2250 Lecture : N10SDSound - Soundness of SD.pdf
5 Feb 2013
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The soundness and consistency of sd and the. Up to now, we have treated the derivation system, sd, as an arbitrarily constructed system of rules to be used to derive sentences from other sentences. In fact, the rules were not arbitrarily constructed. They were designed to serve as a means for demonstrating the truth-functional validity of arguments. It is not immediately obvious that this goal is in fact achieved by the rules of sd. Students who begin working with derivations under the disadvantage of already knowing something about the semantics of sentences of sl will often be suspicious about some of the rules. Soundness: if a sentence, p, of sl is derivable in sd from a set, , of sentences of sl, then truth-functionally entails p. We would also like to be assured that sd is consistent: that you cannot in fact (appearances notwithstanding) derive just anything using the rules of sd.
