tailieunhanh - Logic For Everyone

The discipline known as Mathematical Logic will not specifically be defined within this text. Instead, you will study some of the concepts in this significant discipline by actually doing mathematical logic. Thus, you will be able to surmise for yourself what the mathematical logician is attempting to accomplish. Consider the following three arguments taken from the disciplines of military science, biology, and set-theory, where the symbols (a), (b), (c), (d), (e) are used only to locate specific sentences | arXiv 0601709 vl 29 Jan 2006 LOGIC FOR EVERYONE Robert A. Herrmann 1 Previous titled Logic For Midshipmen Mathematics Department U. S. Naval Academy 572C Holloway Rd. Annapolis MD 21402-5002 2 CONTENTS Chapter 1 Introduction Chapter 2 The Propositional Calculus Constructing a Language by The Propositional Slight Simplification Size Common Pairs. 13 Model Theory Basic Semantics . 15 Valid Formula . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 Equivalent Formula. 22 The Denial Normal Form Logic Circuits. 26 The Princeton Project Valid Consequences. 32 Valid Consequences. 35 Satisfaction and Consistency. 38 Proof Theory. 42 Demonstrations Deduction from Premises . . . . . . . . . . . 45 The Deduction Theorem . . . . . . . . . . . . . . . . 47 Deducibility Relations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 The Completeness Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 Consequence Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 The Compactness Theorem . . . . . . . . . . . . . . . . 57 Chapter 3 Predicate Calculus First-Order Language . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 Free and Bound Variable Occurrences . . . . . . . . . . . . . 67 Structures . . . . . . . . . . . . . . . . . . . 70 Valid Formula in Pd. 76 Valid Consequences and Models . . . . . . . . . . . . . . . . . . . . . . . . . . 82 Formal Proof Theory. 86 Soundness and Deduction Theorem for Pd . 87 Consistency Negation Completeness Compactness Infinitesimals . 91 Ultralogics and Natural Systems . . . . . . . . . . . . . . 97 Appendix Chapter 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 Chapter 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 Answers to Some Index . .