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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- Spring '11
- Readability Unique Readability, main connective, semantics Tautological equivalence