Related papers: Relational Lattice Foundation for Algebraic Logic
A lattice reduction is an algorithm that transforms the given basis of the lattice to another lattice basis such that problems like finding a shortest vector and closest vector become easier to solve. We define a class of bases called…
We describe a classification of pairs $M, N$ of lattices isometric to $EE_8:=\sqrt 2 E_8$ such that the lattice $M + N$ is integral and rootless and such that the dihedral group associated to them has order at most 12. It turns out that…
Information algebras arise from the idea that information comes in pieces which can be aggregated or combined into new pieces, that information refers to questions and that from any piece of information, the part relevant to a given…
A consistent set of six integrable discrete and continuous dynamical systems are suggested corresponding to arbitrary affine Lie algebra. The set contains a system of partial differential equations which can be treated as a version of…
We establish a novel connection between two research areas in non-classical logics which have been developed independently of each other so far: on the one hand, input/output logic, introduced within a research program developing logical…
We develop a random model for relation algebras. We prove some preliminary results and pose questions that lay out a new direction of research.
A finite-dimensional unital and associative algebra over $\mathbb{R}$, or what we shall call simply "an algebra" in this paper for short, generalities the construction by which we derive the complex numbers by "adjoining an element $i$" to…
Conjunctive table algebras are introduced and axiomatically characterized. A conjunctive table algebra is a variant of SPJR algebra (a weaker form of relational algebra), which corresponds to conjunctive queries with equality. The table…
We study so called regular Lie algebras, i.e. Lie algebras in which each nonzero element is regular. We make a connection with an open problem whether any element of reduced trace zero in a simple associative algebra is a commutator.
Duality relations for the correlation functions of $n$ sites on the boundary of a planar lattice are derived for the $(N_{\alpha}, N_{\beta})$ model of Domany and Riedel for $n=2,3$. Our result holds for arbitrary lattices which can have…
The aim of this work is focused on linearizing and found the Lax Pairs of the algebraic complete integrability (a.c.i) Toda lattice associated with the twisted affine Lie algebra \(a_4^{\left(2\right)}\). Firstly, we recall that our case of…
A novel lattice approach is presented for studying systems comprising a large number of interacting nonrelativistic fermions. The construction is ideally suited for numerical study of fermions near unitarity--a strongly coupled regime…
We consider a simple modal logic whose non-modal part has conjunction and disjunction as connectives and whose modalities come in adjoint pairs, but are not in general closure operators. Despite absence of negation and implication, and of…
As the second part of the treatise 'A General Theory of Concept Lattice', this paper speaks of the tractability of the general concept lattice for both its lattice structure and logic content. The general concept lattice permits a feasible…
We develop criteria to decide if an $N=2$ or $N=4$ super conformal algebra is a subalgebra of a super vertex operator algebra in general, and of a super lattice theory in particular. We give some specific examples.
We propose a Relational Calculus based on the concept of unary relation. In this Relational Calculus different axiomatic systems converge to a model called Dynamic Generative System with Symmetry (DGSS). In DGSS we define the concepts of…
By a rectangular distributive lattice we mean the direct product of two non-singleton finite chains. We prove that the retracts (ordered by set inclusion and together with the empty set) of a rectangular distributive lattice $G$ form a…
The foundational character of certain algebraic structures as Boolean algebras and Heyting algebras is rooted in their potential to model classical and constructive logic, respectively. In this paper we discuss the contributions of…
Codd's Theorem, a fundamental result of database theory, asserts that relational algebra and relational calculus have the same expressive power on relational databases. We explore Codd's Theorem for databases over semirings and establish…
In this paper we present the fundamentals of the so-called algebraic approach to propositional quantum logics. We define the set of formulas describing quantum reality as a free algebra freely generated by the set of quantum propositional…