On subreducts of subresiduated lattices and logic

Subresiduated lattices were introduced during the decade of 1970 by Epstein and Horn as an algebraic counterpart of some logics with strong implication previously studied by Lewy and Hacking. These logics are examples of subuintuitionistic logics, i.e., logics in the language of intuitionistic logic that are defined semantically by using Kripke models, in the same way as intuitionistic logic is defined, but without requiring of the models some of the properties required in the intuitionistic case. Also in relation with the study of subintuitionistic logics, Celani and Jansana get these algebras as the elements of a subvariety of that of weak Heyting algebras. Here, we study both the implicative and the implicative-infimum subreducts of subresiduated lattices. Besides, we propose a calculus whose algebraic semantics is given by these classes of algebras. Several expansions of this calculi are also studied together to some interesting properties of them

Approximation to the Dynamic Hypermedial Device modeling for the analysis of interactions

The following research proposes a first approximation to the Dynamic Hypermedial Device modeling based on the analysis of interactions. In addition, the DEVS (Discrete EVents dynamic Systems) formalism is employed, which is particularly suitable for the modeling of discrete event systems with continuous time. In this sense, the descriptive model of the denominated "Hypermedial Package" is presented as a basic conceptual component of the DHD. Then, a functional example of basic analysis of the interactions implemented in the PowerDEVS environment is shown. The ultimate goal of this proposal is to provide a tool to assist in the quality analysis and evaluation of the interaction processes through the Information and Communication Technologies (ICT). Moreover, because of the current use of ICT in research, education, and in other fields, they may help in the responsible construction of a more equitable, pluralistic and open "Knowledge Society".Facultad de Informátic

On the Variety of Heyting Algebras with Successor Generated by All Finite Chains

Contrary to the variety of Heyting algebras, finite Heyting algebras with successor only generate a proper subvariety of that of all Heyting algebras with successor. In particular, all finite chains generate a proper subvariety, SLH!, of the latter. There is a categorical duality between Heyting algebras with successor and certain Priestley spaces. Let X be the Heyting space associated by this duality to the Heyting algebra with successor H. If there is an ordinal and a filtration S on X such that X = X, the height of X is the minimun ordinal ≤ such that Xc = ∅. In this case, we also say that H has height . This filtration allows us to write the space X as a disjoint union of antichains. We may think that these antichains define levels on this space. We study the way of characterize subalgebras and homomorphic images in finite Heyting algebras with successor by means of their Priestley spaces. We also depict the spaces associated to the free algebras in various subcategories of SLH!.

Errata on “On the Variety of Heyting Algebras with Successor Generated by all Finite Chains”

Errata on “On the Variety of Heyting Algebras with Successor Generated by all Finite Chains

The role of ArlRS and VraSR in regulating ceftaroline hypersusceptibility in methicillin-resistant Staphylococcus aureus

Methicillin-resistant Staphylococcus aureus infections are a global health problem. New control strategies, including fifth-generation cephalosporins such as ceftaroline, have been developed, however rare sporadic resistance has been reported. Our study aimed to determine whether disruption of two-component environmental signal systems detectably led to enhanced susceptibility to ceftaroline in S. aureus CA-MRSA strain MW2 at sub-MIC concentrations where cells normally continue to grow. A collection of sequential mutants in all fifteen S. aureus non-essential two-component systems (TCS) was first screened for ceftaroline sub-MIC susceptibility, using the spot population analysis profile method. We discovered a role for both ArlRS and VraSR TCS as determinants responsible for MW2 survival in the presence of sub-MIC ceftaroline. Subsequent analysis showed that dual disruption of both arlRS and vraSR resulted in a very strong ceftaroline hypersensitivity phenotype. Genetic complementation analysis confirmed these results and further revealed that arlRS and vraSR likely regulate some common pathway(s) yet to be determined. Our study shows that S. aureus uses particular TCS environmental sensing systems for this type of defense and illustrates the proof of principle that if these TCS were inhibited, the efficacy of certain antibiotics might be considerably enhanced.This work was supported by the Swiss National Science Foundation grants (AR 310030-169404), (WLK 10030-146540 and 10030-192784). MV was supported by FNS (Fonds National Suisse) through project funding 10030-146540. The funders had no role in study design, data collection, and interpretation or the decision to submit the work for publication