DERIVATIONS IN SENTENTIAL LOGIC - UMass

DERIVATIONS IN SENTENTIAL LOGIC 1. 2. The Basic 3. Argument Forms and Substitution 4. Simple Inference 5. Simple 6. The Official Inference 7. Inference Rules (Initial Set)..155 8. Inference Rules; Official 9. Show-Lines and Show-Rules; Direct 10. Examples of Direct 11. Conditional 12. Indirect Derivation (First Form)..169 13. Indirect Derivation (Second Form)..174 14. Showing Disjunctions Using Indirect 15. Further 16. Showing Conjunctions and 17. The Wedge-Out Strategy ..184 18. The Arrow-Out Strategy ..187 19. Summary of the System Rules for System 20. Pictorial Summary of the Rules of System 21. Pictorial Summary of 22. Exercises for Chapter 23. Answers to Exercises for Chapter 142 Hardegree, Symbolic LOGIC 1. INTRODUCTION In an earlier chapter, we studied a method of deciding whether an argument form of SENTENTIAL LOGIC is valid or invalid the method of truth-tables. Although this method is infallible (when applied correctly), in many instances it can be tedi-ous.

Sometimes failure is due to lack of cleverness; sometimes failure is due to the im-possibility of the task! Chapter 5: Derivations in Sentential Logic 143 2. THE BASIC IDEA Underlying the method of formal derivations is the following fundamental idea.

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