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International Symposium on Distributed Computing and Artificial Intelligence

DCAI 2020: Distributed Computing and Artificial Intelligence, 17th International Conference pp 321–331Cite as

Type-Theory of Parametric Algorithms with Restricted Computations

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Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 1237))

Abstract

The paper extends the formal language and reduction calculus of Moschovakis type-theory of recursion, by adding a restrictor operator on terms with predicative constraints. Terms with restrictions over memory variables formalise inductive algorithms with generalised, restricted parameters. The theory provides restricted computations for algorithmic semantics of mathematical expressions and definite descriptors, in formal and natural languages.

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References

  1. Loukanova, R.: Gamma-reduction in type theory of acyclic recursion. Fundam. Inform. 170(4), 367–411 (2019). https://doi.org/10.3233/FI-2019-1867

  2. Loukanova, R.: Gamma-star canonical forms in the type-theory of acyclic algorithms. In: van den Herik, J., Rocha, A.P. (eds.) Agents and Artificial Intelligence. ICAART 2018. Lecture Notes in Computer Science, vol. 11352, pp. 383–407. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-05453-3_18

  3. Loukanova, R.: Type-theory of acyclic algorithms for models of consecutive binding of functional neuro-receptors. In: Grabowski, A., Loukanova, R., Schwarzweller, C. (eds.) AI Aspects in Reasoning, Languages, and Computation, vol. 889, pp. 1–48. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-41425-2_1

  4. Moschovakis, Y.N.: Sense and denotation as algorithm and value. In: Oikkonen, J., Väänänen, J. (eds.) Logic Colloquium ’90: ASL Summer Meeting in Helsinki. Lecture Notes in Logic, vol. 2, pp. 210–249. Springer, Berlin (1993)

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  5. Moschovakis, Y.N.: A logical calculus of meaning and synonymy. Linguist. Philos. 29(1), 27–89 (2006). https://doi.org/10.1007/s10988-005-6920-7

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Author information

Authors and Affiliations

  1. Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Roussanka Loukanova

  2. Stockholm University, Stockholm, Sweden

    Roussanka Loukanova

Authors
  1. Roussanka Loukanova
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Correspondence to Roussanka Loukanova .

Editor information

Editors and Affiliations

  1. Business School, Sichuan University, Chengdu, China

    Yucheng Dong

  2. Andalusian Research Institute on Data Science and Computational Intelligence (DaSCI), University of Granada, Granada, Spain

    Enrique Herrera-Viedma

  3. Dept. of System Design, Osaka Institute of Technology, Osaka, Japan

    Kenji Matsui

  4. Hiroshima University, Osaka, Japan

    Shigeru Omatsu

  5. GRASIA Research Group, Facultad de Informática, Universidad Complutense de Madrid, Madrid, Spain

    Alfonso González Briones

  6. IoT European Digital Innovation Hub, Bioinformatics Intelligent Systems and Educational Technology Research Group, Department of Computer Science, Faculty of Science, University of Salamanca, Salamanca, Spain

    Sara Rodríguez González

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© 2021 The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG

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Cite this paper

Loukanova, R. (2021). Type-Theory of Parametric Algorithms with Restricted Computations. In: Dong, Y., Herrera-Viedma, E., Matsui, K., Omatsu, S., González Briones, A., Rodríguez González, S. (eds) Distributed Computing and Artificial Intelligence, 17th International Conference. DCAI 2020. Advances in Intelligent Systems and Computing, vol 1237. Springer, Cham. https://doi.org/10.1007/978-3-030-53036-5_35

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