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Lecture_3 - Lecture 3 Lecture 3 Review Review Basic syntax...

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Unformatted text preview: Lecture 3 Lecture 3 Review Review Basic syntax Basic semantics Tautological equivalence Tautologies and contradictions Exercise 2.5 Exercise 2.7 (1,3,5) Unique Readability Unique Readability If A is a sentence, then exactly one of the following holds: A is an atom A = ¬B for a unique B A = (B ∧ C) for a unique pair B,C The Main Connective The Main Connective If A has the form ¬B, then the main connective of A is ¬. If A has the form B ∧ C, then the main connective of A is ∧ . How do we know that this concept is well­ defined? What do we mean by the “form” of the sentence? Components Components informal notion proper components immediate components using the inductive structure of the language to give a precise definition Is ¬B ∧¬A a component of (A ∨¬B) ∧¬A? More Syntactic Structure More Syntactic Structure Substitution Trees Polish notation ...
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