisher","first-page":"163","DOI":"10.1016\/0022-0000(79)90026-6","volume":"19","author":"J Ad\u00e1mek","year":"1979","unstructured":"Ad\u00e1mek, J., Koubek, V.: Least fixed point of a functor. J. Comput. Syst. Sci. 19(2), 163\u2013178 (1979). https:\/\/doi.org\/10.1016\/0022-0000(79)90026-6","journal-title":"J. Comput. Syst. Sci."},{"key":"35_CR5","doi-asserted-by":"publisher","first-page":"41","DOI":"10.1016\/j.jlamp.2017.11.003","volume":"95","author":"J Ad\u00e1mek","year":"2018","unstructured":"Ad\u00e1mek, J., Milius, S., Moss, L.S.: Fixed points of functors. J. Log. Algebraic Methods Program. 95, 41\u201381 (2018). https:\/\/doi.org\/10.1016\/j.jlamp.2017.11.003","journal-title":"J. Log. Algebraic Methods Program."},{"issue":"4","key":"35_CR6","first-page":"589","volume":"015","author":"J Ad\u00e1mek","year":"1974","unstructured":"Ad\u00e1mek, J.: Free algebras and automata realizations in the language of categories. Comment. Math. Univ. Carol. 015(4), 589\u2013602 (1974)","journal-title":"Comment. Math. Univ. Carol."},{"key":"35_CR7","series-title":"Lecture Notes in Computer Science (Lecture Notes in Artificial Intelligence)","doi-asserted-by":"publisher","first-page":"102","DOI":"10.1007\/978-3-642-40564-8_11","volume-title":"Logic Programming and Nonmonotonic Reasoning","author":"C Anti\u0107","year":"2013","unstructured":"Anti\u0107, C., Eiter, T., Fink, M.: Hex semantics via approximation fixpoint theory. In: Cabalar, P., Son, T.C. (eds.) LPNMR 2013. LNCS (LNAI), vol. 8148, pp. 102\u2013115. Springer, Heidelberg (2013). https:\/\/doi.org\/10.1007\/978-3-642-40564-8_11"},{"issue":"3","key":"35_CR8","doi-asserted-by":"publisher","first-page":"211","DOI":"10.1016\/0022-4049(92)90169-G","volume":"82","author":"M Barr","year":"1992","unstructured":"Barr, M.: Algebraically compact functors. J. Pure Appl. Algebra 82(3), 211\u2013231 (1992). https:\/\/doi.org\/10.1016\/0022-4049(92)90169-G","journal-title":"J. Pure Appl. Algebra"},{"key":"35_CR9","unstructured":"Bos, R., Hemerik, C.: An Introduction to the Category-Theoretic Solution of Recursive Domain Equations. Computing Science Notes. Technische Universiteit Eindhoven (1988)"},{"issue":"4\u20135","key":"35_CR10","doi-asserted-by":"publisher","first-page":"725","DOI":"10.1017\/S1471068414000313","volume":"14","author":"A Charalambidis","year":"2014","unstructured":"Charalambidis, A., \u00c9sik, Z., Rondogiannis, P.: Minimum model semantics for extensional higher-order logic programming with negation. Theory Pract. Log. Program. 14(4\u20135), 725\u2013737 (2014). https:\/\/doi.org\/10.1017\/S1471068414000313","journal-title":"Theory Pract. Log. Program."},{"issue":"3\u20134","key":"35_CR11","doi-asserted-by":"publisher","first-page":"421","DOI":"10.1017\/S1471068418000108","volume":"18","author":"A Charalambidis","year":"2018","unstructured":"Charalambidis, A., Rondogiannis, P., Symeonidou, I.: Approximation fixpoint theory and the well-founded semantics of higher-order logic programs. Theory Pract. Log. Program. 18(3\u20134), 421\u2013437 (2018). https:\/\/doi.org\/10.1017\/S1471068418000108","journal-title":"Theory Pract. Log. Program."},{"key":"35_CR12","doi-asserted-by":"publisher","unstructured":"Dasseville, I., van der Hallen, M., Bogaerts, B., Janssens, G., Denecker, M.: A compositional typed higher-order logic with definitions. In: Carro, M., King, A., Saeedloei, N., Vos, M.D. (eds.) Technical Communications of the 32nd International Conference on Logic Programming, ICLP 2016 TCs, New York City, USA, 16\u201321 October 2016. OASIcs, vol. 52, pp. 14:1\u201314:13. Schloss Dagstuhl - Leibniz-Zentrum f\u00fcr Informatik (2016). https:\/\/doi.org\/10.4230\/OASIcs.ICLP.2016.14","DOI":"10.4230\/OASIcs.ICLP.2016.14"},{"key":"35_CR13","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"178","DOI":"10.1007\/978-3-642-30743-0_13","volume-title":"Correct Reasoning","author":"M Denecker","year":"2012","unstructured":"Denecker, M., Bruynooghe, M., Vennekens, J.: Approximation fixpoint theory and the semantics of logic and answers set programs. In: Erdem, E., Lee, J., Lierler, Y., Pearce, D. (eds.) Correct Reasoning. LNCS, vol. 7265, pp. 178\u2013194. Springer, Heidelberg (2012). https:\/\/doi.org\/10.1007\/978-3-642-30743-0_13"},{"key":"35_CR14","doi-asserted-by":"publisher","first-page":"127","DOI":"10.1007\/978-1-4615-1567-8_6","volume-title":"Logic-Based Artificial Intelligence","author":"M Denecker","year":"2000","unstructured":"Denecker, M., Marek, V., Truszczy\u0144ski, M.: Approximations, stable operators, well-founded fixpoints and applications in nonmonotonic reasoning. In: Minker, J. (ed.) Logic-Based Artificial Intelligence, pp. 127\u2013144. Kluwer Academic Publishers, Dordrecht (2000)"},{"issue":"1","key":"35_CR15","doi-asserted-by":"publisher","first-page":"84","DOI":"10.1016\/j.ic.2004.02.004","volume":"192","author":"M Denecker","year":"2004","unstructured":"Denecker, M., Marek, V.W., Truszczynski, M.: Ultimate approximation and its application in nonmonotonic knowledge representation systems. Inf. Comput. 192(1), 84\u2013121 (2004). https:\/\/doi.org\/10.1016\/j.ic.2004.02.004","journal-title":"Inf. Comput."},{"issue":"1\u20132","key":"35_CR16","doi-asserted-by":"publisher","first-page":"25","DOI":"10.1016\/S0304-3975(00)00330-3","volume":"278","author":"M Fitting","year":"2002","unstructured":"Fitting, M.: Fixpoint semantics for logic programming: a survey. Theor. Comput. Sci. 278(1\u20132), 25\u201351 (2002). https:\/\/doi.org\/10.1016\/S0304-3975(00)00330-3","journal-title":"Theor. Comput. Sci."},{"key":"35_CR17","doi-asserted-by":"publisher","unstructured":"Frisch, A., Castagna, G., Benzaken, V.: Semantic subtyping: dealing set-theoretically with function, union, intersection, and negation types. J. ACM 55(4), 19:1\u201319:64 (2008). https:\/\/doi.org\/10.1145\/1391289.1391293","DOI":"10.1145\/1391289.1391293"},{"key":"35_CR18","unstructured":"Gunter, C.A.: Semantics of Programming Languages - Structures and Techniques. Foundations of Computing. MIT Press (1993)"},{"key":"35_CR19","series-title":"Lecture Notes in Computer Science (Lecture Notes in Artificial Intelligence)","doi-asserted-by":"publisher","first-page":"224","DOI":"10.1007\/978-3-319-34111-8_28","volume-title":"Advances in Artificial Intelligence","author":"F Liu","year":"2016","unstructured":"Liu, F., Bi, Y., Chowdhury, M.S., You, J.-H., Feng, Z.: Flexible approximators for approximating fixpoint theory. In: Khoury, R., Drummond, C. (eds.) AI 2016. LNCS (LNAI), vol. 9673, pp. 224\u2013236. Springer, Cham (2016). https:\/\/doi.org\/10.1007\/978-3-319-34111-8_28"},{"issue":"2","key":"35_CR20","doi-asserted-by":"publisher","first-page":"305","DOI":"10.1017\/S1471068421000168","volume":"22","author":"F Liu","year":"2022","unstructured":"Liu, F., You, J.: Alternating fixpoint operator for hybrid MKNF knowledge bases as an approximator of AFT. Theory Pract. Log. Program. 22(2), 305\u2013334 (2022). https:\/\/doi.org\/10.1017\/S1471068421000168","journal-title":"Theory Pract. Log. Program."},{"key":"35_CR21","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-83189-8","volume-title":"Foundations of Logic Programming","author":"JW Lloyd","year":"1987","unstructured":"Lloyd, J.W.: Foundations of Logic Programming, 2nd edn. Springer, Heidelberg (1987). https:\/\/doi.org\/10.1007\/978-3-642-83189-8","edition":"2"},{"issue":"3","key":"35_CR22","doi-asserted-by":"publisher","first-page":"301","DOI":"10.1017\/S1471068406002973","volume":"7","author":"N Pelov","year":"2007","unstructured":"Pelov, N., Denecker, M., Bruynooghe, M.: Well-founded and stable semantics of logic programs with aggregates. Theory Pract. Log. Program. 7(3), 301\u2013353 (2007). https:\/\/doi.org\/10.1017\/S1471068406002973","journal-title":"Theory Pract. Log. Program."},{"key":"35_CR23","doi-asserted-by":"crossref","unstructured":"Pierce, B.C.: Basic Category Theory for Computer Scientists. Foundations of Computing. MIT Press (1991)","DOI":"10.7551\/mitpress\/1524.001.0001"},{"issue":"5\u20136","key":"35_CR24","doi-asserted-by":"publisher","first-page":"974","DOI":"10.1017\/S1471068417000357","volume":"17","author":"P Rondogiannis","year":"2017","unstructured":"Rondogiannis, P., Symeonidou, I.: The intricacies of three-valued extensional semantics for higher-order logic programs. Theory Pract. Log. Program. 17(5\u20136), 974\u2013991 (2017). https:\/\/doi.org\/10.1017\/S1471068417000357","journal-title":"Theory Pract. Log. Program."},{"key":"35_CR25","doi-asserted-by":"publisher","unstructured":"Rondogiannis, P., Symeonidou, I.: Extensional semantics for higher-order logic programs with negation. Log. Methods Comput. Sci. 14(2) (2018). https:\/\/doi.org\/10.23638\/LMCS-14(2:19)2018","DOI":"10.23638\/LMCS-14(2:19)2018"},{"key":"35_CR26","unstructured":"Schmidt, D.A.: Denotational Semantics: A Methodology for Language Development. William C. Brown Publishers (1986)"},{"issue":"4","key":"35_CR27","doi-asserted-by":"publisher","first-page":"761","DOI":"10.1137\/0211062","volume":"11","author":"MB Smyth","year":"1982","unstructured":"Smyth, M.B., Plotkin, G.D.: The category-theoretic solution of recursive domain equations. SIAM J. Comput. 11(4), 761\u2013783 (1982). https:\/\/doi.org\/10.1137\/0211062","journal-title":"SIAM J. Comput."},{"key":"35_CR28","volume-title":"Denotational Semantics: The Scott-Strachey Approach to Programming Language Theory","author":"JE Stoy","year":"1977","unstructured":"Stoy, J.E.: Denotational Semantics: The Scott-Strachey Approach to Programming Language Theory. MIT Press, Cambridge (1977)"},{"key":"35_CR29","doi-asserted-by":"publisher","first-page":"34","DOI":"10.1016\/j.artint.2015.05.003","volume":"226","author":"H Strass","year":"2015","unstructured":"Strass, H., Wallner, J.P.: Analyzing the computational complexity of abstract dialectical frameworks via approximation fixpoint theory. Artif. Intell. 226, 34\u201374 (2015). https:\/\/doi.org\/10.1016\/j.artint.2015.05.003","journal-title":"Artif. Intell."},{"issue":"2","key":"35_CR30","doi-asserted-by":"publisher","first-page":"285","DOI":"10.2140\/pjm.1955.5.285","volume":"5","author":"A Tarski","year":"1955","unstructured":"Tarski, A.: A lattice-theoretical fixpoint theorem and its applications. Pac. J. Math. 5(2), 285\u2013309 (1955)","journal-title":"Pac. J. Math."},{"key":"35_CR31","unstructured":"Tennent, R.D.: Semantics of Programming Languages. Prentice Hall International Series in Computer Science. Prentice Hall (1991)"},{"issue":"4","key":"35_CR32","doi-asserted-by":"publisher","first-page":"765","DOI":"10.1145\/1183278.1183284","volume":"7","author":"J Vennekens","year":"2006","unstructured":"Vennekens, J., Gilis, D., Denecker, M.: Splitting an operator: algebraic modularity results for logics with fixpoint semantics. ACM Trans. Comput. Log. 7(4), 765\u2013797 (2006). https:\/\/doi.org\/10.1145\/1183278.1183284","journal-title":"ACM Trans. Comput. Log."},{"key":"35_CR33","doi-asserted-by":"publisher","first-page":"13","DOI":"10.1016\/0304-3975(79)90053-7","volume":"8","author":"M Wand","year":"1979","unstructured":"Wand, M.: Fixed-point constructions in order-enriched categories. Theor. Comput. Sci. 8, 13\u201330 (1979). https:\/\/doi.org\/10.1016\/0304-3975(79)90053-7","journal-title":"Theor. Comput. Sci."}],"container-title":["Lecture Notes in Computer Science","Logics in Artificial Intelligence"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-031-43619-2_35","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,12,22]],"date-time":"2023-12-22T12:56:03Z","timestamp":1703249763000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-031-43619-2_35"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023]]},"ISBN":["9783031436185","9783031436192"],"references-count":33,"URL":"https:\/\/doi.org\/10.1007\/978-3-031-43619-2_35","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2023]]},"assertion":[{"value":"24 September 2023","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"JELIA","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"European Conference on Logics in Artificial Intelligence","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Dresden","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Germany","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2023","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"20 September 2023","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"22 September 2023","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"18","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"jelia2023","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/www.jelia.eu\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Single-blind","order":1,"name":"type","label":"Type","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"EasyChair","order":2,"name":"conference_management_system","label":"Conference Management System","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"111","order":3,"name":"number_of_submissions_sent_for_review","label":"Number of Submissions Sent for Review","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"41","order":4,"name":"number_of_full_papers_accepted","label":"Number of Full Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"11","order":5,"name":"number_of_short_papers_accepted","label":"Number of Short Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"37% - The value is computed by the equation \"Number of Full Papers Accepted \/ Number of Submissions Sent for Review * 100\" and then rounded to a whole number.","order":6,"name":"acceptance_rate_of_full_papers","label":"Acceptance Rate of Full Papers","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"3","order":7,"name":"average_number_of_reviews_per_paper","label":"Average Number of Reviews per Paper","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"3,6","order":8,"name":"average_number_of_papers_per_reviewer","label":"Average Number of Papers per Reviewer","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"Yes","order":9,"name":"external_reviewers_involved","label":"External Reviewers Involved","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}}]}}