Deductive Systems in Traditional and Modern Logic

The book provides a contemporary view on different aspects of the deductive systems in various types of logics including term logics, propositional logics, logics of refutation, non-Fregean logics, higher order logics and arithmetic

V. Lifschitz, ed., formalizing common sense: papers by John McCarthy

A review is presented of Lifschitz's collection of seventeen papers written by McCarthy on the subject of common sense. The book opens with a fine overview of McCarthy's research in artificial intelligence (AI). Lifschitz offers an admirably succinct account of the development of McCarthy's ideas on common sense from the early days of AI to his current work. Lifschitz's introduction is especially useful in appreciating the dramatically original and permanently influential nature of McCarthy's work. While McCarthy's papers collected in this volume were written over the span of almost three decades, Lifschitz correctly observes that the underlying concern has always been the same: to understand and model the intellectual ability realized by human common sense

Legal Positivism's Answers to the Neoconstitutionalist Challenge

State of the art about legal positivism contemporary debate in Civil law countries

Zero-one laws with respect to models of provability logic and two Grzegorczyk logics

It has been shown in the late 1960s that each formula of first-order logic without constants and function symbols obeys a zero-one law: As the number of elements of finite models increases, every formula holds either in almost all or in almost no models of that size. Therefore, many properties of models, such as having an even number of elements, cannot be expressed in the language of first-order logic. Halpern and Kapron proved zero-one laws for classes of models corresponding to the modal logics K, T, S4, and S5 and for frames corresponding to S4 and S5. In this paper, we prove zero-one laws for provability logic and its two siblings Grzegorczyk logic and weak Grzegorczyk logic, with respect to model validity. Moreover, we axiomatize validity in almost all relevant finite models, leading to three different axiom systems