NMG-代数中同态核的结构刻画

发布时间：2018-05-23 21:12

本文选题：概率计量逻辑 + NMG-代数　；参考：《软件学报》2017年10期

【摘要】：逻辑代数上的Bosbach态与Rie?an态是经典概率论中Kolmogorov公理的两种不同方式的多值化推广,也是概率计量逻辑中语义计量化方法的代数公理化,是非经典数理逻辑领域中的重要研究分支.现已证明具有Glivenko性质的逻辑代数上的Bosbach态与Rie?an态等价,并且逻辑代数的Glivenko性质是研究态算子的构造和存在性的重要工具,因而是态理论中的研究热点之一.研究了NMG-代数基于核算子的Glivenko性质,证明NMG-代数具有核基Glivenko性质的充要条件是该核算子是从此NMG-代数到其像集代数的同态,并给出NMG-代数中同态核的结构刻画.这里,NMG-代数是刻画序和三角模([0,1 2],T_(NM)),([1 2,1],T_M)的逻辑系统NMG的语义逻辑代数.
[Abstract]:Bosbach state and Rie?an state on logic algebra are two different ways of multivalued generalization of Kolmogorov axiom in classical probability theory. They are also algebraic axioms of semantic metrology methods in probabilistic metrological logic. They are important branches in the field of non-classical mathematical logic. It has been proved that the Bosbach state of logic algebra with Glivenko property is equivalent to Rie?an state, and the Glivenko property of logic algebra is an important tool to study the construction and existence of state operator, so it is one of the research hotspots in state theory. In this paper, we study the Glivenko properties of NMG- algebras based on the estimators, and prove that NMG- algebras have kernel basis Glivenko properties if and only if the estimators are homomorphisms from NMG- algebras to their image set algebras, and the structural characterization of homomorphic kernels in NMG- algebras is given. Here NMG- algebra is a semantic logical algebra characterizing the logical system NMG of order and triangular modules ([0 / 12] / T / T / T / T / T / T / T / T / T / T / T / T / T / T / T / T / T).
【作者单位】：陕西师范大学数学与信息科学学院;
【基金】：国家自然科学基金(61473336,11171200) 陕西省青年科技新星计划(2016KJXX-24) 中央高校基本科研业务费专项资金特别支持项目(GK201403001)~~
【分类号】：O153

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