lecture3 - CS245 Winter 2010 Lecture 3 Shai Ben-David The...

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CS245 - Winter 2010, Lecture 3 Shai Ben-David The language of propositional Calculus We no turn back to our main theme of developing formal languages for the analysis of logical implications (as well as other logical notions). The first step in the construction of a formal language is defining the set of expressions of that languages. These play a role similar to that played by words, or sentences, in natural languages. The expressions of the language of Propositional Calculus are called Proposi- tional Formulas . We define the set of propositional formulas using the structural induction tool that we have just introduced. We start by defining the underlying domain set (the set X , in the discussion of definitions by structural induction above). Let Σ = { lower-case English letters with and without subscript indices }∪{→ , , , ¬ , ) , ( } Σ is the set of ”letters” of our language. For any give set Σ, the set of all finite sequences of member of Σ is denoted by Σ * . The domain set for the definition of propositions formulas is the set X = Σ * , where Σ is the set of characters defined above.
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