Mining Modelling

1. Propositional-Logic Form (PL-Form) of the Representation of Real Situations. Mathematical logic and modelling. Propositions and propositional formulae. Propositional-logical analysis. Examples. 2. Logical Analysis of Conditions and Situations. Further possibilities of analytic tableau applications. Combined analytic tableaux. Inconsistency and deducibility. Formalization by the means of predicate logic. Examples. 3. Outline of the Concept of Mathematical-Logical Modelling. Boolean and Pseudo-Boolean Representation. Outline of the modelling concept. Transformation of the representation into pseudo-Boolean form. Decision criteria and the objective function. Logical structure of systems of PB equations and inequalities. 4. Means for Work with PB Models and the Solution of Systems of PB Equations and Inequalities. Solution of a system of PB equations and inequalities. Linear PB equations. Linear PB inequalities. Nonlinear PB equations and inequalities. Minimization (maximization) of a PB function. 5. Further Means for the Description of Real Situations. Principle of inclusion and exclusion. Multisets. Examples. 6. Modelling in Underground Mining and Mining Planning. Pattern situations. Examples. 7. Modelling Situations in Open-Cast Coal Mining. 8. Modelling Situations in Uranium Deposit Mining. Sedimentary deposit working by room and pillar method. Modelling conditions of planning and control in mining a vein deposit. Conclusions. References. Subject Index.