Chapter Five:
Derivations in SL
In this chapter we provide a formal means to give proofs. This
procedure mimics the stepbystep 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
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
Selected Answers
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
Selected Answers
5.3ex
I Derivations Using Conditional Introduction
5.3ex II
More Derivations Using Conditional Introduction
5.3ex III
Multiple Choice: Derivations and Subderivations
Selected Answers
5.4ex
I Derivations Using Negation Rules
5.4ex II
More Derivations Using Negation Rules
Selected Answers
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*
Selected Answers
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
Selected Answers
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)
Selected Answers
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)*
Selected Answers
5 Review Exercise Group 1
Selected Answers
Chapter 5: Statement of the exercises.
