Abstract
In this paper the concept of tense operators on a pseudo-MV algebra is introduced. Since a pseudo-MV algebra can be regarded as an axiomatization of non-commutative infinite-valued Łukasiewicz logic, these tense operators are considered to quantify the dimension, i.e. one expresses “it is always going to be the case that” and the other expresses “it has always been the case that”. We investigate basic properties of tense operators on pseudo-MV algebras and characterize the homomorphism of tense pseudo-MV algebras. Finally, we define a stronger version of tense pseudo-MV algebras and discuss the properties of filters under tense operators.
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Acknowledgments
I would like to show my sincere thanks to the referees for their valuable comments. This project is supported by the National Natural Science Foundation of China (Grant No. 11501245).
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Chen, WJ. (2017). Tense Operators on Pseudo-MV Algebras. In: Fan, TH., Chen, SL., Wang, SM., Li, YM. (eds) Quantitative Logic and Soft Computing 2016. Advances in Intelligent Systems and Computing, vol 510. Springer, Cham. https://doi.org/10.1007/978-3-319-46206-6_34
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DOI: https://doi.org/10.1007/978-3-319-46206-6_34
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