{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,4,28]],"date-time":"2025-04-28T14:33:27Z","timestamp":1745850807189},"reference-count":32,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2022,10,21]],"date-time":"2022-10-21T00:00:00Z","timestamp":1666310400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2022,10,21]],"date-time":"2022-10-21T00:00:00Z","timestamp":1666310400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Log. Univers."],"published-print":{"date-parts":[[2022,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We build a topological model, based on intuitionistic logic, for multi-agent biological systems (such as<jats:italic>Physarum polycephalum<\/jats:italic>, bacterial colonies or any other swarm), reacting to external nourishment stimuli. Our construction follows the topological description of brain activity, where particles (neurons) are activated by an external environment, represented by a topological space<jats:italic>X<\/jats:italic>with an open cover<jats:inline-formula><jats:alternatives><jats:tex-math>$$\\{U_i:i\\in I\\}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mrow><mml:mo>{<\/mml:mo><mml:msub><mml:mi>U<\/mml:mi><mml:mi>i<\/mml:mi><\/mml:msub><mml:mo>:<\/mml:mo><mml:mi>i<\/mml:mi><mml:mo>\u2208<\/mml:mo><mml:mi>I<\/mml:mi><mml:mo>}<\/mml:mo><\/mml:mrow><\/mml:math><\/jats:alternatives><\/jats:inline-formula>. The brain builds the model of this external space via the nerve (trace) of a topological space<jats:italic>X<\/jats:italic>. Here the body of<jats:italic>Physarum polycephalum<\/jats:italic>or a swarm made of networks of tubular structures represents a nerve (trace) of<jats:italic>X<\/jats:italic>also which means that<jats:italic>Physarum polycephalum<\/jats:italic>or a swarm gains orientation in the space of external stimuli even in the absence of any neural system. The logic of living organisms is based on open subsets of<jats:italic>X<\/jats:italic>and thus can be represented by Heyting algebra (i.e. intuitionistically). We also consider the generalisation of the nerve construction to a categorical context, where the category is determined by the network structures of multi-agent biological system. This model can be generalised up to simulating the behaviour of any swarm by means of intuitionistic logic.<\/jats:p>","DOI":"10.1007\/s11787-022-00319-3","type":"journal-article","created":{"date-parts":[[2022,10,21]],"date-time":"2022-10-21T17:10:44Z","timestamp":1666372244000},"page":"671-687","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Brain and Its Universal Logical Model of Multi-Agent Biological Systems"],"prefix":"10.1007","volume":"16","author":[{"given":"Jerzy","family":"Kr\u00f3l","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Andrew","family":"Schumann","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Krzysztof","family":"Bielas","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2022,10,21]]},"reference":[{"key":"319_CR1","doi-asserted-by":"publisher","first-page":"35","DOI":"10.1142\/9789814675321_0002","volume-title":"Atlas of Physarum Computing","author":"J Jones","year":"2015","unstructured":"Jones, J.: Multi-agent model of slime mould for computing and robotics. In: Adamatzky, A. (ed.) Atlas of Physarum Computing, pp. 35\u201346. World Scientific (2015)"},{"key":"319_CR2","doi-asserted-by":"crossref","unstructured":"Margenstern, M.: Bacteria inspired patterns grown with hyperbolic cellular automata. In International Conference on High Performance Computing and Simulation, pp. 757\u2013763 (2011)","DOI":"10.1109\/HPCSim.2011.5999905"},{"key":"319_CR3","doi-asserted-by":"publisher","first-page":"45","DOI":"10.1016\/j.biosystems.2003.08.001","volume":"73","author":"S Tsuda","year":"2004","unstructured":"Tsuda, S., Aono, M., Gunji, Y.P.: Robust and emergent Physarum-computing. Biosystems 73, 45\u201355 (2004)","journal-title":"Biosystems"},{"issue":"3","key":"319_CR4","doi-asserted-by":"publisher","DOI":"10.1088\/1361-6463\/aa9d7b","volume":"51","author":"A Schumann","year":"2018","unstructured":"Schumann, A.: Decidable and undecidable arithmetic functions in actin filament networks. J. Phys. D Appl. Phys. 51(3), 034005 (2018)","journal-title":"J. Phys. D Appl. Phys."},{"key":"319_CR5","doi-asserted-by":"publisher","DOI":"10.7551\/mitpress\/1290.001.0001","volume-title":"Ant Colony Optimization","author":"M Dorigo","year":"2004","unstructured":"Dorigo, M., Stutzle, T.: Ant Colony Optimization. MIT Press, Cambridge (2004)"},{"issue":"1","key":"319_CR6","first-page":"108","volume":"214","author":"D Karaboga","year":"2009","unstructured":"Karaboga, D., Akay, B.: A comparative study of artificial bee colony algorithm. Appl. Math. Comput. 214(1), 108\u2013132 (2009)","journal-title":"Appl. Math. Comput."},{"key":"319_CR7","doi-asserted-by":"publisher","first-page":"239","DOI":"10.3354\/meps273239","volume":"273","author":"S Viscido","year":"2004","unstructured":"Viscido, S., Parrish, J., Grunbaum, D.: Individual behavior and emergent properties of fish schools: a comparison of observation and theory. Mar. Ecol. Prog. Ser. 273, 239\u2013249 (2004)","journal-title":"Mar. Ecol. Prog. Ser."},{"key":"319_CR8","doi-asserted-by":"publisher","first-page":"25","DOI":"10.1145\/37402.37406","volume":"21","author":"CW Reynolds","year":"1987","unstructured":"Reynolds, C.W.: Flocks, herds, and schools: a distributed behavioral model. Comput. Graph. 21, 25\u201334 (1987)","journal-title":"Comput. Graph."},{"issue":"2","key":"319_CR9","doi-asserted-by":"publisher","first-page":"1550030","DOI":"10.1142\/S0218127415500303","volume":"25","author":"A Adamatzky","year":"2015","unstructured":"Adamatzky, A., Mayne, R.: Actin automata: phenomenology and localizations. Int. J. Bifurc. Chaos 25(2), 1550030 (2015)","journal-title":"Int. J. Bifurc. Chaos"},{"issue":"1","key":"319_CR10","doi-asserted-by":"publisher","first-page":"1650019","DOI":"10.1142\/S021812741650019X","volume":"26","author":"R Alonso-Sanz","year":"2016","unstructured":"Alonso-Sanz, R., Adamatzky, A.: Actin automata with memory. Int. J. Bifurc. Chaos 26(1), 1650019 (2016)","journal-title":"Int. J. Bifurc. Chaos"},{"issue":"1","key":"319_CR11","doi-asserted-by":"publisher","first-page":"15","DOI":"10.1016\/j.nancom.2015.01.002","volume":"6","author":"S Siccardi","year":"2015","unstructured":"Siccardi, S., Adamatzky, A.: Actin quantum automata: communication and computation in molecular networks. Nano Commun. Netw. 6(1), 15\u201327 (2015)","journal-title":"Nano Commun. Netw."},{"key":"319_CR12","unstructured":"Kennedy, J., Eberhart, R.: Swarm Intelligence. Morgan Kaufmann Publishers, Inc. (2001)"},{"issue":"3","key":"319_CR13","doi-asserted-by":"publisher","first-page":"52","DOI":"10.1109\/MCS.2002.1004010","volume":"22","author":"KM Passino","year":"2002","unstructured":"Passino, K.M.: Biomimicry of bacterial foraging for distributed optimization and control. Control Syst. 22(3), 52\u201367 (2002)","journal-title":"Control Syst."},{"key":"319_CR14","unstructured":"Karaboga, D.: An idea based on honey bee swarm for numerical optimization. Technical Report-tr06, Engineering Faculty, Computer Engineering Department, Erciyes University (2005)"},{"key":"319_CR15","doi-asserted-by":"publisher","first-page":"5508","DOI":"10.1016\/j.asoc.2011.05.008","volume":"11","author":"R Rajabioun","year":"1987","unstructured":"Rajabioun, R.: Cuckoo optimization algorithm. Appl. Soft Comput. 11, 5508\u20135518 (1987)","journal-title":"Appl. Soft Comput."},{"issue":"16","key":"319_CR16","doi-asserted-by":"publisher","first-page":"6374","DOI":"10.1016\/j.eswa.2013.05.041","volume":"40","author":"E Cuevas","year":"2013","unstructured":"Cuevas, E., Cienfuegos, M., Zaldivar, D., Perez-Cisneros, M.: A swarm optimization algorithm inspired in the behavior of the social-spider. Expert Syst. Appl. 40(16), 6374\u20136384 (2013)","journal-title":"Expert Syst. Appl."},{"key":"319_CR17","unstructured":"Ayzenberg, A.: Topology of nerves and formal concepts. (2019) available online arXiv:1911.05491v1 [math.AT]"},{"key":"319_CR18","doi-asserted-by":"publisher","DOI":"10.1088\/1361-6463\/ab866c","volume":"53","author":"C Oettmeier","year":"2020","unstructured":"Oettmeier, C., Nakagaki, T., D\u00f6bereiner, H.G.: Slime mold on the rise: the physics of Physarum polycephalum. J. Phys. D Appl. Phys. 53, 310201 (2020)","journal-title":"J. Phys. D Appl. Phys."},{"key":"319_CR19","doi-asserted-by":"crossref","unstructured":"Manin, Yu. I.: Neural codes and homotopy types: mathematical models of place field recognition. Moscow Math. J. 15, 4 (2015) (preprint arXiv:1501.00897)","DOI":"10.17323\/1609-4514-2015-15-4-741-748"},{"key":"319_CR20","unstructured":"Youngs, N.E.: The neural ring: using algebraic geometry to analyse neural rings. PHD Thesis, University of Nebraska, Lincoln, Nebraska, USA, (2014) available online arXiv:1409.2544 [q-bio.NC]"},{"key":"319_CR21","unstructured":"Hatcher, A.: Algebraic Topology. Cambridge (2002)"},{"key":"319_CR22","doi-asserted-by":"publisher","first-page":"470","DOI":"10.1038\/35035159","volume":"407","author":"T Nakagaki","year":"2000","unstructured":"Nakagaki, T., Yamada, H., T\u2019oth, A.: Maze-solving by an amoeboid organism. Nature 407, 470 (2000)","journal-title":"Nature"},{"key":"319_CR23","doi-asserted-by":"publisher","first-page":"20772","DOI":"10.1038\/s41598-020-77617-7","volume":"10","author":"K Saito","year":"2020","unstructured":"Saito, K., Aono, M., Kasai, S.: Amoeba-inspired analog electronic computing system integrating resistance crossbar for solving the travelling salesman problem. Sci. Rep. 10, 20772 (2020)","journal-title":"Sci. Rep."},{"key":"319_CR24","doi-asserted-by":"publisher","first-page":"439","DOI":"10.1126\/science.1177894","volume":"327","author":"A Tero","year":"2010","unstructured":"Tero, A., et al.: Rules for biologically inspired adaptive network design. Science 327, 439\u2013442 (2010)","journal-title":"Science"},{"issue":"20","key":"319_CR25","doi-asserted-by":"publisher","first-page":"5136","DOI":"10.1073\/pnas.1618114114","volume":"114","author":"K Alim","year":"2017","unstructured":"Alim, K., Andrew, N., Pringle, A., Brenner, M.P.: Mechanism of signal propagation in Physarum polycephalum. PNAS 114(20), 5136\u20135141 (2017)","journal-title":"PNAS"},{"key":"319_CR26","volume-title":"Sheaves in Geometry and Logic. A First Introduction to Topos Theory","author":"S Mac Lane","year":"1992","unstructured":"Mac Lane, S., Moerdijk, I.: Sheaves in Geometry and Logic. A First Introduction to Topos Theory. Springer, New York (1992)"},{"key":"319_CR27","doi-asserted-by":"crossref","unstructured":"Johnstone, P.: Sketches of an Elephant: A Topos Theory Compendium. Vols. 1,2,3, Oxford Logic Guides, 43, Oxford UP (2002)","DOI":"10.1093\/oso\/9780198515982.003.0004"},{"key":"319_CR28","doi-asserted-by":"publisher","unstructured":"Kr\u00f3l, J., Schumann, A., Bielas, K.: Categorical approach to swarm computations. In Proceedings of the 14th International Joint Conference on Biomedical Engineering Systems and Technologies (BIOSTEC 2021) - Volume 3: BIOINFORMATICS, pp. 218-2 https:\/\/doi.org\/10.5220\/0010389502180224","DOI":"10.5220\/0010389502180224"},{"key":"319_CR29","volume-title":"Handbook of Combinatorics","author":"A Bj\u00f6rner","year":"1995","unstructured":"Bj\u00f6rner, A.: Topological methods. In: Graham, R., Gr\u00f6tschel, M., Lov\u00e1sz, L. (eds.) Handbook of Combinatorics. Elsevier Science, Amsterdam (1995)"},{"key":"319_CR30","volume-title":"Computational Topology","author":"H Edelsbrunner","year":"2010","unstructured":"Edelsbrunner, H., Harer, J.L.: Computational Topology. An Introduction, AMS, USA (2010)"},{"key":"319_CR31","first-page":"253","volume":"69","author":"S Awodey","year":"2020","unstructured":"Awodey, S., Heller, M.: The humunculus brain and categorical logic. Phil. Probl. Sci. 69, 253\u2013280 (2020)","journal-title":"Phil. Probl. Sci."},{"key":"319_CR32","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-91773-3","volume-title":"High-Level Models of Unconventional Computations","author":"A Schumann","year":"2019","unstructured":"Schumann, A., Pancerz, K.: High-Level Models of Unconventional Computations. Springer International Publishing, Berlin (2019)"}],"container-title":["Logica Universalis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11787-022-00319-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11787-022-00319-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11787-022-00319-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,11,29]],"date-time":"2023-11-29T10:32:25Z","timestamp":1701253945000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11787-022-00319-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,10,21]]},"references-count":32,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2022,12]]}},"alternative-id":["319"],"URL":"https:\/\/doi.org\/10.1007\/s11787-022-00319-3","relation":{},"ISSN":["1661-8297","1661-8300"],"issn-type":[{"value":"1661-8297","type":"print"},{"value":"1661-8300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,10,21]]},"assertion":[{"value":"15 August 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"1 November 2021","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"21 October 2022","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}