Correction to: An Overview of Priority Pollutants in Selected Coal Mine Discharges in Europe

Mine Water and the Environment - Correct values for radium have been rewritten in Table 1 and Table 2. Correct radium units in Figure 2(c) are Bq/L (Becquerel per liter). The same applies to...     

An Overview of Priority Pollutants in Selected Coal Mine Discharges in Europe

Coal mine discharges in several European countries were investigated as part of the European Commission’s MANAGER project. The emphasis of the project was identification of priority pollutants and potential remedial approaches. The main identified priority pollutants were sulphate (all countries) and iron (all countries except Greece). High concentrations of chloride (particularly in Germany and Poland) were associated with discharge of saline mine waters linked to the presence of fossil sea water; these mine waters also had high boron concentrations, in contrast to chloride-rich waters in UK that are linked to recent sea water inflow. Concentrations of trace metals vary among countries, but radium is an important contaminant in barium-rich waters with low sulphate concentrations, essentially in Poland. Concentrations of trace metals and metalloids were generally low because of their relative scarcity in coal strata and adsorption onto ferric oxides and hydroxides, but they still often exceeded the environmental quality thresholds.

     

Resolution with Order and Selection for Hybrid Logics

We investigate labeled resolution calculi for hybrid logics with inference rules restricted via selection functions and orders. We start by providing a sound and refutationally complete calculus for the hybrid logic H(@,ˉ,A)\mathcal{H}(@,{\downarrow},\mathsf{A}), even under restrictions by selection functions and orders. Then, by imposing further restrictions in the original calculus, we develop a sound, complete and terminating calculus for the H(@)\mathcal{H}(@) sublanguage. The proof scheme we use to show refutational completeness of these calculi is an adaptation of a standard completeness proof for saturation-based calculi for first-order logic that guarantees completeness even under redundancy elimination. In fact, one of the contributions of this article is to show that the general framework of saturation-based proving for first-order logic with equality can be naturally adapted to saturation-based calculi for other languages, in particular modal and hybrid logics.     

Analyzing the Core of Categorial Grammar

Even though residuation is at the core of Categorial Grammar (Lambek, 1958), it is not always immediate to realize how standard logical systems like Multi-modal Categorial Type Logics (MCTL) (Moortgat, 1997) actually embody this property. In this paper, we focus on the basic system NL (Lambek, 1961) and its extension with unary modalities NL() (Moortgat, 1996), and we spell things out by means of Display Calculi (DC) (Belnap, 1982; Goré, 1998). The use of structural operators in DC permits a sharp distinction between the core properties we want to impose on the logical system and the way these properties are projected into the logical operators. We will show how we can obtain Lambek residuated triple \, / and of binary operators, and how the operators and introduced by Moortgat (1996) are indeed their unary counterpart.In the second part of the paper we turn to other important algebraic properties which are usually investigated in conjunction with residuation (Birkhoff, 1967): Galois and dual Galois connections. Again, DC let us readily define logical calculi capturing them. We also provide preliminary ideas on how to use these new operators when modeling linguistic phenomena.     

Contents of Volume 13

Continuing Education

Contents of Volume 13