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

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@ L ° X± ±±± ±± Other axiom systems 1. Other axiom systems 2. Systems F and M

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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!
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. Following the procedure laid out on

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Proof of X=~(p±q)=>(~pv~q) (p.237). B is a basic formula q1±q2Q … ±qn (for each row). Ex. For row 1, B=p± q. Then B=>q1, … , B=>qn are all axioms. For row 1, p±q=>p; p±q=>q. X1, … , Xk are all non-atomic subformu- las (or their negations) of X.
Then B=>X1, … , B=>Xn, B=>X are all

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

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