次指数模态和括号模态下Lambek演算的不可判定性
Undecidability of the Lambek calculus with subexponential and bracket modalities
摘要：
Lambek演算是一种著名的逻辑形式主义，用于建模自然语言语法。最初的演算涵盖了大量复杂的自然语言现象，但仅限于上下文无关的设置。为了解决更微妙的语言问题，Lambek演算已经以各种方式扩展。特别是，Morrill和Valentin（2015）引入了一种扩展，即所谓的指数和括号模态。他们的扩展是基于一个非标准的收缩规则的指数，相互作用的括号结构在一个复杂的方式。标准的压缩法则在这个演算中是不允许的。本文证明了微积分中可导性问题的不可判定性。我们还调查了限制可判定的片段考虑Morrill和瓦伦丁，我们表明，这些片段属于NP类。
英文摘要：
The Lambek calculus is a well-known logical formalism for modelling natural language syntax. The original calculus covered a substantial number of intricate natural language phenomena, but only those restricted to the context-free setting. In order to address more subtle linguistic issues, the Lambek calculus has been extended in various ways. In particular, Morrill and Valentin (2015) introduce an extension with so-called exponential and bracket modalities. Their extension is based on a non-standard contraction rule for the exponential that interacts with the bracket structure in an intricate way. The standard contraction rule is not admissible in this calculus. In this paper we prove undecidability of the derivability problem in their calculus. We also investigate restricted decidable fragments considered by Morrill and Valentin and we show that these fragments belong to the NP class.
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