命题逻辑公式

Later, based on the same idea, Li Jun gave the theory of truth degrees of formulas in many-valued Lukasiewicz propositional logic and canonical sequence logic system.

随后李骏基于相同思想给出了Lukasiewicz多值命题逻辑与标准序列逻辑系统中公式的真度理论。

At last, we give two simplified proof for the necessary lemma in order to prove the completeness theorem of PI resolving.

第二部分：基于均匀概率的思想，给出了Godel和Kleene三值命题逻辑系统中公式的真度理论。

A formula of propositional logic is said to be satisfiable if logical values can be assigned to its variables in a way that makes the formula true.

公式命题逻辑被认为是符合要求，如果逻辑值可分配给它的变量的方式，使真正的公式。

The concept of relative Γ-tautology degree of formulas in four important propositional logics, Lukasiewicz logic, L(superscript *) logic, Gdel logic and product logic, has been proposed, and basic properties of it are obtained.

基于广义重言式理论，在四种重要的命题逻辑系统Lukasiewicz系统，L系统，Gdel系统和Ⅱ系统中，引入了公式的相对Γ-重言度概念，给出了相对Γ-重言度的若干性质。

Disjunction normal form theorem in the modal logic system S5 is inductively proved, which can be used for representing complex modal formulas by means of conjunction and disjunction of simplest modal formulas with depth at most 1 in the system S5. As application, it is proved that a knowledge base could answer KB-queries if and only if it could answer queries of non-modal propositions and their negations, which is a basic problem on knowledge base.

研究了模态逻辑系统S5中的析取范式定理的归纳证明，给出了在S5中用深度至多等于1的最简模态公式通过析取与合取运算表示含有多重模态词的公式的方法，作为范式定理的应用，讨论了知识库中的一个基本问题，证明了知识库能够回答KB命题式问题的充要条件是该知识库能够回答相关的非模态命题及其否定命题的问题。

The above all the theory of truth degrees of formulas are proposed in propositional logic.

以上各种真度理论都是在命题逻辑中给出的，对于谓词逻辑而言，建立公式的真度理论要复杂得多。

Early in 1952 Rosser and Turquette proposed the idea of distinguishing reliabilities of formulas in the propositional logic, and this idea was discussed and developed by many scholars from different points of view.

关于区分命题逻辑中公式可靠程度的思想早在1952年就由Rosser与Turequtte提出，多年来许多学者从不同的角度提出了确定这类公式真确程度的方法。

By employing the theory of ∑Γ－fuzzy truth degree, the concepts of Γ-pseudometric on F was proposed in the propositional logic system Ln. The results obtained can complement and enhance the original theory of metrology of logic, and can give a new frame for fuzzy reasoning study.

特别地证明了真度关系：τΓ+τΓ≤1+τΓ，并利用这一关系在模糊命题演算系统Ln中的公式集F上引入相对于有限理论的Γ-伪距离，从而为在模糊命题逻辑系统Ln中建立相对于有限理论的近似推理框架奠定了基础。

By employing the theory of ∑Γ－fuzzy truth degree, the concepts of Γ-pseudometric on F was proposed in the propositional logic system Ln.

特别地证明了真度关系：τΓ+τΓ≤1+τΓ，并利用这一关系在模糊命题演算系统Ln中的公式集F上引入相对于有限理论的Γ-伪距离，从而为在模糊命题逻辑系统Ln中建立相对于有限理论的近似推理框架奠定了基础。

We show that there is a polynomial over the rational number field Q corresponding to a given porpositional formula in a given many-valued logic.

本文证明了对于给定的多值逻辑系统中的命题公式，存在有理数域上的多项式与之对应。

Plunder melds and run with this jewel!

掠夺melds和运行与此宝石！

My dream is to be a crazy growing tree and extend at the edge between the city and the forest.

此刻，也许正是在通往天国的路上，我体验着这白色的晕旋。