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Recommender systems usually operate on similarities between recommended items or users. Tag based recommender systems utilize similarities on tags. The tags are however mostly free user entered phrases. Therefore, similarities computed…
We present a general relational semantics framework which, by varying the axiomatization and components of the relational structures, provides a uniform semantics for sentential logics, classical and non-classical alike. The approach we…
Algebraic theories, sometimes called equational theories, are syntactic notions given by finitary operations and equations, such as monoids, groups, and rings. There is a well-known category-theoretic treatment of them that algebraic…
The ability to mimic human notions of semantic distance has widespread applications. Some measures rely only on raw text (distributional measures) and some rely on knowledge sources such as WordNet. Although extensive studies have been…
In this work we develop geometric Sen theory for rigid analytic spaces, generalizing the previous work of Pan for curves. We also extend the axiomatic Sen-Tate formalism of Berger-Colmez to a certain class of locally analytic…
In this paper, we present a purely algebraic formulation of higher gauge theory and gauged sigma models based on the abstract theory of graded commutative algebras and their morphisms. The formulation incorporates naturally BRST symmetry…
Swiss cheese sets have been used in the literature as useful examples in the study of rational approximation and uniform algebras. In this paper, we give a survey of Swiss cheese constructions and related results. We describe some notable…
We develop the basic theory of geometrically closed rings as a generalisation of algebraically closed fields, on the grounds of notions coming from positive model theory and affine algebraic geometry. For this purpose we consider several…
It is shown that softly broken theory is equivalent to a rigid theory in external spurion superfield. The singular part of effective action in a broken theory follows from a rigid one by a simple redefinition of the couplings. This gives an…
We examine non-dual relational extensions of rough set approximations and find an extension which satisfies surprisingly many of the usual rough set properties. We then use this definition to give an explanation for an observation made by…
We study the role of the second language in bilingual word embeddings in monolingual semantic evaluation tasks. We find strongly and weakly positive correlations between down-stream task performance and second language similarity to the…
Let X be an affine real algebraic set . We investigate on the theory of algebraically constructible functions on X and the description of the semi-algebraic subsets of X when we replace the polynomial functions on X by some rational…
With the enourmous popularity of large language models, many researchers have raised ethical concerns regarding social biases incorporated in such models. Several methods to measure social bias have been introduced, but apparently these…
We study possibilities for semantic and syntactic rigidity, i.e., the rigidity with respect to automorphism group and with respect to definable closure. Variations of rigidity and their degrees are studied in general case, for special…
Cross-lingual word sense disambiguation (WSD) tackles the challenge of disambiguating ambiguous words across languages given context. The pre-trained BERT embedding model has been proven to be effective in extracting contextual information…
A formal theory based on a binary operator of directional associative relation is constructed in the article and an understanding of an associative normal form of image constructions is introduced. A model of a commutative semigroup, which…
We propose an abstract notion of a type theory to unify the semantics of various type theories including Martin-L\"{o}f type theory, two-level type theory and cubical type theory. We establish basic results in the semantics of type theory:…
Inspired by the work of Wang and Zhou [4] for Rota-Baxter algebras, we develop a cohomology theory of Rota-Baxter systems and justify it by interpreting the lower degree cohomology groups as formal deformations and as abelian extensions of…
In this text, we outline a theory of schemes associated with a site, which generalizes a variety of geometries, such as manifolds, schemes, analytic spaces, simplicial complexes, and more. We present an abstract process of gluing model…
Molodtsov \cite{molodtsov-1999} proposed the concept of soft set theory in 1999, which can be used as a mathematical tool for dealing with problems that contain uncertainty. Sabir and Naz \cite{shabir-2013} defined notion of bipolar soft…