In the second volume of his Wissenschaftslehre from 1837, the Bohemian philosopher, theologian, and mathematician Bernard Bolzano (1781-1848) introduced his concept of consequence, named derivability (Ableitbarkeit), together with a variety of theorems and further considerations. Derivability is an implication relation between sentences in themselves (Sätze an sich), which are not meant to be l...

Sir Austin Bradford Hill, honorary fellow of the London School of Hygiene and Tropical Medicine, dean of the school from 1955 to 1957, and professor of medical statistics from 1946 to 1961, died on 18 April 1991. With his death the country lost a man who has been described as the greatest medical statistician of the twentieth century, despite the fact that he held no degree in either medicine o...

The technical problem addressed in this paper is, given two rule systems for consequence relations X and Y, how to construct Y-approximations of a given X-relation. While an upper Yapproximation can be easily constructed if all Yrules are Horn, the construction of lower Yapproximations is less straightforward. We address the problem by defining the notion of coclosure under co-Horn rules, that ...

In The Concept of Logical Consequence (CLC) [13], I presented an extended argument that the standard, Tarskian analysis of logical consequence and logical truth is wrong. In the years since its publication, over a score of authors have written reviews, articles, or portions of books criticizing various arguments I gave in the book.1 Nearly all have presented what the authors considered devastat...

A binary relation R on a set S is transitive iff for all a, b, c ∈ S, if aRb and bRc, then aRc. This almost never applies to the relations logicians tend to think of as consequence relations; where such relations are relations on a set at all, they are rarely transitive. Yet it is common to hear consequence relations described as ‘transitive’, and to see rules imposed to ensure ‘transitivity’ o...

Tarski’s definition of logical consequence for an interpreted language rests on the distinction between extra-logical symbols, whose interpretation is allowed to vary across models, and logical symbols, aka logical constants, whose interpretation remains fixed. In this perspective, logicality come first, and consequence is a byproduct of the division between logical and extra-logical symbols. O...

In this paper some basic aspects of the theory of graded consequence are reconsidered, based on many results that appeared since the inception of graded consequences in 1986. Relationships of the notion of graded consequence with the notions of consequence in many-valued and fuzzy logics are discussed. Following this, a detailed study is carried out on the necessary conditions that follow from ...

introduction: today, with development of various industries, the adverse events originated from explosion and emission of toxic and chemical substances have increased. these events may cause serious environmental problems that threaten human health and safety. therefore, knowledge about the risk of toxic substances from industrial facilities is essential. although, chlorine is extensively utili...

The study  attempts to answer two basic  questions. Firstly, whether  religiosity  is  efficient  in  reducing  delinquent   behavior   and , secondly, if the answer is yes , how much is its effect? The samples was divided into common people and delinquent youth in prison. The scholars like Durkheim, Weber, Stark, Glock and those assertions regarding delinquency as Merton, Hirschi learning the...