IF多值逻辑及博弈语义

IF Many-valued Logic and Game-theoretical Semantics

本文基于经典一阶逻辑句法的逻辑优先性分析,把Hintikka的独立联结词和独立量词扩展到多值逻辑中。我们给出IF多值逻辑的句法,并使用不完全信息的语义赋值博弈解释了IF多值逻辑。

In classical first order logic the scopes of quantifiers are always either nested or disjoint. But we have no reason to limit a quantifier to be dependent on the quantifiers which have precedence over it. Hintikka and Sandu introduced a slash operator to make other dependency patterns possible. This operator can be introduced into ordinary first order formulas to remove quantifications and connectives from the scope of previous quantification. In this paper, we clarify the concept of logical priority in IF logic of Hintikka, and then extend many-valued logic to IF many-valued logic by the independent connectives and independent quantifiers. We provide the syntax and semantics of IF many-valued logic, which is based on semantic evaluation game of incomplete information.