In this paper, we consider first-order mathematical fuzzy logic expanded by many hedges. This is based on the fact that, in the real world, many hedges can be used simultaneously, and some hedge modifies truth (or meaning of sentences) more than another hedge. Moreover, each hedge may or may not have a dual one. We expand two axiomatizations for propositional mathematical fuzzy logic with many hedges to the first-order level and prove a number of completeness results for the resulting logics. We also consider logics with many hedges based on -core fuzzy logics.

1. David C. Wyld et al. (Eds) : DBDM, CICS, CSIP, AI&FL, SCOM, CSE, CCNET-2016
pp. 85–96, 2016. © CS & IT-CSCP 2016 DOI : 10.5121/csit.2016.60509
FIRST-ORDER MATHEMATICAL FUZZY
LOGIC WITH HEDGES
Van-Hung Le
Faculty of Information Technology,
Hanoi University of Mining and Geology, Vietnam
levanhung@humg.edu.vn
ABSTRACT
In this paper, we consider first-order mathematical fuzzy logic expanded by many hedges. This
is based on the fact that, in the real world, many hedges can be used simultaneously, and some
hedge modifies truth (or meaning of sentences) more than another hedge. Moreover, each hedge
may or may not have a dual one. We expand two axiomatizations for propositional
mathematical fuzzy logic with many hedges to the first-order level and prove a number of
completeness results for the resulting logics. We also consider logics with many hedges based
on -core fuzzy logics.
KEYWORDS
Mathematical Fuzzy Logic, First-Order Logic, Hedge, Strong Completeness, Standard
Completeness
1. INTRODUCTION

2. 86 Computer Science & Information Technology (CS & IT)
2. PRELIMINARIES
2.1. Preliminaries on Mathematical Fuzzy Logic

3. Computer Science & Information Technology (CS & IT) 87
2.2. An Axiomatization for Many Hedges

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2.3. Mathematical Fuzzy logic with Many Dual Hedges

5. Computer Science & Information Technology (CS & IT) 89

6. 90 Computer Science & Information Technology (CS & IT)
3. FIRST-ORDER MATHEMATICAL FUZZY LOGIC WITH HEDGES

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8. 92 Computer Science & Information Technology (CS & IT)

9. Computer Science & Information Technology (CS & IT) 93
4. LOGICS WITH HEDGES BASED ON A -CORE FUZZY LOGIC

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5. CONCLUSION
ACKNOWLEDGEMENTS
Funding from HUMG under grant number T16-02 is acknowledged.
REFERENCES

12. 96 Computer Science & Information Technology (CS & IT)
AUTHOR
Van-Hung Le received a B.Eng. degree in Information Technology from Hanoi
University of Science and Technology (formerly, Hanoi University of Technology) in
1995, an M.Sc. degree in Information Technology from Vietnam National University,
Hanoi in 2001, and a PhD degree in Computer Science from La Trobe University,
Australia in 2010. He is a lecturer in the Faculty of Information Technology at Hanoi
University of Mining and Geology. His research interests include Fuzzy Logic, Logic
Programming, Soft Computing, and Computational Intelligence.