Nilpotent Minimum Logic NM and Pretabularity

Eunsuk Yang

Bulletin of the Section of Logic (2020)

  • Volume: 49, Issue: 1
  • ISSN: 0138-0680

Abstract

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This paper deals with pretabularity of fuzzy logics. For this, we first introduce two systems NMnfp and NM½, which are expansions of the fuzzy system NM (Nilpotent minimum logic), and examine the relationships between NMnfp and the another known extended system NM-. Next, we show that NMnfp and NM½ are pretabular, whereas NM is not. We also discuss their algebraic completeness.  

How to cite

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Eunsuk Yang. "Nilpotent Minimum Logic NM and Pretabularity." Bulletin of the Section of Logic 49.1 (2020): null. <http://eudml.org/doc/295553>.

@article{EunsukYang2020,
abstract = {This paper deals with pretabularity of fuzzy logics. For this, we first introduce two systems NMnfp and NM½, which are expansions of the fuzzy system NM (Nilpotent minimum logic), and examine the relationships between NMnfp and the another known extended system NM-. Next, we show that NMnfp and NM½ are pretabular, whereas NM is not. We also discuss their algebraic completeness.  },
author = {Eunsuk Yang},
journal = {Bulletin of the Section of Logic},
keywords = {pretabularity; nilpotent minimum logic; algebraic semantics; fuzzy logic; finite model property},
language = {eng},
number = {1},
pages = {null},
title = {Nilpotent Minimum Logic NM and Pretabularity},
url = {http://eudml.org/doc/295553},
volume = {49},
year = {2020},
}

TY - JOUR
AU - Eunsuk Yang
TI - Nilpotent Minimum Logic NM and Pretabularity
JO - Bulletin of the Section of Logic
PY - 2020
VL - 49
IS - 1
SP - null
AB - This paper deals with pretabularity of fuzzy logics. For this, we first introduce two systems NMnfp and NM½, which are expansions of the fuzzy system NM (Nilpotent minimum logic), and examine the relationships between NMnfp and the another known extended system NM-. Next, we show that NMnfp and NM½ are pretabular, whereas NM is not. We also discuss their algebraic completeness.  
LA - eng
KW - pretabularity; nilpotent minimum logic; algebraic semantics; fuzzy logic; finite model property
UR - http://eudml.org/doc/295553
ER -

References

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  10. [10] C. Noguera, F. Esteva, and J. Gispert, On triangular norm based axiomatic extensions of the weak nilpotent minimum logic, Mathematical Logic Quarterly, Vol. 54 (2008), pp. 387–409. 
  11. [11] V. Rybakov, V. Kiyatkin, and M. Terziler, Independent bases for rules admissible in pretabular logics, Logic Journal of the Interest Group in Pure and Applied Logics, Vol. 7 (1999), pp. 253–266. 
  12. [12] T. Sugihara, Strict implication free from implicational paradoxes, Memoirs of the Faculty of Liberal Arts, Fukui University, Series 1, 1955, pp. 55–59. 
  13. [13] K. Świrydowicz, There exists an uncountable set of pretabular extensions of the relevant logic R and each logic of this set is generated by a variety of nite height, The Journal of Symbolic Logic, Vol. 73 (2008), pp. 1249–1270. 

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