PHIL 210 Lecture Notes - Lecture 11: Double Negation, Disjunctive Normal Form, Atomic Sentence
21 Feb 2018
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Document Summary
A sentence is in nnf just in case it s a combination using conjunctions and disjunctions of literals. i. e. a sentence is in nnf just in case the only negations it contains apply just to atomic sentences. From the above laws of double negation and de morgan"s, we can show that: any sentence can be put into nnf. De morgan"s law let us push the negation that sits outside of a sentence (terms inside the parenthesis) into the same sentence transformed e. g. consider the following transformation. P is built up from atomics and negation of atomics by finitely many uses of connectives principle of substitution of tautological equivalents. Tautological consequences relies on truth-functionality: replacing s(p) with s(q) = replacing p with q i. e. q has the same truth value column as p"s. Note : any sentence can be put into nnf any nnf sentence can be transformed in dnf or cnf this is true by the following two theorems.
