First order linear logic and tensor type calculus for categorial grammars
This work provides a theoretical foundation for using ETTC in computational linguistics, though it is incremental as it builds on existing logic and grammar frameworks.
The paper establishes a correspondence between a fragment of first-order multiplicative linear logic (MLL1) and the extended tensor type calculus (ETTC), showing that ETTC serves as an alternative syntax and deductive system for representing categorial grammars.
We study relationship between first order multiplicative linear logic (MLL1), which has been known to provide representations to different categorial grammars, and the recently introduced extended tensor type calculus (ETTC). We identify a fragment of MLL1, which seems sufficient for many grammar representations, and establish a correspondence between ETTC and this fragment. The system ETTC, thus, can be seen as an alternative syntax and intrinsic deductive system together with a geometric representation for the latter. We also give a natural deduction formulation of ETTC, which might be convenient.