Abstract:
The work is devoted to basic categorial grammars with unique type assignment (BCGUTA). For this class, a number of algorithmic properties are examined. It is proven that, for an arbitrary context-free language $L$, the problem of verifying whether is generated by a grammar from the BCGUTA class is algorithmically undecidable. Furthermore, it is proven that for any two BCGUTA grammars, the problem of determining the emptiness of the intersection of the languages generated by these grammars is also algorithmically undecidable.
