no code implementations • 17 Jun 2022 • Sergey Slavnov
It is known that different categorial grammars have surface representation in a fragment of first order multiplicative linear logic (MLL1).
no code implementations • 31 Dec 2021 • Sergey Slavnov
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).
no code implementations • 19 Jul 2021 • Sergey Slavnov
We propose a concrete surface representation of abstract categorial grammars in the category of word cobordisms or cowordisms for short, which are certain bipartite graphs decorated with words in a given alphabet, generalizing linear logic proof-nets.
no code implementations • 20 May 2020 • Sergey Slavnov
They can be seen as a surface representation of abstract categorial grammars ACG in the sense that derivations of ACG translate to derivations of tensor grammars and this translation is isomorphic on the level of string languages.
no code implementations • 10 Nov 2019 • Sergey Slavnov
This category is symmetric monoidal closed and compact closed and thus is a model of linear $\lambda$-calculus and classical, as well as intuitionistic linear logic.
no code implementations • 16 Jul 2019 • Sergey Slavnov
A well-known approach to treating syntactic island constraints in the setting of Lambek grammars consists in adding specific bracket modalities to the logic.
no code implementations • 4 Oct 2018 • Sergey Slavnov
We propose a categorial grammar based on classical multiplicative linear logic.