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Multimodal epistemic Łukasiewicz logics with application in immune system

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Abstract

We offer a new logic, a multimodal epistemic Łukasiewicz logic, which is an extension of the infinitely valued Łukasiewicz logic, the language of the logic is an extended by unary connectives that are interpreted as modal operators (knowledge operators). We propose the use such a logic in studying immune system. A relational system is developed as a semantic of this logic. The relational systems represent the immune system which in its turn is a part of relational biology.

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Notes

  1. The logic EŁ(n) (EŁ\(^{\Box }(n))\) is obtained by elimination of Ł\(_3\)-axiom \((\varphi \) & \(\varphi ) \leftrightarrow (\varphi \) & \(\varphi \) & \(\varphi )\) from the axioms of EŁ(n) (EŁ\(^{\Box }(n))\).

References

  • Belluce LP, Grigolia R, Lettieri A (2005) Representations of monadic MV-algebras. Stud. Log. 81:125–144

    MathSciNet  Google Scholar 

  • Blackburn P, de Rijke M, Venema Y (2001) Modal logic. In: Cambridge tracts in theoretical computer science, vol 53. Cambridge University Press, Cambridge

  • Bou F, Esteva F, Godo L, Rodríguez R (2007) \(n\)-Łukasiewicz modal logic. Manuscript

  • Caicedo X, Rodríguez R (2007) A Gödel similarity based modal logic, Manuscript. A shortened version was published as A Gödel modal logic. In: Proceedings of logic, computability and randomness 2004. Cordoba, Argentina

  • Chagrov A, Zakharyaschev M (1997) Modal logic. In: Oxford logic guides, vol 35. Oxford University Press, Oxford

  • Di Nola A, Grigolia R (2004) On monadic MV-algebras. APAL 128(1–3):125–139

    MATH  Google Scholar 

  • Fitting M (1992a) Many-valued modal logics. Fundam Inform 15:235–254

  • Fitting M (1992b) Many-valued modal logics, II. Fundam Inform 17:55–73

  • Häggström M (2014) Medical gallery of Mikael Hggstrm 2014. Wikiversity J Med 1(2). doi:10.15347/wjm/2014.008. ISSN 20018762

  • Hajek P (1998) Metamathematics of fuzzy logic. Kluwer Academic Publishers, Dordrecht

    Book  MATH  Google Scholar 

  • Hansoul G, Teheux B (2006) Completeness results for many-valued Łukasiewicz modal systems and relational semantics. Available at arXiv:math/0612542

  • Koutras CD (2003) A catalog of weak many-valued modal axioms and their corresponding frame classes. J Appl Non-Class Log 13(1):4772

    Article  MathSciNet  Google Scholar 

  • Li MO, Wan YY, Flavell RA (2007) T cell-produced transforming growth factor-1 controls T cell tolerance and regulates Th1- and Th17-cell differentiation. Immunity 26(5):579–591

    Article  Google Scholar 

  • Luckheeram RV, Zhou R, Verma AD, Xia B (2012) CD4+T cells: differentiation and functions. Clin Dev Immunol 2012:12. doi:10.1155/2012/925135

  • Mironov AM (2005) Fuzzy modal logics. J Math Sci 128(6):3461–3483

    Article  MathSciNet  Google Scholar 

  • Ostermann P (1988) Many-valued modal propositional calculi. Zeitschrift für Mathematische Logik und Grundlagen der Mathematik 34(4):343–354

    Article  MATH  MathSciNet  Google Scholar 

  • Porter T (2003) Geometric aspects of multiagent systems. In: Electronic notes in theoretical computer science, vol 81. http://www.elsevier.nl/locate/entcs/volume81.html

  • Rang HP (2003) Pharmacology. Churchill Livingstone, Edinburgh, p 223. ISBN: 0-443-07145-4

  • Rashevsky N (1972) Organismic sets. J.M. Richards Lab, Grosse-Pointe Park, MI

  • Rosen R (1958a) A relational theory of biological systems. Bull Math Biophys 20:245–260

  • Rosen R (1958b) The representation of biological systems from the standpoint of the theory of categories. Bull Math Biophys 20:317–342

  • Rutledge JD (1959) A preliminary investigation of the infinitely many-valued predicate calculus. PhD Thesis, Cornell University

  • Suzuki NY (1997) Kripke frame with graded accessibility and fuzzy possible world semantics. Stud Log 59(2):249269

    Article  Google Scholar 

  • Tao X, Constant S, Jorritsma P, Bottomly K (1997) Strength of TCR signal determines the costimulatory requirements for Th1 and Th2 CD4\(^+\) T cell differentiation. J Immunol 159(12):5956–5963

  • Trinchieri G, Pflanz S, Kastelein RA (2003) The IL-12 family of heterodimeric cytokines: new players in the regulation of T cell responses. Immunity 19(5):641–644

    Article  Google Scholar 

  • Woodger H (1937) The axiomatic method in biology. Cambridge University Press, Cambridge

    MATH  Google Scholar 

  • Yagi H, Nomura T, Nakamura K et al (2004) Crucial role of FOXP3 in the development and function of human CD25\(^+\)CD4\(^+\) regulatory T cells. Int Immunol 16(11):1643–1656

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, University of Salerno, Fisciano, Italy

    Antonio Di Nola

  2. Department of Mathematics, Iv. Javakhishvili Tbilisi State University, Tbilisi, Georgia

    Revaz Grigolia

  3. Department of Biology, Iv. Javakhishvili Tbilisi State University, Tbilisi, Georgia

    Nunu Mitskevich

Authors
  1. Antonio Di Nola
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  2. Revaz Grigolia
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  3. Nunu Mitskevich
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Correspondence to Antonio Di Nola.

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Communicated by V. Loia.

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Di Nola, A., Grigolia, R. & Mitskevich, N. Multimodal epistemic Łukasiewicz logics with application in immune system. Soft Comput 19, 3341–3351 (2015). https://doi.org/10.1007/s00500-015-1804-4

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