逻辑演算

An axiomatization of the object calculus as an extension of the axiom system of the trace calculus is also contributed in this paper.

作为逻辑系统，文章还讨论了对象演算的公理化，它是Trace演算公理系统的扩充。

The course contains four sections as follows: mathematical logic (including basic concepts of propositional logic and predicate logic, propositional calculuses and inference theories), set theory (including set algebras, relations, functions and cardinal numbers), algebraic structure (including algebraic systems, semigroups and groups, rings and fields, lattices and Boolean algebras), graph theory (including basic concepts of graph, Euler graphs and Hamiltonian graphs, trees, planar graphs and coloring graphs, some special vertex subsets and edge subsets).

本课程包含四部分内容：数理逻辑（包含命题逻辑与一阶逻辑的基本概念、等值演算以及推理理论），集合论（包含集合代数、二元关系、函数和基数），代数结构（包含代数系统、半群与群、环与域、格与布尔代数），图论（包含图的基本概念、欧拉图与哈密顿图、树、平面图及图的着色、图的某些特殊的顶点子集与边子集）。

This theory emerged from those philosophical and logical inquires Russell made in his early stage, when Russell use logical analysis to solve the semantics problem his meaning theory suffered. The foundation of the theory of descriptions is a theory of meaning, as this thesis presents, and its central notion includes two syntax rules. Based on the first order predicates calculus, this theory seems successfully solve some notable semantics problems and then assures Russell's denotation theory.

本文认为，摹状词理论有深刻的哲学渊源，它脱胎于罗素早期的哲学和逻辑研究，直接缘起于罗素想要利用逻辑的分析方法去解决意义指谓论所面临的语义学难题；摹状词理论的基础是它的意义理论，核心是两个句法规则，它基于带等词的一阶谓词演算成功地解决了一些著名的语义学难题，维护了直观的指谓论，从而产生了巨大而深刻的哲学影响。

Based on the eight Chinese traditional yin and yang contradiction categories to analyze among the open and close areas in mathematics to achieve the triple unity of opposite composing relation of identical,resemble,diversity and contrary,the four basic types of logical inference.

用中华传统8大阴阳矛盾范畴分析数学中的开闭区间，得出相同、相似、相异、相反这4大逻辑推理基础类型间存在着三极对立统一的组成关系，进而提出涉及此组成关系的逻辑推理基础类型的互蕴公理及其描述内涵的反演算和逻辑外延的非演算。

It introduces the basic knowledge and ideas of mathematical logic and classic set theory, including proposition logic and predicate logic, reasoning calculus and theorem proving methods, basic operations and properties of sets and relations, functions of any sets and their properties, the cardinals of infinite sets, and the applications of knowledge and ideas above in computer sciences.

本课程系统介绍数理逻辑与朴素集合论的基础知识，包括：命题逻辑和谓词逻辑、定理的推理演算和机器证明方法，集合和二元关系的基本运算和性质、任意集合中的函数及其性质，无穷集合的基数，以及上述知识在计算机科学中的应用。

In the meantime, we also can change the status of the logic situations and describe the allying process and cooperative process. In addition, we represent the virtual enterprise ontology in the formal logic situation calculus and can define the core elements more accurately. It maintains the consistency and integrality of the ontology. Accordingly, the process model based on the ontology will have strong reusability, accessibility and consistency.

相应地，我们可通过逻辑情景演算这种形式化逻辑框架来表示虚拟企业本体论，以支持虚拟企业本体论中核心术语的更精确定义，维持其一致性和完整性；进而，构建于该本体论之上的虚拟企业过程模型就具有很强的重用性和可访问性，并能够保持建模过程的一致性。

To the predicate calculus on Intuitionistic Fuzzy Logic, a symmetric synthetic method for finding the truth of IFL propositions using membership and hesitancy degree is proposed on the basis of the hypothesis of an equilibrium state of supportability and opposability of neutral evidences indicated in the intuitionistic index. The fundamental operation rules on IFL propositions are presented.

摘要针对直觉模糊逻辑及命题演算，基于直觉指数所表征的中立证据中支持与反对的程度呈均衡状态的假设，提出利用隶属度与犹豫度计算直觉模糊逻辑命题真值的对称合成方法，给出直觉模糊逻辑命题的运算规则。

But for those of us who move onto this more advanced stage, Lee's team said "this shift in strategy is analogous to shifting from proofs in the first-order predicate calculus to proofs in the first-order modal predicate calculus"- in other words, it's a pretty impressive display of logical prowess and further evidence of our ability to "make deductions about abstract matters remote from our mundane life".

但是我们中的那些进入更高等级的玩家，Lee的团队说，"这次策略的转换同从一阶谓词演算证据到一阶情态谓词演算证据非常类似"——换句话说，这是一次令人印象深刻的展示：逻辑的力量和我们具备对"远离日常生活的抽象事物进行演绎"的能力。

In 1879, the publication of ""Concept Writing"" marks the foundation of propositional calculus and the predicate calculus —— the basic part of mathematical logic.

1879年《概念文字》的出版，标志着数理逻辑的基础部分——命题演算和谓词演算正式建立。

Prepositional logic: also known as prepositional calculus or sentential calculus, is the study of the truth conditions for propositions: how the truth of a composite proposition is determined by the truth value of its constituent propositions and the connections between them.

命题逻辑：也叫命题演算或句子演算，研究命题的真值条件：复合命题真值是如何由成分命题真值及成分命题之间的关系决定的。

This is not an ordinary box, which is used as a background picture of the dialog box, very pretty.

详细说明：这可不是一个一般的对话框，它是用图片作为背景的对话框，非常好看。

Conceal me what I am,and be my aid for such disguise as haply shall become the form of my intent.

遮掩我的身份，帮助我，我的面具将成为我的目的。