Implicative filters in quasi-ordered residuated system
DOI:
https://doi.org/10.22199/issn.0717-6279-2021-02-0025Keywords:
Quasi-ordered residuated system, Implicative filter in quasi-ordered residuated systemAbstract
The concept of residuated relational systems ordered under a quasiorder relation was introduced in 2018 by S. Bonzio and I. Chajda as a structure ? = 〈A, ·,→, 1, R〉, where (A, ·) is a commutative monoid with the identity 1 as the top element in this ordered monoid under a quasi-order R. The author introduced and analyzed the concepts of filters in this type of algebraic structures. In this article, as a continuation of previous author’s research, the author introduced and analyzed the concept of implicative filters in quasi-ordered residuated systems.
References
E. Bonzio, "Algebraic structures from quantum and fuzzy logics", PhD Thesis, Università degli studi di Cagliari, 2016. [On line]. Available: https://bit.ly/3bUmb5N
S. Bonzio and I. Chajda, “Residuated relational systems”, Asian-European journal of mathematics, vol. 11, no. 2, Art ID. 1850024, 2018, doi: 10.1142/S1793557118500249
B. Jónsson and A. Tarski, “Representation problems for relation algebras” [Abstract], in Bulletin of the American Mathematical Society, 1948, vol. 54, no. 1, p. 80, doi: 10.1090/S0002-9904-1948-08948-0
R. D. Maddux, “The origin of relation algebras in the development and axiomatization of the calculus of relations”, Studia logica, vol. 50, no. 3, pp. 421-455, 1991, doi: 10.1007/BF00370681
D. A. Romano, “Filters in residuated relational system ordered under quasi-order”, Bulletin International Mathematics Virtual Institute, vol. 10, no. 3, pp. 529-534, 2020, doi: 10.7251/BIMVI2003529R
A. Tarski, “On the calculus of relations”, The journal of symbolic logic, vol. 6, no. 3, pp. 73-89, 1941, doi: 10.2307/2268577
A. Tarski and S. R. Givant, A formalization of set theory without variables. Providence, RI: AMS, 1987.
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