6 citations · 15 across the 13 of their papers we have counts for
14 papers
Tensor term logic for categorial grammars: simple unification of commutative and noncommutative structure
Sergey Slavnov
A prototypical example of categorial grammars are those based on Lambek calculus, i.e. noncommutative intuitionistic linear logic. However, it has been noted that purely noncommuta…
Making first order linear logic a generating grammar
Sergey Slavnov
It is known that different categorial grammars have surface representation in a fragment of first order multiplicative linear logic (MLL1). We show that the fragment of interest is…
First order linear logic and tensor type calculus for categorial grammars
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 int…
Cobordisms and commutative categorial grammars
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 decorate…
On embedding Lambek calculus into commutative categorial grammars
Sergey Slavnov
We consider tensor grammars, which are an example of \commutative" grammars, based on the classical (rather than intuitionistic) linear logic. They can be seen as a surface represe…
Classical linear logic, cobordisms and categorial grammars
Sergey Slavnov
We propose a categorial grammar based on classical multiplicative linear logic. This can be seen as an extension of abstract categorial grammars (ACG) and is at least as expressive…
Abstract categorial grammars with island constraints and effective decidability
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. We adapt this approach…
Classical linear logic, cobordisms and categorical semantics of categorial grammars
Sergey Slavnov
We propose a categorial grammar based on classical multiplicative linear logic. This can be seen as an extension of abstract categorial grammars (ACG) and is at least as expressive…
Linear logic in normed cones: probabilistic coherence spaces and beyond
Sergey Slavnov
Ehrhard, Pagani and Tasson proposed a model of probabilistic functional programming in a category of normed positive cones and stable measurable cone maps, which can be seen as a c…
On noncommutative extensions of linear logic
Sergey Slavnov
Pomset logic introduced by Retoré is an extension of linear logic with a self-dual noncommutative connective. The logic is defined by means of proof-nets, rather than a sequent cal…
On partial traces and compactification of -autonomous Mix-categories
Sergey Slavnov
We study the question when a -autonomous Mix-category has a representation as a -autonomous Mix-subcategory of a compact one. We define certain partial trace-like operation o…
Compactification of *-autonomous categories
Sergey Slavnov
We study the question when a *-autonomous (Mix-)category has a representation as a -autonomous category of a compact one. We prove that necessary and sufficient condition is tha…
On Banach spaces of sequences and free linear logic exponential modality
Sergey Slavnov
We introduce a category of vector spaces modelling full propositional linear logic, similar to probabilistic coherence spaces and to Koethe sequences spaces. Its objects are {\it r…
Linear logic with idempotent exponential modalities: a note
Sergey Slavnov
In this note we discuss a variant of linear logic with idempotent exponential modalities. We propose a sequent calculus system and discuss its semantics. We also give a concrete re…