Related papers: Consequence Relations An Introduction to the Tarsk…
The pioneering work of Blok and J\'onsson and its further development by Galatos and Tsinakis initiated an abstract study of consequence relations using the tools of module theory, where consequence relations over all types of syntactic…
This paper establishes a purely syntactic representation for the category of algebraic L-domains with Scott-continuous functions as morphisms. The central tool used here is the notion of logical states, which builds a bridge between…
In this article, a new approach based on linear algebra is adopted to study a hybrid Sheffer polynomial sequences. The recurrence relations and differential equation for these polynomials are derived by using the properties and…
Several Lebesgue-type decomposition theorems in analysis have a strong relation to the operation called: parallel sum. The aim of this paper is to investigate this relation from a new point of view. Namely, using a natural generalization of…
In these lectures we provide a basic introduction into the topic of dispersion relation and analyticity. The properties of 2-point functions are discussed in some detail from the viewpoint of the K\"all\'en-Lehmann and general dispersion…
The aim of this work is to provide a special kind of conservative translation between abstract logics, namely an \textit{abstract Glivenko's theorem}. Firstly we define institutions on the categories of logic, algebraizable logics, and…
Contextuality is a key feature of quantum mechanics. We present the sheaf-theoretic approach to contextuality introduced by Abramsky and Brandenburger, and show how it covers a range of logical and physical phenomena "at the borders of…
We define a general notion of entropy in elementary, algebraic terms. Based on that, weak forms of a scalar product and a distance measure are derived. We give basic properties of these quantities, generalize the Cauchy-Schwarz inequality,…
We extend the theory of d-separation to cases in which data instances are not independent and identically distributed. We show that applying the rules of d-separation directly to the structure of probabilistic models of relational data…
We prove a version of the Gr\"atzer-Schmidt theorem for the Lindenbaum-Tarski algebra associated to the Implicational Propositional Calculus.
Suszko's problem is the problem of finding the minimal number of truth values needed to semantically characterize a syntactic consequence relation. Suszko proved that every Tarskian consequence relation can be characterized using only two…
The growing demand for structured knowledge has led to great interest in relation extraction, especially in cases with limited supervision. However, existing distance supervision approaches only extract relations expressed in single…
In longitudinal studies where units are embedded in space or a social network, interference may arise, meaning that a unit's outcome can depend on treatment histories of others. The presence of interference poses significant challenges for…
This paper aims at reviewing and analysing the method of reflections. The latter is an iterative procedure designed to linear boundary value problems set in multiply connected domains. Being based on a decomposition of the domain boundary,…
A. Tarski proposed the study of infinitary consequence operations as the central topic of mathematical logic. He considered monotonicity to be a property of all such operations. In this paper, we weaken the monotonicity requirement and…
Extracting cause and effect phrases from a sentence is an important NLP task, with numerous applications in various domains, including legal, medical, education, and scientific research. There are many unsupervised and supervised methods…
Terms of Church's $\lambda$-calculus can be considered equivalent along many different definitions, but context equivalence is certainly the most direct and universally accepted one. If the underlying calculus becomes probabilistic,…
The logico-algebraic study of Lewis's hierarchy of variably strict conditional logics has been essentially unexplored, hindering our understanding of their mathematical foundations, and the connections with other logical systems. This work…
An Onsager-like relation is proposed as a new criterion for constructing and analysing the lattice Boltzmann (LB) method. For LB models obeying the relation, we analyse their linearized stability, establish their diffusive limit, and find…
Kontsevitch's work on Airy matrix integrals has led to explicit results for the intersection numbers of the moduli space of curves. In a subsequent work Okounkov rederived these results from the edge behavior of a Gaussian matrix integral.…