Logic1207 - Other axiom systems M u 1. 2. Other axiom...

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Final exam: Monday (12/14) 7pm , Room 412 Covers Chs.13-21 (except for Ch.19) Typos in Ch.21 p.251: (3) From S1 and S2 and F6 p.254, last line: if X is deducible from Y p.258, line 5: ~~X means that ~X can be disproved, but not necessarily that X can be proved!
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HW #10 (last HW set due Wednesday, 12/9 ) 1. There is no ambiguity involved in the formula X1; … & Xn. Show this by proving the following claim by induction: Any formula X, in which the only connective that can occur is &, is true iff all the propositional variable(s) in X are true. 2. Let X be ((p=>q)&~q)=>~p.
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Proof of X=~(p&q)=>(~pv~q) (p.237). B is a basic formula q1&q2Q … &qn (for each row). Then B=>q1, … , B=>qn are all axioms. For row 1, p&q=>p; X1, … , Xk are all non-atomic subformu- las (or their negations) of X.
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Then B=>X1, … , B=>Xn, B=>X are all obtainable from the above axioms by the (repeated) application(s) of Rules I-II. For row 1, p&q => each of ~~p, ~~q, p± q,
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This note was uploaded on 02/04/2010 for the course HSS Hss105 taught by Professor Yeelee during the Fall '09 term at Korea Advanced Institute of Science and Technology.

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Logic1207 - Other axiom systems M u 1. 2. Other axiom...

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