Chapter Eight:
Derivations for Predicate Logic

In this chapter we provide rules of derivation for the new language PL. But not to worry: There are only four rules to learn for PD, our new system!

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.


Some thoughts for a final exam:

  • Most of you will be tested on paper in a few weeks. So, make sure you write down some derivations; use the computer to check this work afterwards.
  • Derivations can be tricky at first. Practice! If you feel you're not understanding well enough to practice by doing derivations with hints, look to the answers (provided below), get an understanding of the problem, then try to do these on your own (with the answer now hidden).

Tutorials for Chapter Eight


Introduction to the derivation system PD


The last two rules of PD


PD strategy

4. The one new rule of PD+: QN

Exercises for Chapter Eight

8.1ex I Simple Derivations with ^E and %I
8.1ex II More Simple Derivations with ^E and %I
     Selected Answers

8.2ex I Simple Derivations with ^I
8.2ex II More Derivations with ^I
8.2ex III Derivations for %E
8.2ex IV More Derivations for %E
     Selected Answers

8.3ex I Derivations and Strategy
8.3ex II More Complicated Derivations
8.3ex III Logical Truth
8.3ex IV Logical Equivalence
8.3ex V Logical Falsehood and Inconsistency
8.3ex VI Preparation for 8.4
8.3ex VII PD Derivations for any problem*
     Selected Answers

8.4ex I Derivations with QN
8.4ex II PD+ Derivations
8.4ex III Logical Truth
8.4ex IV Logical Equivalence
8.4ex V Logical Falsehood and Inconsistency
8.4ex VI PD+ Derivations for any problem*
     Selected Answers

Chapter 8: Statement of the exercises.