On the expressive power of the Lambek calculus extended with a structural modality
نویسنده
چکیده
We consider EL, the product-free associative Lambek calculus (Lambek, 1958) extended with a structural modality à la Girard (Girard, 1987), which allows the left strucrural rules (weakening, contraction, and exchange) to be performed in a controlled way. We show that any recursively enumerable language can be described by a categorial grammar based on EL. As an immediate corollary, we get the undecidability of EL.
منابع مشابه
Comparing and evaluating extended Lambek calculi
Lambeks Syntactic Calculus, commonly referred to as the Lambek calculus, was innovative in many ways, notably as a precursor of linear logic. But it also showed that we could treat our grammatical framework as a logic (as opposed to a logical theory). However, though it was successful in giving at least a basic treatment of many linguistic phenomena, it was also clear that a slightly more expre...
متن کاملUndecidability of the Lambek Calculus with a Relevant Modality
Morrill and Valent́ın in the paper “Computational coverage of TLG: Nonlinearity” considered an extension of the Lambek calculus enriched by a so-called “exponential” modality. This modality behaves in the “relevant” style, that is, it allows contraction and permutation, but not weakening. Morrill and Valent́ın stated an open problem whether this system is decidable. Here we show its undecidabilit...
متن کاملDialectica Categories for the Lambek Calculus
We revisit the old work of de Paiva on the models of the Lambek Calculus in dialectica models making sure that the syntactic details that were sketchy on the first version got completed and verified. We extend the Lambek Calculus with a κ modality, inspired by Yetter’s work, which makes the calculus commutative. Then we add the of-course modality !, as Girard did, to re-introduce weakening and ...
متن کاملProof nets for the Lambek calculus — an overview
There are both linguistic and mathematical reasons for studying proof nets the perspective of categorial grammar. It is now well known that the Lambek calculus corresponds to intuitionnistic non-commutative multiplicative linear logic — with no empty antecedent, to be absolutely precise. As natural deduction underlines the constructive contents of intuitionistic logic (Curry-Howard isomorphism)...
متن کاملLambek Calculus Proofs and Tree Automata
We investigate natural deduction proofs of the Lambek calculus from the point of view of tree automata. The main result is that the set of proofs of the Lambek calculus cannot be accepted by a finite tree automaton. The proof is extended to cover the proofs used by grammars based on the Lambek calculus, which typically use only a subset of the set of all proofs. While Lambek grammars can assign...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2013