Related papers: Encoding Sequences in Intuitionistic Real Algebra
In recent years, algebraic topology and its modern development, the theory of persistent homology, has shown great potential in graph representation learning. In this paper, based on the mathematics of algebraic topology, we propose a novel…
We study Smarandache sequences of numbers, and related problems, via a Computer Algebra System. Solutions are discovered, and some conjectures presented.
This article provides an algebraic study of intermediate inquisitive and dependence logics. While these logics are usually investigated using team semantics, here we introduce an alternative algebraic semantics and we prove it is complete…
Intuitionistic grammar logics fuse constructive and multi-modal reasoning while permitting the use of converse modalities, serving as a generalization of standard intuitionistic modal logics. In this paper, we provide definitions of these…
We consider random fields admitting a spectral representation with infinitely divisible integrator and prove some of their properties.
We construct some irreducible representations of the Leavitt path algebra of an arbitrary quiver. The constructed representations are associated to certain algebraic branching systems. For a row-finite quiver, we classify algebraic…
In rule-based systems, goal-oriented computations correspond naturally to the possible ways that an observation may be explained. In some applications, we need to compute explanations for a series of observations with the same domain. The…
In this extended abstract, we investigate the design of learning representation for human intention inference. In our designed human intention prediction task, we propose a history encoding representation that is both interpretable and…
In this work I look at the distribution of primes by calculation of an infinite number of intersections. For this I use the set of all numbers which are not elements of a certain times table in each case. I am able to show that it exists a…
We show that probabilistic computable functions, i.e., those functions outputting distributions and computed by probabilistic Turing machines, can be characterized by a natural generalization of Church and Kleene's partial recursive…
We investigate when a computable automorphism of a computable field can be effectively extended to a computable automorphism of its (computable) algebraic closure. We then apply our results and techniques to study effective embeddings of…
The problem of construction of irreducible representations of quantum $A^q_n$ algebras is solved at the level of explicit integration of the linear (inhomogeneous) system in finite differences in the n-dimensional space. The general…
We introduce a novel positional encoding strategy for Transformer-style models, addressing the shortcomings of existing, often ad hoc, approaches. Our framework provides a flexible mapping from the algebraic specification of a domain to an…
In this paper we consider the class of truth-functional many-valued logics with a finite set of truth-values. The main result of this paper is the development of a new \emph{binary} sequent calculi (each sequent is a pair of formulae) for…
We prove that the sequent calculus $\mathsf{L_{RBL}}$ for residuated basic logic $\mathsf{RBL}$ has strong finite model property, and that intuitionistic logic can be embedded into basic propositional logic $\mathsf{BPL}$. Thus…
Ramsey algebras are algebras that induce Ramsey spaces, which are generalizations of the Ellentuck space and Milliken's space. Previous work suggests a possible local version of Ramsey algebras induced by infinite sequences. Hence, we…
We study coherent $I$-indexed algebras and associated noncommutative projective schemes, where the index set $I$ is a locally finite directed poset. Our main result is a characterisation of such noncommutative projective schemes in terms of…
This paper introduces a class of objects called decision rules that map infinite sequences of alternatives to a decision space. These objects can be used to model situations where a decision maker encounters alternatives in a sequence such…
We give an overview of the recursive characterisations of random matrix ensembles that are currently at the forefront of random matrix theory by way of studying two classes of ensembles using two different types of recursive schemes:…
In this case study in ``fully automated enumeration'', we illustrate how to take full advantage of symbolic computation by developing (what we call) `symbolic-dynamical-programming' algorithms for computing many terms of `hard to compute…