Exam #2 & Derivation Guide

Exam #2 will be held at the beginning of class on Tuesday, December 4th. It lasts 50 minutes, and will cover derivations in sentential logic and translations in predicate logic. Also, below is the systematic approach to solving derivations we learned in class.

Derivation Guide: Work Backwards
1. What do we need? What do we got? Does what we need to derive appear EXACTLY AS IS anywhere in an ACCESSIBLE part* of any line above it?

• If you answer YES: Try to break down the sentence in which what you need appears in an accessible part. Use an ELIMINATION RULE on the main connective of that sentence.
• If you answer NO: Try to construct what you need. Use an INTRODUCTION RULE on the main connective of the sentence you're trying to derive.
  
• If you answer NO, but there isn't any connective in what you need to derive, then PUNT: use either disjunction elimination (if there is a disjunction in a line above) or negation elimination.
• If all other attempts to break down or construct fail, then PUNT (see above).
  

2. Flip it to the flap, then stick it: Check your derivation introduction and elimination rules (on the front flap of the textbook) to see how to set up the proper derivation above what you need to derive. Often, this involves creating SUBGOALS: new lines that you must now try to derive somehow.

3. Rinse and repeat: Repeat steps 1 and 2 for each new subgoal you create, until each and every subgoal you need to derive JUST IS a complete sentence in one of the lines above.


*Accessible parts of sentences: either side of a conjunction; either side of a biconditional; the RIGHT side of a conditional; neither side of a disjunction.