Chapter Five, Tutorial Two In the last tutorial, we presented three rules for drawing conclusions in a derivation. These are all rules of inference: they allow one to draw a conclusion (the "output") from specified "input". In this and the next two tutorials, we shall describe a system of such rules. Taken together, this collection of rules is called "SD" for "Sentence-logic Derivations". All rules we introduce correspond to valid arguments. For example, our rule "&I" corresponds to the following argument form: P And all arguments of this form are trivially To do a derivation, then, is just to make a sequence of valid inferences from the original premises. Thus, a derivation from premises to its conclusion (its final line) shows that an argument is valid. All the exercises you've just done in 5.1ex I show that arguments (from the given premises to the given conclusion) are valid. This is just a new way, the SD way, of showing an argument is valid. Most importantly, it's a method much like our normal way of thinking through to a conclusion. We begin by looking at a rule called "reiteration". As its name implies, it allows one to repeat a sentence already on the derivation.
Even though you may see no immediate use for reiteration -- after all it just repeats! -- it is clear that is corresponds to a valid inference: any truth value assignment making P true, makes P true! Now, to review. Given the single premise... Premise 1. (A>B)&A ...which of the following sentences can you derive from one of our four
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