Related papers: Leibniz's law and its paraconsistent models
Doob's theorem provides guarantees of consistent estimation and posterior consistency under very general conditions. Despite the limitation that it only guarantees consistency on a set with prior probability 1, for many models arising in…
This article aims to explain essential elements of perturbation theory and their conceptual underpinnings. It is not meant as a summary of popular perturbation methods, though some illustrative examples are given to underline the main…
A new method for the Lie group classification of differential equations is proposed. It is based of the determination of all possible cases of linear dependence of certain indeterminate appearing in the determining equations of symmetries…
The goal of computational logic is to allow us to model computation as well as to reason about it. We argue that a computational logic must be able to model interactive computation. We show that first-order logic cannot model interactive…
In this paper, we consider Leibniz algebras with derivations. A pair consisting of a Leibniz algebra and a distinguished derivation is called a LeibDer pair. We define a cohomology theory for LeibDer pair with coefficients in a…
This article provides a concise overview of the main mathematical theory of Benford's law in a form accessible to scientists and students who have had first courses in calculus and probability. In particular, one of the main objectives here…
In this article, the hierarchy of LFIs L$_n^k$, Logics of Controlled Consistency (LCC), is introduced. Inspired by da Costa's original C$_n$ systems, this hierarchy can represent different degrees of paraconsistent commitment and different…
We discuss three problems related to connections on bimodules. These are left and right Leibniz rule for connections, left and right linearity of their curvatures and extension of connections to tensor products of modules.
In this paper, we compare the abelian subalgebras and ideals of maximal dimension for finite-dimensional Leibniz algebras. We study Leibniz algebras containing abelian subalgebras of codimension 1, solvable and supersolvable Leibniz…
The requirements for stability of a Lorentz violating theory are analyzed. In particular we conclude that Einstein-aether theory can be stable when its modes have any phase velocity, rather than only the speed of light as was argued in a…
The major obstacle to a supersymmetric theory on the lattice is the failure of the Leibniz rule. We analyze this issue by using the Wess-Zumino model and a general Ginsparg-Wilson operator, which is local and free of species doublers. We…
Radical binomial ideals associated with finite lattices are studied. Gr\"obner basis theory turns out to be an efficient tool in this investigation.
The paper discusses the problem of the Lorentz contraction in accelerated systems, in the context of the special theory of relativity. Equal proper accelerations along different world lines are considered, showing the differences arising…
The concept of paradeduction is presented in order to justify that we can overlook contradictory information taking into account only what is consistent. Besides that, paradeduction is used to show that there is a way to transform any…
The fundamental ideas of aplicability of Levi-Malcev Theorem for Bol algebras, which plays a basic role in structural theory are outlined
In this paper we continue the study of the subalgebra lattice of a Leibniz algebra. In particular, we find out that solvable Leibniz algebras with an upper semi-modular lattice are either almost-abelian or have an abelian ideal spanned by…
Consider a Leibniz superalgebra $\mathfrak L$ additionally graded by an arbitrary set $I$ (set grading). We show that $\mathfrak L$ decomposes as the sum of well-described graded ideals plus (maybe) a suitable linear subspace. In the case…
In this paper we study the notion of isoclinism on Lie-central extensions of Leibniz algebras, this yields to introduce the concept of Lie-isoclinic Leibniz algebras. We provide several equivalent conditions under which Leibniz algebras are…
This is an introduction to the theory of disconjugacy for a second order linear differential equation. We give new proofs of some of basic results and obtain new sufficient conditions for disconjugacy (in particular, on the whole real…
The Gr\"uneisen relation is shown to be important for the thermodynamics of dense liquids.