多值逻辑与语义赋值博弈

文章在扩展博弈上，给出了多值逻辑的语义赋值博弈的一般框架，避免了博弈者在多值逻辑的语义博弈中声明无穷对象的问题；然后通过Eloise赢的策略定义博弈的语义概念——赋值，证明了多值逻辑的博弈语义与Tarski语义是等价的；最后，根据语义赋值博弈框架对经典逻辑进行了博弈化。

Many-valued Logic and Semantic Evaluation Games

The study of relation between game theory and logic can be traced back to the argumentation of C. S. Peirce. Nevertheless the current boom in game semantics began in the 1980s with the work of Jaakko Hintikka and his followers. Since then game semantics has been extensively studied, and a lot of logics, such as linear logic, modal logic and epistemic logic, have accepted the interpretation of game semantics.
The use of semantic games in many-valued logic was pioneered by Shier Ju and his collaborators. He introduced two external connectives, ＂and＂ and ＂or＂, to describe the truth condition of a formula. The players state the truth-value of many-value logic formu- la with statements, which make it possible for the player to finitely state any truth-value of a formula in finite-valued logic under finite model.
We contribute to this paper by focusing on the framework of semantic evaluation games for many-valued logic. A formula in many-valued logic can be given a ＂gambling＂ interpretation in semantic evaluation game. Formally the semantic evaluation games for many-valued logic are similar to the classical one. The games are defined by a formula φ, a truth-value t and an assignment σ. The positions of the games are labeled by a sub-formula of φ, something about truth-value, such as 〈 t1, t2 〉 , t, and truthvalue set S, and an assignment σ. It can be proven that the many-valued logic is complete with respect to the corresponding semantic evaluation games.
In this semantic evaluation games, the classical implication can be interpreted, which can not be interpreted in Hintikka＇s game, and the infinite statements of Ju＇s game can be avoided.