Related papers: Pregroup Grammars, their Syntax and Semantics
The method of constructing of Grothendieck's topology basing on a neighbourhood grammar, defined on the category of syntax diagrams is described in the article. Syntax diagrams of a formal language are the multigraphs with nodes, signed by…
In this paper we apply a recently proposed algebraic theory of integration to projective group algebras. These structures have received some attention in connection with the compactification of the $M$ theory on noncommutative tori. This…
Lexical semantics theories differ in advocating that the meaning of words is represented as an inference graph, a feature mapping or a vector space, thus raising the question: is it the case that one of these approaches is superior to the…
Many neural network models nowadays have achieved promising performances in Chit-chat settings. The majority of them rely on an encoder for understanding the post and a decoder for generating the response. Without given assigned semantics,…
In the mid thirties Murray and von Neumann found a natural way to associate a von Neumann algebra $L(\Gamma)$ to any countable discrete group $\Gamma$. Classifying $L(\Gamma)$ in term of $\Gamma$ is a notoriously complex problem as in…
We study tensor products of two structures situated, in a sense, between normed spaces and (abstract) operator spaces. We call them Lambert and proto-Lambert spaces and pay more attention to the latter ones. The considered two tensor…
In this paper we begin the systematic study of group equations with abelian predicates in the main classes of groups where solving equations is possible. We extend the line of work on word equations with length constraints, and more…
We extend Borel's theorem on the dominance of word maps from semisimple algebraic groups to some perfect groups. In another direction, we generalize Borel's theorem to some words with constants. We also consider the surjectivity problem for…
Various NLP problems -- such as the prediction of sentence similarity, entailment, and discourse relations -- are all instances of the same general task: the modeling of semantic relations between a pair of textual elements. A popular model…
We prove a convolution formula for the conjugacy classes in symmetric groups conjectured by the second author. A combinatorial interpretation of coefficients is provided. As a main tool we introduce new semigroup of partial permutations. We…
Vector-space representations provide geometric tools for reasoning about the similarity of a set of objects and their relationships. Recent machine learning methods for deriving vector-space embeddings of words (e.g., word2vec) have…
Recently, a number of interesting relations have been discovered between generalised Pauli/Dirac groups and certain finite geometries. Here, we succeeded in finding a general unifying framework for all these relations. We introduce…
The Lambek calculus provides a foundation for categorial grammar in the form of a logic of concatenation. But natural language is characterized by dependencies which may also be discontinuous. In this paper we introduce the displacement…
In the theory of formal languages, the understanding of concatenation hierarchies of regular languages is one of the most fundamental and challenging topic. In this paper, we survey progress made in the comprehension of this problem since…
The linguistic applications of the Lambek calculus suggest its semantics over algebras of formal languages. A straightforward approach to construct such semantics indeed yields a brilliant completeness theorem (Pentus 1995). However,…
Pre-Tannakian categories are a natural class of tensor categories that can be viewed as generalizations of algebraic groups. We define a pre-Tannkian category to be discrete if it is generated by an \'etale commutative algebra; these…
Due to the increased complexity of software development projects more and more systems are described by models. The sheer size makes it impractical to describe these systems by a single model. Instead many models are developed that provide…
We describe a logarithmic tensor product theory for certain module categories for a ``conformal vertex algebra.'' In this theory, which is a natural, although intricate, generalization of earlier work of Huang and Lepowsky, we do not…
We consider a combinatorial problem occurring naturally in a group theoretical setting and provide a constructive solution in a special case. More precisely, in 1999 the author established a logarithmic bound for the derived length of the…
These are notes from the lectures I gave at the Oberwolfach seminar `Tensor Triangular Geometry and Interactions' which was held in October 2025. The aim of these notes is to give an introduction to tensor triangular geometry, for both…