Representation of Nelson Algebras by Rough Sets Determined by Quasiorders

In this paper, we show that every quasiorder $R$ induces a Nelson algebra $\mathbb{RS}$ such that the underlying rough set lattice $RS$ is algebraic. We note that $\mathbb{RS}$ is a three-valued {\L}ukasiewicz algebra if and only if $R$ is an equivalence. Our main result says that if $\mathbb{A}$ is a Nelson algebra defined on an algebraic lattice, then there exists a set $U$ and a quasiorder $R$ on $U$ such that $\mathbb{A} \cong \mathbb{RS}$.Comment: 16 page

The kitchen as a pedagogical strategy. Addressing celiac disease from the encounter with "Others" is to build a "We", which leads to accessing a good living

This work arises within the framework of the Pehuajó Solidarity Network (RSP), where a voluntary group, independent since 1997, meets alternating kitchen/s to discuss some issues of interest related to signs and symptoms that a member of their family suffered, without know the condition of Celiac disease. Currently, the fact of being celiac in the social context where one lives and/or in the tourist places that they visit, do not always meet the nutritional needs of children, adolescents, young people, adults, people in general who they suffer from Celiac disease. That is to say, the achievement of Municipal Ordinance 94/2019 in district 079 of the province of Buenos Aires and the Laws: National and Provincial in Argentina are still known and are gradually being complied with, being the Gastronomic offer, sale of food, services of confectionery, among other insufficient. They do not have at least one menu for celiacs, with few exceptions. In other words, the group of aware independent volunteers not only incorporates knowledge to self-manage celiac disease, but as an informal entity it is managing to transpose in formal institutions, the community of the contextterritory, non-profit activities with the objective of: disseminate, raise awareness and make celiac disease visible as a pedagogical strategy. That is, to make visible the advances developed in the 21st century, the very concept of this chronic disease, which went from being defined as a mere food intolerance, to being recognized as a systemic pathology with an autoimmune basis

El abordaje de la capacidad de resolución de problema en las prácticas de enseñanza para pluriaño de escuelas secundarias del ámbito rural bonaerense

Fil: Cignoli, María de los Ángeles. Universidad Católica de Córdoba. Facultad de Educación; Argentina

Proof Theory and Ordered Groups

Ordering theorems, characterizing when partial orders of a group extend to total orders, are used to generate hypersequent calculi for varieties of lattice-ordered groups (l-groups). These calculi are then used to provide new proofs of theorems arising in the theory of ordered groups. More precisely: an analytic calculus for abelian l-groups is generated using an ordering theorem for abelian groups; a calculus is generated for l-groups and new decidability proofs are obtained for the equational theory of this variety and extending finite subsets of free groups to right orders; and a calculus for representable l-groups is generated and a new proof is obtained that free groups are orderable

A representation theorem for MV-algebras

An {\em MV-pair} is a pair $(B,G)$ where $B$ is a Boolean algebra and $G$ is a subgroup of the automorphism group of $B$ satisfying certain conditions. Let $\sim_G$ be the equivalence relation on $B$ naturally associated with $G$. We prove that for every MV-pair $(B,G)$, the effect algebra $B/\sim_G$ is an MV- effect algebra. Moreover, for every MV-effect algebra $M$ there is an MV-pair $(B,G)$ such that $M$ is isomorphic to $B/\sim_G$

Stable non-standard imprecise probabilities

Stability arises as the consistency criterion in a betting interpretation for hyperreal imprecise previsions, that is imprecise previsions (and probabilities) which may take infinitesimal values. The purpose of this work is to extend the notion of stable coherence introduced in [8] to conditional hyperreal imprecise probabilities. Our investigation extends the de Finetti-Walley operational characterisation of (imprecise) prevision to conditioning on events which are considered "practically impossible" but not "logically impossible"

Electron-hole asymmetry in two-terminal graphene devices

A theoretical model is proposed to describe asymmetric gate-voltage dependence of conductance and noise in two-terminal ballistic graphene devices. The model is analyzed independently within the self-consistent Hartree and Thomas-Fermi approximations. Our results justify the prominent role of metal contacts in recent experiments with suspended graphene flakes. The contact-induced electrostatic potentials in graphene demonstrate a power-law decay with the exponent varying from -1 to -0.5. Within our model we explain electron-hole asymmetry and strong Fabri-Perot oscillations of the conductance and noise at positive doping, which were observed in many experiments with submicrometer samples. Limitations of the Thomas-Fermi approximation in a vicinity of the Dirac point are discussed.Comment: 7 pages, 8 figure

Information completeness in Nelson algebras of rough sets induced by quasiorders

In this paper, we give an algebraic completeness theorem for constructive logic with strong negation in terms of finite rough set-based Nelson algebras determined by quasiorders. We show how for a quasiorder $R$, its rough set-based Nelson algebra can be obtained by applying the well-known construction by Sendlewski. We prove that if the set of all $R$-closed elements, which may be viewed as the set of completely defined objects, is cofinal, then the rough set-based Nelson algebra determined by a quasiorder forms an effective lattice, that is, an algebraic model of the logic $E_0$, which is characterised by a modal operator grasping the notion of "to be classically valid". We present a necessary and sufficient condition under which a Nelson algebra is isomorphic to a rough set-based effective lattice determined by a quasiorder.Comment: 15 page