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if and only if
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    The notions of FSI ideals and FSC ideals are introduced. It is shown that a fuzzy subset of a BCI algebra is an FSI ideal if and only if it is both an FSC ideal and a fuzzy BCI positive implicative ideal.
    引入FSI理想和FSC理想的概念,证明了BCI代数的一个Fuzzy子集是一个FSI理想当且仅当它是一个FSC理想和一个Fuzzy BCI正定关联理想.
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    It is shown that a nonempty subset of a BCI algebra is a BCI implicative ideal if and only if it is both a BCI commutative ideal and a BCI positive implicative ideal. This generalizes the famous result in BCK algebras: a nonempty subset of a BCK algebra is an implicative ideal if and only if it is both a commutative ideal and a positive implicative ideal.
    证明了BCI代数的一个非空子集是BCI关联理想当且仅当它既是BCI交换理想又是BCI正定关联理想,从而揭示了这三类理想之间的内在联系,并将BCK代数中知名论断:BCK代数的一个非空子集是关联理想当且仅当它既是交换理想又是正定关联理想,推广到BCI代数上去。
短句来源
    An epistemic proposition is true if and only if it is a member of corresponding world.
    一个认知命题是真的,当且仅当它属于相应的认知世界之中。
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This implies that a system is algebraically integrable (i.e., its eigenvalue problem is explicitly solvable in quadratures) if and only if the differential Galois group is commutative for generic eigenvalues.
      
TheS-arithmetic group г is of typeFn, resp.FPn, if and only if for allp inS thep-adic completionGp of the corresponding algebraic groupG is of typeCn resp.CPn.
      
We show that in the modular case, the ring of invariants in is of this form if and only if is a polynomial algebra and all pseudoreflections in ?(G) are diagonalizable.
      
Specifically, a subset is complete if and only if it contains infinitely many even-order autocorrelation functions.
      
We next show that this result is best possible by including a result of Kalton: A frame can be represented as a linear combination of two orthonormal bases if and only if it is a Riesz basis.
      
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The preferential inference system P, the cumulative monotonic inference system CM and the formal deductive system L~* for fuzzy propositional calculus have been studied. In system L~*, the consequence relation |~: for A,B∈F(S),A|~B if and only if A~2├B are defined. It is proved that this consequence relation satisfies the all rules of nonmonotonic inference system CM and nonmonotonic inference system P, but this consequence relation does not satisfy the rule of contraposition in monotonic system M. Therefore,...

The preferential inference system P, the cumulative monotonic inference system CM and the formal deductive system L~* for fuzzy propositional calculus have been studied. In system L~*, the consequence relation |~: for A,B∈F(S),A|~B if and only if A~2├B are defined. It is proved that this consequence relation satisfies the all rules of nonmonotonic inference system CM and nonmonotonic inference system P, but this consequence relation does not satisfy the rule of contraposition in monotonic system M. Therefore, this paper presents an example of combining the nonmonotonic system with fuzzy inference logic system. A new idea is presented for studying the theory and application of two systems in fuzzy controlling and expert system.

研究了非单调优先推理系统P和累积单调推理系统CM,以及模糊命题演算的形式演绎系统L ,在L 系统中定义了后承关系|~:A|~B当且仅当A2├B,证明了在L 系统中的这种后承关系满足累积单调推理系统CM,非单调优先推理系统P的全部规则,但这种后承关系不满足单调推理系统M的逆否律规则,从而在L 系统中建立了一个介于非单调推理系统和单调推理系统之间的逻辑系统.这为两种系统的理论研究建立一个桥梁以及为模糊控制提供了一种新的思路.

The epistemic worlds can be partitioned into three parts: belief world,doubting world and ignorance world.Epistemic propositions are elements of them.The three worlds form an epistemic wholeness,and they are not overlapped.An epistemic proposition is true if and only if it is a member of corresponding world.According to such tri-partitioning of epistemic worlds,doubting logic which researches logic relationship among propositions of doubting world is independent.It couldn't be established by transformation...

The epistemic worlds can be partitioned into three parts: belief world,doubting world and ignorance world.Epistemic propositions are elements of them.The three worlds form an epistemic wholeness,and they are not overlapped.An epistemic proposition is true if and only if it is a member of corresponding world.According to such tri-partitioning of epistemic worlds,doubting logic which researches logic relationship among propositions of doubting world is independent.It couldn't be established by transformation of belief logic.Belief logic,doubting logic and ignorance logic are three independent epistemic logic.

主体的认知世界可以划分为“信念世界(WB)”、“怀疑世界(WD)”和“无知世界(WU)”,这三个世界中的元素是认知命题。这三个世界之间是不重叠的,并且它们构成一个认知世界全集。一个认知命题是真的,当且仅当它属于相应的认知世界之中。有了这样的划分,研究怀疑世界中的认知命题之间的逻辑关系的怀疑逻辑是独立的,它不能通过信念逻辑的变形而得到。怀疑逻辑、无知逻辑与信念逻辑构成三个相互独立的逻辑系统。

 
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