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1. chinaXiv:201812.00137 [pdf]


黄潇潇; 张宝山; 张媛
Subjects: Psychology >> Developmental Psychology


submitted time 2018-12-16 Hits6511Downloads975 Comment 0

2. chinaXiv:201709.00007 [pdf]

On derivations of MV-algebras

王军涛; Bijan Davvaz; 贺鹏飞
Subjects: Physics >> General Physics: Statistical and Quantum Mechanics, Quantum Information, etc.

In this paper, we investigate related properties of some particular derivations and give some characterizations of additive derivations in MV-algebras. Then, we obtainthat the #12;xed point set of additive derivations is still an MV-algebra. Also,we study Boolean additive derivations and their adjoint derivations. In particular, we get that the #12;xed point set of Boolean addition derivations and that of their adjoint derivations are isomorphism. Moreover, we prove that every MV-algebra is isomorphic to the direct product of the #12;xed point set of Boolean additive derivations and that of their adjoint derivations. Finally, we show that the structure of a Boolean algebra is completely determined by its set of all Boolean additive (implicative) derivations.

submitted time 2017-09-09 Hits1260Downloads542 Comment 0

3. chinaXiv:201703.00918 [pdf]

Monadic NM-algebras

王军涛; 辛小龙; 贺鹏飞
Subjects: Mathematics >> Mathematics (General)

The main goal of this paper is to investigate (strong) monadic NM-algebras and to prove the (chain) completeness of the monadic NM-logic. In this paper, we introduce monadic NM-algebras: a variety of NM-algebras equipped with universal quanti#12;ers. Also, we study some properties of them and obtain some conditions under which a monadic NM-algebra becomes a monadic Boolean algebra. Besides, we show that the variety of NM-algebras are the equivalent algebraic semantics of the monadic fragment of NM predicate logic. Furthermore, we discuss relations between monadic NM-algebras and some related structures, likeness modal NMalgebras and rough approximation spaces. In addition, we introduce and investigate monadic #12;lters in monadic NM-algebras. In particular, by using monadic #12;lters on monadic NM-algebras, we characterize two kinds of monadic NM-algebras, which are simple and subdirectly irreducible. Moreover, we focus on a monadic analogous of representation theorem for NM-algebras and obtain that every strong monadic NM-algebra can be represented as subalgebras of products of linearly ordered ones. Then, we present monadic NM-logic, a system of many-valued logic capturing the tautologies of the predicate logics of nilpotent minimum t-norm and it's residua. As an application of (strong) monadic NM-algebras, we prove the (chain)completeness of monadic NM-logic. Our results constitute a crucial #12;rst step for providing a solid algebraic foundation for the one element fragment of NM predicate logic.

submitted time 2017-03-29 Hits7061Downloads1079 Comment 0

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