{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,15]],"date-time":"2025-10-15T00:23:31Z","timestamp":1760487811466,"version":"build-2065373602"},"reference-count":40,"publisher":"Springer Science and Business Media LLC","issue":"7-8","license":[{"start":{"date-parts":[[2025,5,17]],"date-time":"2025-05-17T00:00:00Z","timestamp":1747440000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,5,17]],"date-time":"2025-05-17T00:00:00Z","timestamp":1747440000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100004801","name":"Shota Rustaveli National Science Foundation","doi-asserted-by":"publisher","award":["STEM-22-2186","STEM-22-2186","STEM-22-2186","STEM-22-2186"],"award-info":[{"award-number":["STEM-22-2186","STEM-22-2186","STEM-22-2186","STEM-22-2186"]}],"id":[{"id":"10.13039\/501100004801","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Arch. Math. Logic"],"published-print":{"date-parts":[[2025,11]]},"DOI":"10.1007\/s00153-025-00974-5","type":"journal-article","created":{"date-parts":[[2025,5,17]],"date-time":"2025-05-17T12:43:51Z","timestamp":1747485831000},"page":"1103-1126","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["On the theory of epistemic \u0141ukasiewicz logic corresponding to the Chang algebra with application in Immune system"],"prefix":"10.1007","volume":"64","author":[{"given":"Revaz","family":"Grigolia","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ramaz","family":"Liparteliani","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Nunu","family":"Mitskevich","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tamar","family":"Tsertsvadze","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tekle","family":"Kalichava","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2025,5,17]]},"reference":[{"key":"974_CR1","volume-title":"The Axiomatic Method in Biology","author":"H Woodger","year":"1937","unstructured":"Woodger, H.: The Axiomatic Method in Biology. Cambridge University Press, Cambridge (1937)"},{"key":"974_CR2","volume-title":"Organismic sets","author":"N Rashevsky","year":"1972","unstructured":"Rashevsky, N.: Organismic sets. J.M, Richards Lab (1972)"},{"key":"974_CR3","doi-asserted-by":"publisher","first-page":"245","DOI":"10.1007\/BF02478302","volume":"20","author":"R Rosen","year":"1958","unstructured":"Rosen, R.: A relational theory of biological systems. Bull. Math. Biophysics 20, 245\u2013260 (1958)","journal-title":"Bull. Math. Biophysics"},{"key":"974_CR4","doi-asserted-by":"publisher","first-page":"317","DOI":"10.1007\/BF02477890","volume":"20","author":"R Rosen","year":"1958","unstructured":"Rosen, R.: The representation of biological systems from the standpoint of the theory of categories. Bull. Math. Biophysics 20, 317\u2013342 (1958)","journal-title":"Bull. Math. Biophysics"},{"issue":"11","key":"974_CR5","doi-asserted-by":"publisher","first-page":"3341","DOI":"10.1007\/s00500-015-1804-4","volume":"19","author":"A Di Nola","year":"2015","unstructured":"Di Nola, A., Grigolia, R., Mitskevich, N.: Multimodal epistemic \u0142ukasiewicz logics with application in immune system. Soft Computing 19(11), 3341\u20133351 (2015)","journal-title":"Soft Computing"},{"key":"974_CR6","doi-asserted-by":"crossref","unstructured":"Porter, T.: Geometric aspects of multi-agent systems. Electronic Notes in Theoretical Computer Science 81 (2003)","DOI":"10.1016\/S1571-0661(04)80837-5"},{"key":"974_CR7","doi-asserted-by":"crossref","unstructured":"Blackburn, P., De\u00a0Rijke, M., Venema, Y.: Modal Logic. Cambridge Tracts in Theoretical Computer Science, vol. 53. Cambridge University Press, (2001)","DOI":"10.1017\/CBO9781107050884"},{"key":"974_CR8","unstructured":"Bou, F., Esteva, F., Godo, L., Rodr\u00edguez, R.: $$n$$-\u0141ukasiewicz modal logic. Manuscript (2007)"},{"key":"974_CR9","unstructured":"Caicedo, X., Rodr\u00edguez, R.: A G\u00f6del similarity-based modal logic. Manuscript (2007)"},{"key":"974_CR10","doi-asserted-by":"crossref","unstructured":"Chagrov, A., Zakharyaschev, M.: Modal Logic. Oxford Logic Guides, vol. 35. Oxford University Press, (1997)","DOI":"10.1093\/oso\/9780198537793.001.0001"},{"key":"974_CR11","doi-asserted-by":"publisher","first-page":"235","DOI":"10.3233\/FI-1991-153-404","volume":"15","author":"M Fitting","year":"1992","unstructured":"Fitting, M.: Many-valued modal logics. Fundamenta Informaticae 15, 235\u2013254 (1992)","journal-title":"Fundamenta Informaticae"},{"key":"974_CR12","doi-asserted-by":"publisher","first-page":"55","DOI":"10.3233\/FI-1992-171-205","volume":"17","author":"M Fitting","year":"1992","unstructured":"Fitting, M.: Many-valued modal logics, ii. Fundamenta Informaticae 17, 55\u201373 (1992)","journal-title":"Fundamenta Informaticae"},{"key":"974_CR13","unstructured":"Hansoul, G., Teheux, B.: Completeness results for many-valued \u0142ukasiewicz modal systems and relational semantics (2006). Available at http:\/arxiv.org\/abs\/math\/0612542"},{"issue":"1","key":"974_CR14","doi-asserted-by":"publisher","first-page":"47","DOI":"10.3166\/jancl.13.47-71","volume":"13","author":"CD Koutras","year":"2003","unstructured":"Koutras, C.D.: A catalog of weak many-valued modal axioms and their corresponding frame classes. Journal of Applied Non-Classical Logics 13(1), 47\u201372 (2003)","journal-title":"Journal of Applied Non-Classical Logics"},{"issue":"6","key":"974_CR15","doi-asserted-by":"publisher","first-page":"3641","DOI":"10.1007\/s10958-005-0281-1","volume":"128","author":"AM Mironov","year":"2005","unstructured":"Mironov, A.M.: Fuzzy modal logics. Journal of Mathematical Sciences 128(6), 3641\u20133483 (2005)","journal-title":"Journal of Mathematical Sciences"},{"issue":"2","key":"974_CR16","doi-asserted-by":"publisher","first-page":"249","DOI":"10.1023\/A:1004956418185","volume":"59","author":"NY Suzuki","year":"1997","unstructured":"Suzuki, N.Y.: Kripke frame with graded accessibility and fuzzy possible world semantics. Studia Logica 59(2), 249\u2013269 (1997)","journal-title":"Studia Logica"},{"key":"974_CR17","first-page":"87","volume-title":"Selected works by Jan \u0141ukasiewicz","author":"J \u0141ukasiewicz","year":"1970","unstructured":"\u0141ukasiewicz, J.: O logice tr\u00f3jwarto\u015bciowej. Ruch filozoficzny 5 (1920). (in Polish). English translation: On three-valued logic. In: Borkowski, L. (ed.) Selected works by Jan \u0141ukasiewicz, pp. 87\u201388. North Holland, Amsterdam (1970)"},{"key":"974_CR18","doi-asserted-by":"publisher","first-page":"77","DOI":"10.2307\/2271339","volume":"28","author":"LS Hay","year":"1963","unstructured":"Hay, L.S.: Axiomatisation of the infinite-valued predicate calculus. Journal of Symbolic Logic 28, 77\u201386 (1963)","journal-title":"Journal of Symbolic Logic"},{"key":"974_CR19","unstructured":"\u0141ukasiewicz, J., Tarski, A.: Untersuchungen \u00fcber den aussagenkalk\u00fcl. Comp. Rend. Soc. Sci. et Lettres Varsovie Cl. III 23, 30\u201350 (1930)"},{"key":"974_CR20","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-011-5300-3","volume-title":"Metamathematics of Fuzzy Logic","author":"P Hajek","year":"1998","unstructured":"Hajek, P.: Metamathematics of Fuzzy Logic. Kluwer Academic Publishers, Dordrecht (1998)"},{"key":"974_CR21","first-page":"177","volume":"20","author":"H Ono","year":"2003","unstructured":"Ono, H.: Substructural logics and residuated lattices - an introduction. Trends in Logic 20, 177\u2013212 (2003)","journal-title":"Trends in Logic"},{"key":"974_CR22","doi-asserted-by":"publisher","first-page":"467","DOI":"10.1090\/S0002-9947-1958-0094302-9","volume":"88","author":"CC Chang","year":"1958","unstructured":"Chang, C.C.: Algebraic analysis of many-valued logics. Trans. Amer. Math. Soc. 88, 467\u2013490 (1958)","journal-title":"Trans. Amer. Math. Soc."},{"key":"974_CR23","doi-asserted-by":"publisher","first-page":"15","DOI":"10.1016\/0022-1236(86)90015-7","volume":"65","author":"D Mundici","year":"1986","unstructured":"Mundici, D.: Interpretation of af $$c^{\\ast }$$-algebras in \u0141ukasiewicz sentential calculus. J. Funct. Analysis 65, 15\u201363 (1986)","journal-title":"J. Funct. Analysis"},{"key":"974_CR24","doi-asserted-by":"crossref","unstructured":"Cignoli, R.L.O., D\u2019Ottaviano, I.M.L., Mundici, D.: Algebraic Foundations of Many-valued Reasoning. Trends in Logic, vol. 7. Kluwer, (2000)","DOI":"10.1007\/978-94-015-9480-6_2"},{"key":"974_CR25","first-page":"467","volume":"88","author":"A Di Nola","year":"1994","unstructured":"Di Nola, A., Lettieri, A.: Perfect $$mv$$-algebras are categorically equivalent to abelian $$\\ell $$-groups. Studia Logica 88, 467\u2013490 (1994)","journal-title":"Studia Logica"},{"issue":"1\u20132","key":"974_CR26","doi-asserted-by":"publisher","first-page":"135","DOI":"10.1007\/s10485-007-9069-4","volume":"15","author":"LP Belluce","year":"2007","unstructured":"Belluce, L.P., Di Nola, A., Gerla, B.: Perfect $$mv$$-algebras and their logic. Applied Categorical Structures 15(1\u20132), 135\u2013151 (2007)","journal-title":"Applied Categorical Structures"},{"key":"974_CR27","unstructured":"Rutledge, J.D.: A preliminary investigation of the infinitely many-valued predicate calculus. PhD thesis, Cornell University (1959)"},{"issue":"1\u20133","key":"974_CR28","first-page":"125","volume":"128","author":"A Di Nola","year":"2004","unstructured":"Di Nola, A., Grigolia, R.: On monadic $$mv$$-algebras. APAL 128(1\u20133), 125\u2013139 (2004)","journal-title":"APAL"},{"key":"974_CR29","doi-asserted-by":"publisher","first-page":"125","DOI":"10.1007\/s11225-005-2805-6","volume":"81","author":"LP Belluce","year":"2005","unstructured":"Belluce, L.P., Grigolia, R., Lettieri, A.: Representations of monadic mv-algebras. Studia Logica 81, 125\u2013144 (2005)","journal-title":"Studia Logica"},{"key":"974_CR30","first-page":"437","volume":"5","author":"A Di Nola","year":"2016","unstructured":"Di Nola, A., Grigolia, R., Lenzi, G.: On the lattice of the subvarieties of monadic $$mv(c)$$-algebras. The IFCOLOG journal of logics and their applications 5, 437\u2013454 (2016)","journal-title":"The IFCOLOG journal of logics and their applications"},{"key":"974_CR31","doi-asserted-by":"publisher","first-page":"177","DOI":"10.1007\/BF01110090","volume":"122","author":"RW Quackenbush","year":"1971","unstructured":"Quackenbush, R.W.: Demi-semi-primal algebras and malcev-type conditions. Mathematische Zeitschrift 122, 177\u2013188 (1971)","journal-title":"Mathematische Zeitschrift"},{"issue":"2","key":"974_CR32","first-page":"38","volume":"7","author":"A Di Nola","year":"2017","unstructured":"Di Nola, A., Grigolia, R., Liparteliani, R.: Projectivity and unification problem in the variety generated by monadic perfect mv-algebras. Azerbaijan Journal of Mathematics 7(2), 38\u201361 (2017)","journal-title":"Azerbaijan Journal of Mathematics"},{"issue":"6","key":"974_CR33","doi-asserted-by":"publisher","first-page":"733","DOI":"10.1093\/logcom\/7.6.733","volume":"7","author":"S Ghilardi","year":"1997","unstructured":"Ghilardi, S.: Unification through projectivity. J. Logic Comput. 7(6), 733\u2013752 (1997)","journal-title":"J. Logic Comput."},{"issue":"3","key":"974_CR34","doi-asserted-by":"publisher","first-page":"912","DOI":"10.2307\/2275439","volume":"57","author":"VV Rybakov","year":"1992","unstructured":"Rybakov, V.V.: Rules of inference with parameters for intuitionistic logic. J. Symbolic Logic 57(3), 912\u2013923 (1992)","journal-title":"J. Symbolic Logic"},{"key":"974_CR35","volume-title":"Admissibility of Logical Inference Rules","author":"VV Rybakov","year":"1997","unstructured":"Rybakov, V.V.: Admissibility of Logical Inference Rules. North-Holland, Amsterdam (1997)"},{"issue":"3","key":"974_CR36","doi-asserted-by":"publisher","first-page":"227","DOI":"10.1093\/jigpal\/10.3.229","volume":"10","author":"S Ghilardi","year":"2002","unstructured":"Ghilardi, S.: A resolution\/tableaux algorithm for projective approximations in ipc. Logic J. of the IGPL 10(3), 227\u2013241 (2002)","journal-title":"Logic J. of the IGPL"},{"key":"974_CR37","doi-asserted-by":"publisher","unstructured":"Di Nola, A., Grigolia, R., Mitskevich, N., Vitale, G., Gielis, J., Ricci, P. E., Tavkhelidze, I.: Dynamic \u0141ukasiewicz logic and its application to immune system. Soft Computing, 9773\u20139780 (2021). Springer. https:\/\/doi.org\/10.1007\/s00500-021-05955-3","DOI":"10.1007\/s00500-021-05955-3"},{"key":"974_CR38","doi-asserted-by":"publisher","unstructured":"Di Nola, A., Grigolia, R., Mitskevich, N., Gielis, J., Ricci, P. E., Tavkhelidze, I.: Modal Epistemic \u0141ukasiewicz Logic with Constant and Its Application in Immune System. Modeling in Mathematics, 53\u201365 (2017). Atlantis Press. https:\/\/doi.org\/10.2991\/978-94-6239-261-8_5","DOI":"10.2991\/978-94-6239-261-8_5"},{"key":"974_CR39","doi-asserted-by":"publisher","unstructured":"Di Nola, A., Grigolia, R., Vitale, G.,: Epistemic \u0141ukasiewicz logic of partial knowledge. Soft Computing, 9823\u20139830 (2022). Springer. https:\/\/doi.org\/10.1007\/s00500-022-07281-8","DOI":"10.1007\/s00500-022-07281-8"},{"key":"974_CR40","unstructured":"Di\u00a0Nola, A., Grigolia, R., Lenzi, G.: Structural Completeness and Unification Problem of the Logic of Chang Algebra. Azerbaijan Journal of Mathematics, 6(2), 23\u201338 (12016)"}],"container-title":["Archive for Mathematical Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00153-025-00974-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00153-025-00974-5\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00153-025-00974-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,14]],"date-time":"2025-10-14T06:06:50Z","timestamp":1760422010000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00153-025-00974-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,5,17]]},"references-count":40,"journal-issue":{"issue":"7-8","published-print":{"date-parts":[[2025,11]]}},"alternative-id":["974"],"URL":"https:\/\/doi.org\/10.1007\/s00153-025-00974-5","relation":{},"ISSN":["0933-5846","1432-0665"],"issn-type":[{"type":"print","value":"0933-5846"},{"type":"electronic","value":"1432-0665"}],"subject":[],"published":{"date-parts":[[2025,5,17]]},"assertion":[{"value":"16 November 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"25 April 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"17 May 2025","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}