非结合Lambek演算经典扩张的聚焦和相位模型
Focalization and phase models for classical extensions of non-associative Lambek calculus
摘要：
Lambek的非联想句法演算（NL）在其资源意识方面表现出色：通常的弱化，收缩，交换甚至结合性的结构规则都被丢弃。最近，有人提出了一些保守的扩展，以免除NL对具有单一结论的序列的直觉偏见：De Groote和Lamarche的经典非结合Lambek演算（CNL）和Moortgat及其同事的Lambek-Grishin演算（LG）。我们证明了Andreoli的聚焦属性所述的建议：一个规范化的结果，确定在很大程度上，那些不同的只是由平凡的规则排列的切免费的cirrhosis推导。在这样做的时候，我们从一个“统一的”CCN介绍，通过增加结构规则从LG派生CNL。规范化的证明收益的句法阶段模型的建设，其中每一个“真理”有一个集中的证明，类似于冈田和Herbelin和李的工作。
英文摘要：
Lambek's non-associative syntactic calculus (NL) excels in its resource consciousness: the usual structural rules for weakening, contraction, exchange and even associativity are all dropped. Recently, there have been proposals for conservative extensions dispensing with NL's intuitionistic bias towards sequents with single conclusions: De Groote and Lamarche's classical non-associative Lambek calculus (CNL) and the Lambek-Grishin calculus (LG) of Moortgat and associates. We demonstrate Andreoli's focalization property for said proposals: a normalization result for Cut-free sequent derivations identifying to a large extent those differing only by trivial rule permutations. In doing so, we proceed from a `uniform' sequent presentation, deriving CNL from LG through the addition of structural rules. The normalization proof proceeds by the construction of syntactic phase models wherein every `truth' has a focused proof, similar to work of Okada and of Herbelin and Lee.
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