We propose a notion of the Kripke-style model for intersection logic. Using a game interpretation, we prove soundness and completeness of the proposed semantics. In other words, a formula is provable (a type is inhabited) if and only if it is forced in every model. As a by-product, we obtain another proof of normalization for the Barendregt–Coppo–Dezani intersection type assignment system.

中文翻译：

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交点公式的 Kripke 语义

我们提出了交叉逻辑的 Kripke 风格模型的概念。使用游戏解释，我们证明了所提出语义的合理性和完整性。换句话说，一个公式是可证明的（一个类型被居住）当且仅当它被强制在每个模型中。作为副产品，我们获得了 Barendregt-Coppo-Dezani 交叉口类型分配系统的另一个规范化证明。