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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.
The main aim of this book is to offer an exposition of the principles and applications of an original method which was introduced by the authors, developed gradually in the course of time, and applied extensively in the most diverse fields of management in the mining industry and power engineering. It is a relatively universal method of mathematical model construction and application intended to aid managerial personnel at various management levels in decision-making situations, which are frequently characterized by complicated relations of a quantitative as well as logical character.
The method, called by the authors simply the ``method of mathematical-logical modelling'' (MLM for short), is based upon an interesting and effective combination of tools from mathematical logic, Boolean algebra and computer programming. From the mathematical point of view it is based primarily on the construction and solution of systems of pseudo-Boolean equations and inequalities with a generalized logical structure. The principal features of the method are its universality, iterativity, interactivity, and advanced and broadly applicable software, coded in FORTRAN 77. Due in particular to these properties, MLM is a powerful tool for modelling real-life situations in the mining industry (and, naturally, in other fields of human activity as well).
The exposition is illustrated by a considerable number of examples. Some of these are rather simple and aimed at helping the reader verify his correct understanding of the text. Other examples, especially in the second part of the book (Chapters 6, 7 and 8), are more complicated and extensive. In some instances they have the character of case studies and demonstrate typical approaches applied when modelling mining situations.
The book will be of interest to a broad range of specialists working in the mining industry - research workers, designers, computer personnel, system analysts, management personnel at all managerial levels, and also undergraduate as well as graduate students.
- © Elsevier Science 1990
- 16th May 1990
- Elsevier Science
- eBook ISBN:
Czechoslovak Ambassador to Hungary, Budapest, Hungary
Federal Ministry of Fuel and Energy, Prague, Czechoslovakia
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