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On the recognizing power of the Lambek calculus with brackets. (English) Zbl 1427.03040

Summary: Every language recognized by the Lambek calculus with brackets is context-free. This is shown by combining an observation by G. Jäger [Res. Lang. Comput. 1, No. 1–2, 105–125 (2003; Zbl 1066.68134)] with an entirely straightforward adaptation of the method Pentus used for the original Lambek calculus. The case of the variant of the calculus allowing sequents with empty antecedents is slightly more complicated, requiring a restricted use of the multiplicative unit.

MSC:

03B47 Substructural logics (including relevance, entailment, linear logic, Lambek calculus, BCK and BCI logics)
68Q42 Grammars and rewriting systems
68Q45 Formal languages and automata

Citations:

Zbl 1066.68134
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References:

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