Chapter Five:
Derivations in SL

In this chapter we provide a formal means to give proofs. This procedure mimics the step-by-step reasoning procedures we use in everyday reasoning. We will try to develop your talents at this natural procedure by making the steps very explicit.

These formal proofs are called "derivations". We give exact rules for each reasoning step. At first, we will have only a few rules and the derivations will seem a bit slow. But learn the procedures well even if they seem simple at first: slowly we will add complexity. Only after we have presented all rules will our derivations seem like natural language reasoning.

Start with the introductory tutorials presented below, then print out the reference manual for this chapter (that way you'll have a concise statement of this chapter's details to refer to even when away from the computer.) Finally, and most importantly, carefully work your way through the chapter exercises. Many of the following exercises are derivations best done on the computer. But statements of the problems involved may be found here in one place.

Tutorials for Chapter Five 1. An Introduction to Derivations  — Derivations in 5.1  — RealPlayer Movie: A First Derivation          (Problems with RealTime?: Movie Help)  — Presentation: Another Derivation 2. Further Rules for SD Derivations 3. Subderivations: Conditional Proof  — Presentation: Subderivations  — RealPlayer Movie: Using >I 4. Subderivations: Indirect Proof 5. SD Tests 6. Safeguards and Strategy —Part I: Safeguards —Part II: Strategy — Strategy Demo — ~E Strategy Demo — Presentation: Strategy for more complex derivations 7. Adding "Short-cut" rules: SD+ 8. Strategy for SD+

Exercises for Chapter Five 5.1ex I Problems using >E, &E, &I 5.1ex II Multiple Choice: Derivations Basics 5.1ex III More problems using >E, &E, &I 5.2ex I Further Derivations ('=' and 'v' rules) 5.2ex II Multiple Choice: Derivations 5.2ex III More derivations ('=' and 'v' rules) 5.2ex IV Harder Derivations 5.3ex I Derivations Using Conditional Introduction 5.3ex II More Derivations Using Conditional Introduction 5.3ex III Multiple Choice: Derivations and Subderivations 5.4ex I Derivations Using Negation Rules 5.4ex II More Derivations Using Negation Rules 5.5ex I Derivation Tests of Basic Concepts 5.5ex II More Derivation Tests of Basic Concepts 5.5ex III Still More Derivation Tests 5.5ex IV Optional: Test Your Own Problems* 5.5ex IV Optional: Longer Page for Your Own Problems* 5.5ex IV Optional: XL Page for Doing Lots of Problems on one Page*
Hints to make the subderivations a little easier 5.6ex I Derivations and Strategy 5.6ex II Derivations Requiring Complex Subderivation Structure 5.6ex III More Derivations Requiring Complex Subderivation Structure 5.6ex IV Reward Set -- Finish these (relatively easy problems) and reap the rewards... 5.6ex V Optional: Your Problems with assistance* (To be used after previous exercise.) 5.6ex VI Optional: Your Problems with assistance, Longer Mode* 5.6ex VII Logical Truth 5.6ex VIII Logical Falsehood and Inconsistency 5.6ex IX Logical Equivalence 5.6ex X Harder Derivations 5.7ex I Derivations using new rules of inference (MT,DS,HS) 5.7ex II Multiple Choice: DN,AS,CM,DM,IM 5.7ex III Derivations (using DN,AS,CM,DM,IM) 5.7ex IV More Derivations (using all rules) 5.7ex V Still More Derivations (using all rules) 5.8ex I SD+ Derivations (using DN,AS,CM,DM,IM) 5.8ex II Harder SD+ Derivations (using all rules) 5.8ex III Logical Truth 5.8ex IV Logical Falsehood and Inconsistency 5.8ex V Logical Equivalence 5.8ex VI Optional: Blank Slate (for your own SD+ problems)* 5 Review Exercise Group 1