The Kuznetsov-Gerčiu and Rieger-Nishimura logics

We give a systematic method of constructing extensions of the Kuznetsov-Gerčiu logic KG without the finite model property (fmp for short), and show that there are continuum many such. We also introduce a new technique of gluing of cyclic intuitionistic descriptive frames and give a new simple proof of Gerčiu’s result [9, 8] that all extensions of the Rieger-Nishimura logic RN have the fmp. Moreover, we show that each extension of RN has the poly-size model property, thus improving on [9]. Furthermore, for each function f: \omega -> \omega, we construct an extension Lf of KG such that Lf has the fmp, but does not have the f-size model property. We also give a new simple proof of another result of Gerčiu [9] characterizing the only extension of KG that bounds the fmp for extensions of KG. We conclude the paper by proving that RN.KC = RN + (¬p \vee ¬¬p) is the only pre-locally tabular extension of KG, introduce the internal depth of an extension L of RN, and show that L is locally tabular if and only if the internal depth of L is finite

Properties of Intuitionistic Provability Logics

Abstract. We study the modal properties of intuitionistic modal logics that belong to the provability logic or the preservativity logic of Heyting Arithmetic. We describe thefragment of some preservativity logics and we present fixed point theorems for the logics iL and iP L, and show that they imply the Beth property. These results imply that the fixed point theorem and the Beth property hold for both the provability and preservativity logic of Heyting Arithmetic. We present a frame correspondence result for the preservativity principle W p that is related to an extension of Löb's principle

National laboratory-based surveillance system for antimicrobial resistance: a successful tool to support the control of antimicrobial resistance in the Netherlands

An important cornerstone in the control of antimicrobial resistance (AMR) is a well-designed quantitative system for the surveillance of spread and temporal trends in AMR. Since 2008, the Dutch national AMR surveillance system, based on routine data from medical microbiological laboratories (MMLs), has developed into a successful tool to support the control of AMR in the Netherlands. It provides background information for policy making in public health and healthcare services, supports development of empirical antibiotic therapy guidelines and facilitates in-depth research. In addition, participation of the MMLs in the national AMR surveillance network has contributed to sharing of knowledge and quality improvement. A future improvement will be the implementation of a new semantic standard together with standardised data transfer, which will reduce errors in data handling and enable a more real-time surveillance. Furthermore, the

Intuicionismo

[ES] Tras una introducción histórica al intuicionismo como filosofía de las matemáticas, se introduce la lógica intuicionista. Comenzamos desde sus fundamentos según la interpretación BHK, y continuamos con las reglas del cálculo de deducción natural adecuado. Se discuten las diferencias con la lógica clásica estándar que la caracterizan. El tema siguiente lo constituyen los modelos de Kripke para la lógica intuicionista, y tras él se tratan la aritmética y el análisis intuicionista. Finalmente se explican las secuencias de elección libre de Brouwer. Hay una corta discusión del concepto de realizabilidad y del papel de la lógica intuicionista en los sistemas formales intuicionistas. El artículo concluye con una nueva clase de juegos para el cálculo intuicionista proposicional introducido recientemente por Mezhirov.[EN] After a historical introduction to intuitionism as a philosophy of Mathematics intuitionistic logic is introduced. We start with its basis in the BHK-interpretation, and continue with the corresponding natural deduction rules. The characteristic differences with standard classical logic are discussed. The next topic is formed by the Kripke models for intuitionistic logic, after which Intuitionistic arithmetic and analysis are treated. In the latter the role of Brouwer’s free choice sequences is explained. A short discussion is given of realizability and of the role of intuitionistic logic in intuitionistic formal systems. The paper concludes with a new kind of games for the intuitionistic propositional calculus recently introduced by Mezhirov

Intuicionismo

RESUMEN: Tras una introducción histórica al intuicionismo como filosofía de las matemáticas, se introduce la lógica intuicionista. Comenzamos desde sus fundamentos según la interpretación BHK, y continuamos con las reglas del cálculo de deducción natural adecuado. Se discuten las diferencias con la lógica clásica estándar que la caracterizan. El tema siguiente lo constituyen los modelos de Kripke para la lógica intuicionista, y tras él se tratan la aritmética y el análisis intuicionista. Finalmente se explican las secuencias de elección libre de Brouwer. Hay una corta discusión del concepto de realizabilidad y del papel de la lógica intuicionista en los sistemas formales intuicionistas. El artículo concluye con una nueva clase de juegos para el cálculo intuicionista proposicional introducido recientemente por Mezhirov.ABSTRACT: After a historical introduction to intuitionism as a philosophy of Mathematics intuitionistic logic is introduced. We start with its basis in the BHK-interpretation, and continue with the corresponding natural deduction rules. The characteristic differences with standard classical logic are discussed. The next topic is formed by the Kripke models for intuitionistic logic, after which Intuitionistic arithmetic and analysis are treated. In the latter the role of Brouwer’s free choice sequences is explained. A short discussion is given of realizability and of the role of intuitionistic logic in intuitionistic formal systems. The paper concludes with a new kind of games for the intuitionistic propositional calculus recently introduced by Mezhirov.</p