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A semantics and a logic for Fuzzy Arden Syntax

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Abstract

Fuzzy programming languages, such as the Fuzzy Arden Syntax (FAS), are used to describe behaviours which evolve in a fuzzy way and thus cannot be characterized neither by a Boolean outcome nor by a probability distribution. This paper introduces a semantics for FAS, focusing on the weighted parallel interpretation of its conditional statement. The proposed construction is based on the notion of a fuzzy multirelation which associates with each state in a program a fuzzy set of weighted possible evolutions. The latter is parametric on a residuated lattice which models the underlying semantic ‘truth space’. Finally, a family of dynamic logics, equally parametric on the residuated lattice, is introduced to reason about FAS programs.

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Notes

  1. Note that while the most common nomenclature for \(\leftarrow \) (\(\rightarrow \)) is right (left) division, we follow reference Kozen (1993), where \(\leftarrow \) (\(\rightarrow \)) is called left (right) residual.

  2. Note that the system only suggests a modification in the value of PIP_inc and such alteration is carried out manually by some health professional.

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Acknowledgements

This work was founded by the ERDF—European Regional Development Fund through the Operational Programme for Competitiveness and Internationalisation—COMPETE 2020 Programme and by National Funds through the Portuguese funding agency, FCT—Fundação para a Ciência e a Tecnologia, within projects POCI-01-0145-FEDER-030947 and POCI-01-0145-FEDER-029946

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The three authors contributed to the planning, design and writing of the manuscript. The conception of the definitions, results and correspondent proofs were regularly discussed by the three authors. The first draft of the manuscript was written by Leandro Rafael Moreira Gomes, and all authors read and comment on each version and future directions to take. The final version was read and approved by all authors.

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Correspondence to Leandro Gomes.

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Communicated by Tomas Veloz.

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Gomes, L., Madeira, A. & Barbosa, L.S. A semantics and a logic for Fuzzy Arden Syntax. Soft Comput 25, 6789–6805 (2021). https://doi.org/10.1007/s00500-021-05593-9

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