Lecture 4 (1)

Lecture 4 (1) - Lecture 4 Logic is a Game What is a Logic...

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Lecture 4 Logic is a Game
What is a Logic? The word Logic has many meanings, e.g. check: http://en.wikipedia.org/wiki/Logic . In our context, a logic is a set of sentences, written in a formal language, and has: A Syntax: Rules for defining legal sentences. A Semantics: Rules for giving meaning to those sentences.

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Propositional (Boolean) Logic Syntax: Formed from propositional variables X, Y, Z, etc. using the operations: ¬ A, (A B), (A B). A different notation: A , A+B, AB Semantics: Each propositional variable says something that is true or false about our world. ¬ A means not A. (A B) means A and B. (A B) means A or B (or both).
Consider the sentence: A = (( ¬ X Y) ¬ Z) ¬ (( ¬ Y Z) X). Let X and Y be true, and Z be false. Question: Is A true or false? Notes: We build the truth values of the parts of A bottom-up. We can visualize A as a tree or as a Boolean

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Lecture 4 (1) - Lecture 4 Logic is a Game What is a Logic...

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