Related papers: A Language Hierarchy of Binary Relations
We present an approach to learning multi-sense word embeddings relying both on monolingual and bilingual information. Our model consists of an encoder, which uses monolingual and bilingual context (i.e. a parallel sentence) to choose a…
Mitsch's natural partial order on the semigroup of binary relations is here characterised by equations in the theory of relation algebras. The natural partial order has a complex relationship with the compatible partial order of inclusion,…
Patterns are words with terminals and variables. The language of a pattern is the set of words obtained by uniformly substituting all variables with words that contain only terminals. In their original definition, patterns only allow for…
Pretrained multilingual models exhibit the same social bias as models processing English texts. This systematic review analyzes emerging research that extends bias evaluation and mitigation approaches into multilingual and non-English…
In order to use the Dual Simplex Method, one needs to prove a certain bijection between the dictionaries associated with the primal problem and those associated with its dual. We give a short conceptual proof of why this bijection exists.
We investigate the quantifier alternation hierarchy in first-order logic on finite words. Levels in this hierarchy are defined by counting the number of quantifier alternations in formulas. We prove that one can decide membership of a…
In many situations one encounters an entity that resembles a monoid. It consists of a carrier and two operations that resemble a unit and a multiplication, subject to three equations that resemble associativity and left and right unital…
Purpose: Terminology is the set of technical words or expressions used in specific contexts, which denotes the core concept in a formal discipline and is usually applied in the fields of machine translation, information retrieval,…
A special inverse monoid is one defined by a presentation where all the defining relations have the form $r = 1$. By a result of Ivanov Margolis and Meakin the word problem for such an inverse monoid can often be reduced to the word problem…
Word choice is dependent on the cultural context of writers and their subjects. Different words are used to describe similar actions, objects, and features based on factors such as class, race, gender, geography and political affinity.…
We generalize the notion of identities among relations, well known for presentations of groups, to presentations of n-categories by polygraphs. To each polygraph, we associate a track n-category, generalizing the notion of crossed module…
We transform the method of Glasson into a sufficient condition under which a monoid is non-finitely related, add a new member to the collection of interlocking word-patterns, and use it to show that the monoid $M(ab^2a, a^2b^2)$ is…
Cross-lingual representations of words enable us to reason about word meaning in multilingual contexts and are a key facilitator of cross-lingual transfer when developing natural language processing models for low-resource languages. In…
A structure called a decision making problem is considered. The set of outcomes (consequences) is partially ordered according to the decision maker's preferences. The problem is how these preferences affect a decision maker to prefer one of…
In this work, we introduce a new notion for representing graph classes with formal languages. In contrast to the seminal work by Kitaev and Pyatkin to represent graphs by words, we use formal binary languages in order to have a set of…
Waring problem for forms is important and classical in mathematics. It has been widely investigated because of its wide applications in several areas. In this paper, we consider the Waring problem for binary forms with complex coefficients.…
Larrauri and \v{Z}ivn\'y [ICALP'25/ACM ToCL'24] recently established a complete complexity classification of the problem of solving a system of equations over a monoid $N$ assuming that a solution exists over a monoid $M$, where both…
There are several notions of duality between lines and points. In this note, it is shown that all these can be studied in a unified way. Most interesting properties are independent of specific choices. It is also shown that either dual…
An interesting line of research in natural language processing (NLP) aims to incorporate linguistic typology to bridge linguistic diversity and assist the research of low-resource languages. While most works construct linguistic similarity…
Selectional preference learning methods have usually focused on word-to-class relations, e.g., a verb selects as its subject a given nominal class. This papers extends previous statistical models to class-to-class preferences, and presents…