论文标题
兰贝克微积分的某些扩展的语言模型
Language Models for Some Extensions of the Lambek Calculus
论文作者
论文摘要
我们研究了Lambek演算的两个扩展的语言解释：具有添加剂的结合和脱节，并具有添加剂的结合和单位常数。对于具有添加剂连接剂的扩展，我们表明连词和分离的行为不同。添加它们两个导致由于分配法而导致不完整。我们表明，通过连词没有出现分发性问题。相比之下，语言中存在分布性法的必然性，仅在非分布系统中无法衍生。此外，这种差异对于具有置换和/或削弱结构规则的系统，即直觉的线性和仿射逻辑以及仿射乘法性添加的lambek cyculus保持有效。对于用单位常数扩展Lambek，我们提出了一个演算，它反映了空词的自然代数特性。我们没有要求对此微积分声称完整性，但是我们证明了整个系统范围的范围不可证明，扩展了这种最小的演算和声音W.R.T.语言模型。作为推论，我们表明，在使用单元的语言中，如果所有变量都用常规语言解释，但在语言模型中不正确，则是真实的。
We investigate language interpretations of two extensions of the Lambek calculus: with additive conjunction and disjunction and with additive conjunction and the unit constant. For extensions with additive connectives, we show that conjunction and disjunction behave differently. Adding both of them leads to incompleteness due to the distributivity law. We show that with conjunction only no issues with distributivity arise. In contrast, there exists a corollary of the distributivity law in the language with disjunction only which is not derivable in the non-distributive system. Moreover, this difference keeps valid for systems with permutation and/or weakening structural rules, that is, intuitionistic linear and affine logics and affine multiplicative-additive Lambek calculus. For the extension of the Lambek with the unit constant, we present a calculus which reflects natural algebraic properties of the empty word. We do not claim completeness for this calculus, but we prove undecidability for the whole range of systems extending this minimal calculus and sound w.r.t. language models. As a corollary, we show that in the language with the unit there exissts a sequent that is true if all variables are interpreted by regular language, but not true in language models in general.
