lecture03_logic2 - The Logic of Quantified Statements...

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Unformatted text preview: The Logic of Quantified Statements Mariusz Bajger COMP2781/8781 School of Computer Science, Engineering and Mathematics March 16, 2011 1/13 Reading and Exercises Reading Epp, Chapter 3 Exercises Sec. 3.1 (all blue), Sec. 3.2 (all blue), Sec.3.3 (all blue, may drop 46-54 and 59-61), Sec. 3.4 (all blue) Good learning strategy: BE ACTIVE! I Regularly revise lectures I Solve the suggested exercises I Be critical when reading textbook/lectures I Ask your colleagues, ask the lecturer, don’t be shy! I It is OK to ask for help any time 2/13 Statement calculus vs predicate calculus I Propositional calculus - analysis of ordinary statements I For example, Canberra is a capital city. or 21 divides 40 I Logic also deals with more general structures where some variables are involved I Consider expressions: If x ̸ = 0, then x 2 > 0 or It is the biggest city in the world. I Are they statements? I No, in logic we call them predicates I Predicates become statements once variables are determined I Predicate calculus- analysis of predicates 3/13 Predicates Definition A predicate R is a sentence that contains a finite number of variables and becomes a statement when specific values are substituted for the variables. The set D of all values which can be substituted in place of variables (for which the predicate makes sense) is the domain of the predicate....
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lecture03_logic2 - The Logic of Quantified Statements...

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