论文标题
Lambek演算与相交和常数的关系模型
Relational Models for the Lambek Calculus with Intersection and Constants
论文作者
论文摘要
我们考虑使用与零和单位的相交和显式常数扩展的Lambek微积分的关系语义（R模型）。对于没有常数的变体和不允许空前的限制，Andreka and Mikulas（1994）证明了强烈的完整性。我们表明，它在没有这种限制的情况下失败了，但另一方面，它证明了对常数的非标准解释的完整性较弱。对于标准解释，即使是弱的完整性也会失败。弱完整性结果扩展到了无限的环境，用于所谓的迭代师（下属的克莱恩之星）。我们还证明了无产品碎片的完整性结果。
We consider relational semantics (R-models) for the Lambek calculus extended with intersection and explicit constants for zero and unit. For its variant without constants and a restriction which disallows empty antecedents, Andreka and Mikulas (1994) prove strong completeness. We show that it fails without this restriction, but, on the other hand, prove weak completeness for non-standard interpretation of constants. For the standard interpretation, even weak completeness fails. The weak completeness result extends to an infinitary setting, for so-called iterative divisions (Kleene star under division). We also prove strong completeness results for product-free fragments.
