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...

background: the burden of obesity and diet-related chronic diseases is increasing in iran, and prevention and treatment strategies are needed to address this problem. the aim of this study was to determine the outcome, cost, safety and cost-consequence of non-invasive weight loss interventions in iran.   methods: we performed a systematic review to compare non-invasive interventions (cryolipoly...

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 ...

This work proposes a method for prioritising critical water mains (CWMs) with high risk, in terms of both failure probability and consequence costs. The proposed method can improve the prioritisation of high-risk CWMs requiring condition assessment in the near future and will further optimise the operational maintenance of water utilities. Due to the improved prioritisation, water utilities can...

Two hazard risk assessment matrices for the ranking of occupational health risks are described. The qualitative matrix uses qualitative measures of probability and consequence to determine risk assessment codes for hazard-disease combinations. A walk-through survey of an underground metalliferous mine and concentrator is used to demonstrate how the qualitative matrix can be applied to determine...